Technology, Effort, and the Relative Efficiency of Organizations*

by

Seung C. Ahn, Josef C. Brada and José A. Méndez

Department of Economics, Arizona State University

Tempe, AZ 85287-3806 USA

ABSTRACT

In this paper we explore how the modeling of effort as a factor of production affects the relative competitiveness of different economic organizations. We construct a simple model of privately-owned and labor-managed firms to show that the more important the role of effort in production, the greater the differences in the efficiency of the two types of firms even if monitoring is held fixed. Using data on cooperative and private farms in El Salvador, we show much greater differences in efficiency between cooperatives and private farms for coffee, an effort-intensive crop, than for maize and sugar, which are less effort intensive. In all cases, private farms elicit higher levels of effort than do cooperative farms. The results suggest that the way in which effort enters the production function may determine the number of organizational forms that can coexist in a competitive industry. Keywords: Effort, Incentives, Competition, Efficiency JEL Classification: D23, D24, O13, P50

Corresponding author: Jose A. Mendez, Economics Department, Arizona State University, Tempe, AZ 85287-3806 * The authors are grateful to Mauricio Canas, Roselia Funes and Alfonso Zuniga for assistance in developing the data used in this study. Méndez acknowledges financial support from the W.P. Carey School of Business, Arizona State University.

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I. Introduction The ways in which firms organize themselves in order to elicit effort from workers

is a problem that has been extensively studied by economists. This research has

examined a wide range of incentive and monitoring schemes, internal organizational

arrangements and ownership structures. By way of contrast, the role that workers’ effort

plays in the process of production has generally been modeled in only one way; lack of

effort is treated as the equivalent of supplying less labor time. Thus, differences in the

productivity of two alternative organizations could be seen as the result of shirking, which

reduces the effective labor time worked. One of the paradoxical implications of this

formulation is that numerous empirical studies, some of which we discuss below, have

found large differences in productivity between organizations, and this suggests that, in

the less productive organizations, shirking would have to be endemic and highly visible

to account for such large differences in labor input. In this paper we argue that a different

formulation of the role of effort in the production process, one that makes effort much

more central to output, may explain why even small differences between alternative ways

of monitoring and incenting workers to supply effort and, consequently, small

interorganizational differences in effort supplied, may lead to large differences in output

and labor productivity. Thus, the ability of firms with different incentive structures to

survive in a competitive industry may depend critically on the technology used by those

firms. Technologies where effort is not central to the production process may be

compatible with a wider range of monitoring and incentive arrangements than is the case

for firms operating in an industry whose production processes place a premium on effort.

We develop our argument within the context of two extensively studied ways of

organizing production and motivating workers, the privately owned firm and the producer

3

cooperative. We construct a simple model of these two organizations, and we show that,

as the role of effort becomes more critical to the production process, the productivity

differences between private firms and cooperatives increase relative to differences

observed when we use more traditional characterizations of the role of effort in

production, such as the Cobb-Douglas production function, even if monitoring and

incentives are held fixed across organizations. We also provide an empirical test of the

hypothesis using data on private and collective farms in El Salvador. Our empirical

research is consistent with the theory in that it shows that differences in productivity

between private and collective farms as well as within each type of farm are greater for

corps whose production is more dependent on effort than they are for crops produced

using technologies that more closely approximate the traditional way of introducing effort

into the production function.

The coexistence, in market economies, of privately-owned firms and producer

cooperatives, whether in manufacturing or in agriculture, as well as the extensive

reliance on collective farms under communism, has led to a rich theoretical and empirical

literature comparing the economic performance of the two ways of owning and managing

productive units. The work of Ward (1958), Domar (1966), Vanek (1970) and Ireland and

Law (1981) suggests that the cooperative firm can be as economically efficient in its

resource use as is its capitalist counterpart. Much less settled, both from a theoretical

standpoint and from an empirical one, is whether cooperatives are, by virtue of their

collective nature, better suited to elicit higher levels of effort from their members than is a

capitalist firm from its employees and what the implications of such differences are for

the viability of cooperatives. 1 Advocates of cooperative firms point to the greater

1 See Bonin, Jones and Putterman (1993) for a survey of the literature on this topic.

4

commitment that worker-owners will have to the welfare of their firm, to the higher morale

created by the absence of the hierarchical supervision characteristic of capitalist firms,

to lower labor turnover and the willingness of the cooperative firm and its members to

engage in firm-specific human capital accumulation, and to the likelihood of cooperative

members to engage in group monitoring of effort and to the emulation of fellow

members' supply of effort. 2

Critics of cooperative firms have argued that the supply of effort depends in part

on the way in which cooperatives reward their members. As Sen (1966) showed, even if

effort were perfectly observable, a payment scheme that shared the net income of the

cooperative equally among all members would result in no effort being supplied, and

even mixed payment schemes based on a combination of income sharing and reward for

work may elicit suboptimal effort. Sen's result was particularly telling for collective farms

in socialist countries, because, in the socialist environment, the inefficient low-effort

cooperative did not have to compete with more efficient organizations. Lin (1988) argued

that the failure of Chinese collectivization was due to the undersupply of effort in an

environment where the labor contribution of collective farm members was difficult to

measure.

Empirical research on the ability of cooperative firms to match the productivity of

private firms or to elicit higher levels of effort has taken two forms. One is to compare the

factor productivity of cooperative firms that have different levels of worker-owner

participation. Such studies suggest that greater participation is associated with higher

levels of productivity.3 On the other hand, studies that compare privately-owned and

2 See Bradley and Gelb (1981) and particularly Ireland and Law (1988) for discussions of the organization of monitoring in cooperative firms. 3 Bonin, Jones and Putterman (1993, pp. 1303-1305).

5

cooperative producers find either no differences in technical efficiency, a measure of

productivity and, implicitly, of effort, or that higher productivity is to be found among the

private producers.4

Despite the considerable emphasis on the role of incentives and of monitoring on

private firms' and cooperatives' ability to elicit effort, this research has been framed in the

context of a single view of the role of effort in production and of the way that effort enters

into the production function. Both in theoretical models and in the empirical work, effort is

viewed as being identical with "true" labor time, often viewed as time "actually spent

working". That is, in the traditional view of production, if effort cannot be varied, output is

seen as a function of available capital services and of (observed) labor time, L, or, with a

fixed number of hours of work, the number of workers. If monitoring arrangements are

such that workers can supply less than full effort, then output will be lower than

suggested by L because the true labor input is eL, where 0 ≤ e ≤ 1 is a measure of effort

supplied. Such a way of modeling the role of effort in the production process makes effort

equivalent to time worked; shirking effectively reduces the number of hours that the

worker actually works.

The foregoing conception of effort is appropriate for many technologies,

particularly those where there is little interaction between the output of one worker and

that of others. Thus if one worker shirks, she produces less than her fellow workers, but

she does not impinge on their ability to produce output based on their own inputs of time

and effort. On the other hand, there exist technologies that require a sequence of steps

in the production of the final product. In such technologies, the equivalence of effort and

labor time breaks down and the amount of effort becomes critical, so that even small

4 See, for example, studies by Boyd (1988), Berman and Berman (1989), Estrin (1991), Brada and King (1993).

6

reductions in effort by one worker can have a large impact on the total output of the firm.5

As we demonstrate in this paper, in firms employing such technologies, the ability to elicit

effort is much more crucial to the competitiveness of the firm than it is for firms that

employ technologies where there are few or no sequential steps. Thus, if privately-

owned and cooperative firms do differ in their ability to elicit effort, then we would expect

to see smaller differences between the potential efficiency of private and cooperative

firms in industries characterized by the former, simpler, type of technology.

Consequently, in industries characterized by such technologies, different ways of

organizing production and monitoring workers could coexist even in a competitive

environment. For industries where the second, more effort-critical, type of technology is

used, there should be large potential differences between the productivity of different

types of firms, even if their individual monitoring efforts were to result in relatively small

differences in the amount of effort supplied. In such an industry, different ways of

organizing the firm could not be sustained in a competitive environment because those

firms that elicited less effort would find themselves at a major disadvantage in

productivity and, thus, in costs of production.

In the next section of this paper we develop a model of cooperative and private

firms with sequential technologies and show that, as the complexity of the technology, as

measured by the number of productive steps, increases, even small differences in the

ability to elicit effort lead to large differences in technical efficiency. In the third section

we use a sample of private and cooperative farms in El Salvador to show that increases

in the complexity of production are in fact associated with decreasing technical efficiency,

both within private and cooperative producers and also among them.

5 This notion is central to Kremer's (1993) so-called O-Ring technology, which we exploit in this paper.

7

II. A Simple Analytical Framework

In this section, we develop a simple model to show how moving from a traditional to

a sequential production technology, even with monitoring and incentives held fixed, can

magnify productivity differences between the cooperative firm and a private firm with the

same resources. Because our empirical test of the model draws on data from private and

cooperative farms, we will motivate the model with an example from agriculture. The

production process in farming is sequential, involving a series of steps or stages that are

carried out over a lengthy time period. Land is first prepared; crops are then planted; all of

this is followed at different times by the application of fertilizers, insecticides, and

herbicides, and by the pruning or tending of the plants; all prior to the harvesting of the

crop. Low or poor quality worker effort at any of these stages has severe consequences

for final output. For instance, failure during planting to carefully cover a seed with dirt so it

is not blown away by the wind or eaten by birds will have very large effects on the size of

the harvest; all the worker effort devoted to fertilizing, weeding, etc. cannot make up for the

failure of seeds to germinate. Moreover, this is true along all stages as small changes in

the quality of a worker’s effort at one stage can translate into large changes in production.

In some instances, the difficulty of monitoring effort in agricultural production aggravates

this effect because it may be very difficult to identify the stage during which the poor

quality performance occurred. 6

To illustrate how the organization of production in private or cooperative firms

interacts with this type of production technology, we construct models of cooperatives and

private farms that use traditional Cobb-Douglas production functions and the so-called O-

Ring (OR) production function of Kremer (1993), which is a characterization of a sequential

6 See Bradley and Clark (1972) for an excellent early discussion of these issues.

production process. Then we show that, holding incentives that have been proposed in

the literature on labor-managed firms fixed, changes in the sequential complexity of the

technology cause very large changes in the relative performance of private and

cooperative firms. Note that our focus is on the relationship between organizational form

and technology, independent of the complications introduced by the difficulties in

monitoring. Thus we assume that both private firms and cooperatives face identical

difficulties in monitoring workers who are using the same technology.7

A. Production Technology

The characteristics of the production technologies that we employ are central to our

analysis, so we begin by describing Kremer’s (1993) OR production function and adapting

it to our needs. In Kremer’s formulation, the production process is characterized by N

tasks, and, although not essential for the analysis, it is assumed that each task requires

only one worker so that N also equals the number of laborers. How a worker is likely to

carry out a particular task is represented by a random variable, ei, whose realization

ranges from zero to one and which Kremer (p. 553) defines as “the expected percentage

of maximum value the product retains if the worker performs the task” perfectly. For

instance, an ei of 0.80 may mean that a worker has an 80 percent chance of being

successful in performing a task or the task is always performed in such a way that the

product retains 80 percent of its value. The sensitivity of total production to an individual

worker’s performance is then captured by assuming that each ei enters production

multiplicatively, so that, for the N workers, output will equal . Thus, even though i

N

ie

1=∏

8

7 This approach thus differs from the insightful paper by Eswaran and Kotwal (1985b), who also consider the problem of worker effort under different technologies and institutional arrangements in agriculture. Eswaran and Kotwal explicitly introduce a role for monitoring effort, but, by necessity, they introduce assumptions about differences in monitoring ability that in turn drive their results.

workers' effort levels are assumed to be stochastically independent of one another, a low

realization of ei at any point will dramatically lessen the productivity of all workers.

In our models of privately-owned and cooperative firms, we, too, introduce ei

multiplicatively and assume that it ranges from zero to one; however, we employ a more

traditional interpretation of ei. We assume it is nonstochastic and define it as the quantity

of effort exerted by a worker, or, alternatively, it represents an index of the quality of a

worker’s effort where each worker possesses one unit of time. In either case, the quantity

N can be interpreted as the total "effective" labor input. i

N

ie

1=∏

Kremer also defines a technological parameter, B, that depends on N and is defined

as “output per worker with a single unit of [land] if all tasks are performed perfectly”

(p.561). Note that in a conventional Cobb-Douglas(CD) production function with two inputs

and α the nonlabor input’s output share, B is equal to [N ( )] i

N

ie

1=∏ -α, conditional on = 1.

To see this, rewrite a CD production function as

i

N

ie

1=∏

QCD = Tα (N )i

N

ie

1=∏ 1-α

= Tα (N ) (N )i

N

ie

1=∏ i

N

ie

1=∏ -α Eq. 1

where Q is production, T is the stock of land, α is land’s output share, and N is the number

of workers. In Kremer's characterization of the OR production function, the term on the far

right, [N ( )] i

N

ie

1=∏ -α, simplifies to [N]-α conditional on = 1. In contrast to Kremer, we

include this term with the stock of land because we hold the stock of land fixed throughout

our analysis. We define t* as the output per worker with T units of land if all tasks are

i

N

ie

1=∏

9

performed perfectly: t* = T/ [N ( )] = T/N conditional on = 1. Our form of the OR

production is thus expressed as

i

N

ie

1=∏ i

N

ie

1=∏

QOR = (t*)α (N ) Eq. 2 i

N

ie

1=∏

Note that except for the multiplicative way in which labor’s effort enters the

production function and the interpretation of t, this production function is a Cobb-Douglas

production function in t and total labor effort and is comparable to the "intensive" form of

the CD production function popular in the international trade literature more than two

decades ago.8 It is also related to the "external economies" or "Marshallian factor-

generated" increasing returns production function used extensively in the international

trade literature. Indeed, in line with that literature, the derivative of QOR with respect to ei is

identical to what Panagariya (1983) refers to as the "social" marginal product of the i-th

worker, which we express as follows:

(∂QOR/∂ei) = QE N ( ) (ei

N

ie

1=∏ i)-1 N η Eq. 3

where QE = (t*)α captures the change in production in response to a change in total labor

effort, E, where

E = N ( ), Eq. 4 i

N

ie

1=∏

and

η = (1/N){1 + (∂ei

N

ie

2=Σ j/∂ei) (ei/ej)} Eq. 5

Thus η is an elasticity that measures the percentage response of total labor effort to a

marginal change in the i-th worker’s effort. This elasticity is comparable to what Chinn

10

8 See, e.g., Kemp (1969) and Takayama (1972).

(1979) defines as a "cohesion coefficient" that captures the extent to which other workers

emulate the actions of the i-th worker. It is also a "social" marginal product because it

takes into account the externality generated by the action of the i-th worker on total labor

effort. Chinn (1979) argues that η varies from a lower bound of 1/N when other workers

choose not to emulate the response of an individual worker up to an upper bound value of

1 when other workers respond in an identical fashion to the i-th worker’s change in effort.

However, for cooperatives, it is not inconceivable that members may reduce their effort in

response to an increase in the effort by other members.

The second production function we employ is similar to a conventional CD

production function. The key differences are that we include the sum of each individual

worker’s effort, , as the aggregate labor input and we incorporate Kremer’s B

parameter within the stock of land as we did earlier. The CD production function is

i

N

ie

1=Σ

QCD = (t*)α ( ) Eq. 6 i

N

ie

1=Σ

where Q is output, and, as before, α is land’s output share, N is the number of workers,

and t* is the output per worker with T units of land if all tasks are performed perfectly: t* =

T/( ) = T/N conditional on ei

N

ie

1=Σ i = 1 for all i = 1,…,N. Differentiating QCD with respect to a

marginal increase in ei, we obtain

(∂QCD/∂ei) = QE ( ) (ei

N

ie

1=Σ i)-1 N ηw Eq. 7

where QE = (t*)α captures the change in production in response to a change in total labor

effort, E = , and i

N

ie

1=Σ

11

ηw = (1/N){δ1 + δN

i 2=Σ j (∂ej/∂ei) (ei/ej)} Eq. 8

is an elasticity comparable to η, except that each term of ηw is weighted by δi , individual i’s

(i = 1,…,N) share of total effort provided. Note that, if the δi‘s are identical, then ηw =

(1/N)η because δ = e/ = e/Ne = 1/N. We use this result later. i

N

iie

1=Σ

B. Behavioral and Environmental Assumptions

We now set out several simplifying behavioral and environmental assumptions.

First, like Berman (1977) and Conte (1980), we are concerned only with a time span in

which cooperatives are not free to adjust membership but are free to adjust work effort.9

Second, like Conte (1980), we assume that workers care only about income and leisure

but not about working conditions. For simplicity, individual workers are assumed to

possess one unit of effort, which they allocate between effort at work, ei, and leisure,1-ei;

thus, ei ranges from 0 to 1, with higher numbers indicating greater worker supply of effort.

Finally, the objective of the cooperative is to maximize the utility of a typical worker where

ei is the choice variable. In contrast, the capitalist or private farm is assumed to operate in

a competitive environment and to hire labor until the marginal revenue product is equated

to the exogenously given market wage rate. In such an environment, changes in an

individual’s work effort have no effect on the market wage and workers act independently

while focusing on their own income. 10

The cooperative’s maximization problem is expressed as:

Max Ui= Ui(yi, 1-ei)

12

9 This is consistent with the empirical tests we carry our in the next section. During our sample period, cooperatives in El Salvador were not free to fire or expel members and private farms faced increased enforcement of a worker’s right to severance pay, which served to raise the cost of adjusting employment but not of work hours. 10 For more details, see the discussion in Ireland and Law (1981).

13

where Ui is the utility of the i-th member, yi is her income and l=1-ei is the leisure

consumed. Ignoring the member superscript for U, we assume that U is quasi-concave,

and that Uy, Ul > 0 and Uyy, Ull, Uyl < 0, where Ui is the partial derivative with respect to the

i-th variable.

We assume that V, the cooperative's residual income computed as total revenue,

PQj (j = OR, CD), less R, the payment or rent for land, is distributed to the cooperative's

workers in two payments.11 First, a portion of net revenue, aV, is set aside for meeting

basic needs, and each member receives an equal share of this portion of V. Second,

what remains of the residual income is paid out to each member in proportion to his or her

share of total work effort, δi = ei /Σei. Thus, a member’s income is

yi,j = si [PQj - R] (i = 1, …, N, j = OR, CD) Eq. 9

where

si = [δi(1-a) + (1/N)a]. Eq. 10

C. Comparative Productivity

Our next step is to develop the first-order conditions (FOCs) for the private and

cooperative firm under both Cobb-Douglas and OR technologies. We do this explicitly to

demonstrate that our main results regarding the incentive structure facing cooperative

workers are largely consistent with those developed in a large theoretical literature on

labor-managed firms, although the introduction of the OR technology does modify them in

an important way. We also develop these FOCs in order to obtain explicit expressions for

the optimal effort levels in cooperatives using OR and CD production technology, denoted

(eor-c)* and (ecd-c)*, and for private firms, also denoted (eor-p)* and (ecd-p)*. These

11 In the more general case, the cooperative would subtract its payments for all non-labor inputs, but, because we develop our model of production in terms of two inputs only, we ignore intermediate inputs without any loss of generality.

expressions for the optimal effort levels, once substituted into the appropriate production

function, will then permit us to compare the optimal production level of a cooperative to

that of a private firm using the same technology and the same amount of land or other

inputs. These comparative-productivity ratios are denoted, respectively, by (QOR-C/QOR-P)*

and (QCD-C/QCD-P)*.

Beginning with the FOCs for those workers employed in cooperatives that use an

OR production technology, we obtain

Uy{si PQE ( )(ei

N

ie

1=∏ i)-1 N2 η + (1-a)(1-Nηw)(VOR/Σei)}- Ul = 0 Eq.11

where P is the exogenously-given price of the output. Note that the above FOC is similar

to equation 5 in Israelsen (1980), equations 5a and 5b in Ireland and Law (1981), and

equation 11 in Lin (1988).

To solve for (eor-c)*, we now make several additional simplifying assumptions. First,

we assume that, at the initial point of differentiation, we can ignore land rent and that

workers are identical. The former allows us to set V = PQi (i=OR, CD) and the latter

implies that ηw = (1/N)η, s = (1/N) and = Ne. Second, like Ireland and Law (1981), we

adopt a specific functional form for the member's utility function, U =( y

eN

i 1=Σ

i ) 1-β (1- ei )β, in order

to simplify our computations. After making the appropriate substitutions, we obtain the

optimal effort level for the cooperative member

(eor-c)* = (1-β)[Nη + (1-a)(1-η)] / {(1-β)[Nη + (1-a)(1-η)] + β} Eq. 12

(eor-c)* is bounded from 0 to 1. To obtain (eor-p)*, we set both η and a equal to zero

because workers of privately-owned firms are assumed not to influence each others'

supply of effort and there are no needs payments. The result is identical to the result

obtained by assuming that workers employed by the private firm are also only concerned

14

15

with maximizing their utility, but by assumption their only source of income is wage

income, yi = wei where w is the exogenously given competitive wage.

Carrying out the same exercise for the cooperative operating with a CD technology,

the optimal level of effort is

(ecd-c)* = (1-β)[η + (1-a)(1-η)] / {(1-β)[η + (1-a)(1-η)] + β} Eq. 13

which differs from (eor-c)* in that N does not appear in the numerator or denominator as a

multiplier of η, the cohesion coefficient. In contrast, the worker’s optimal effort level when

private firms operate with a CD rather than an OR production function, (ecd-p)*, remains

unchanged.

To compute the ratio of production under a cooperative versus that under private

production when both employ the optimal amount of labor and the same technology, (QOR-

C/QOR-P)* and (QCD-C/QCD-P)*, we substitute the expressions for (eor-c)*, (ecd-c)*, (eor-p)* and

(ecd-p)* into their respective production functions. We obtain, respectively,

(QOR-C/QOR-P)* = [{Nη + (1-a)(1-η)} / {(1-β)(Nη + (1-a)(1-η)) + β}]N Eq. 14

and

(QCD-C/QCD-P)* = {η + (1-a)(1-η)} / {(1-β)(η + (1-a)(1-η)) + β} Eq. 15

Note that, a priori, it is not possible to determine whether cooperative production will

be higher or lower than that of private firms, and this holds regardless of the technology.

Such an indeterminacy is consistent with the large body of inconclusive empirical work on

the issue of which organizational form has higher productivity (Bonin, Jones and

Putterman, 1993). Note also that parameter changes influence relative productivity in a

manner consistent with our intuition. For instance, cooperatives exhibiting a degree of

cohesion or enthusiasm among members, i.e., those with a cohesion coefficient closer to

one, are more likely to exhibit higher production than do private firms. Moreover, as theory

16

suggests, increases in a, the share of output devoted to needs payments, increase the

likelihood that cooperative production will fall short of private production. Finally, notice

from Equation 14 that an increase in N, which we would interpret as an increase in the

number of stages in, or the complexity of, the production process, the greater the

difference in production between the two types of firms. To be able to say more about the

possible magnitude of these productivity differences, we calculate comparative productivity

values for alternative levels of a and η. These calculations are presented in the next

section.

D. Simulations of Comparative Productivity

Table 1 summarizes the results of computing values of our comparative productivity

measure for each technology with β = 0.4, N = 2, and alternative values of a and η. We

present values for OR production technology with only two stages because that is

sufficient to demonstrate our main point that differences in the technology of production

can lead to large differences in private firm and cooperative performance

The top panel of Table 1 examines the effect of differences in η and a on the

productivity of cooperatives relative to private farms when both employ a Cobb-Douglas

technology. Generally, except for the topmost row and the first column, cooperatives are

less productive than private firms but only marginally so for low values of a, the share of

income distributed according to need. Differences in productivity of no more than 10

percent, which characterize the top-left portion of the Table, are unlikely to be of material

importance in actual practice, and, under such productivity differentials, cooperatives and

private firms could coexist in a competitive market. As the share of cooperative revenue

devoted to needs payments rises beyond 0.2, a movement along any row from left to right,

the cooperative becomes increasingly less productive in comparison to private firms.

17

Finally, note that as we move up each column, productivity for the cooperatives rises

relative to that of private firms; that is, the more sensitive other cooperative members are

to an increase in the i-th worker’s effort, the more productive the cooperative becomes.

The bottom panel of Table 1 presents values of comparative productivity when both

firm types use an O-Ring production technology. The values are computed for the same

set of parameters as in the top portion of the table; the principal difference is that there are

now two production stages, i.e., N = 2. Productivity differences between private and

cooperative firms are now much more striking. For a range of cohesion and sharing

variables, cooperative firms can exceed private firm productivity by over 50% and a

productivity advantage of more than 20% is evident in over half the cells in the lower panel

of Table 1. Such a productivity advantage requires a combination of high levels of

cohesion and low levels of income sharing. Conversely, for low levels of cohesion and high

levels of sharing, cooperative productivity is much lower than that of private firms. For any

given pair of values of a and η, productivity is dramatically larger or smaller in cooperatives

in comparison to private firms. Thus, with the same monitoring technology and incentives,

the differences in actual output are much greater than they are with the CD technology.

These computations demonstrate the ability of small differences in technology to

create large differences in the productivity, and, in a market economy, in the economic

viability of different ways of organizing production and in the ownership of productive

assets. While the literature has largely focussed on monitoring and incentives as the key

determinants of differences in the performance of firms, our results show that, even when

we hold monitoring and incentives fixed, a change in technology can yield very large

differences in firm performance. This suggests that private firms and cooperatives may not

be able to coexist in many industries unless cooperatives are able to constrain their

18

choices of a and η to a narrow range and thus that the coexistence of these two

organization forms may be tightly constrained by technology to a few industries.

III. An Empirical Test of the Effect of Technology on Productivity

The results provided above have at least two testable implications. The first is that

the more complex an OR technology, as indicated by a higher value of N, the greater the

productivity loss from a failure by workers to supply a full measure of effort. The second is

that the productivity differences between cooperative and private farms should be greater

for products requiring OR technology than for those requiring CD technology. In this

section we will test these hypotheses using a data set on private and collective farms in El

Salvador. The data set is particularly valuable because it enables us to test both

hypotheses. The first hypothesis can be tested because the data set provides information

on the output and inputs used in each unit to produce three different crops. If we make the

not-unreasonable assumption that a given private or collective farm provides the same set

of incentives and level of monitoring effort for all its members or workers and thus elicits

the same level of effort in all its activities, then we should expect to see a different level of

productivity for high-N OR technology-produced products and low-N or CD technology-

produced products when we look only at private farms or only at collective farms. Second,

by comparing the productivity of cooperatives to that of private farms, we can test whether,

indeed, the difference is greater for products produced by high-N OR technologies than it

is for low-N or CD technologies.

In the remainder of this section, we will provide a brief history of the cooperative

sector in El Salvador, describe the data used, characterize the crops produced as

requiring complex or simple production technologies, and then describe our specification

and the results obtained.

19

A. Land Reform in El Salvador

The replacement of large, privately-held estates with cooperative enterprises was a

major component of the land reform program initiated in 1980 by the reformist junta that

ousted the government of General Carlos Romero on October 15, 1979.12 Decree 153,

issued on March 5, 1980, lay the basis for the land reform. The reform applied to all farms

in excess of 100 hectares or 150 if the land was of poor quality. Phase I of the land reform

applied to all estates exceeding 500 hectares, while Phase II applied to farms between

100 and 500 hectares. Former owners were to be compensated for the land and all the

livestock and buildings, machinery and equipment located permanently on the estate.

Ownership of the land was to be transferred to salaried employees and peasants who

worked and lived on the farm under the previous owner, but the new owners assumed a

debt equal to the compensation to be paid the former owners. To ensure the benefits of

scale economies, the farm was to be kept intact and organized into a production

cooperative run by an elected committee of the workers and a co-manager (co-gestor)

appointed by the Salvadoran Land Reform Institute (ISTA).

Phase I was immediately implemented under Decree 154, also issued on March 5,

1980. Under the decree, some 477 properties were seized during 1980, comprising

315,535 hectares or 22 percent of farm land in El Salvador. Of this, 219,524 hectares or

15 percent of El Salvadoran farm land was used to create 317 cooperatives with some

31,359 member families, about 187,000 persons. These cooperatives became known as

the Phase I cooperatives, although a handful of cooperatives formed during the mid-1970s

as part of a prior land reform were later incorporated into the present reform.

12 There is an extensive literature on the reform of agriculture in El Salvador. Strasma (1990) and Seligson (1996) provide good overviews.

20

Conditions during the implementation period and the immediate years following it

were particularly difficult due to the reform's hasty implementation, which, in addition to

producing widespread confusion, had not given the government sufficient time to develop

an adequate institutional capacity for either implementing or administering the reform,

leaving unclear a variety of factors critical for the operation of the new cooperatives. For

instance, the implementing legislation left unclear how members were to be compensated

and earnings distributed, as well as the rights and responsibilities of cooperative members.

Compounding all these problems were efforts by landowners and the right-wing party,

Alianza Republicana Nacional (ARENA), to undermine the reform.

After this initial period, the situation improved considerably for cooperatives. By the

end of 1983, violence directed specifically at them had virtually ended, and the Christian

Democrats, led by Napoleon Duarte and sympathetic to the reform, won the mid-1984

presidential elections and wrested control of the legislature from ARENA in 1986.

Following the findings of studies such as Checchi (1981, 1983, 1985), concerned officials

had also begun to lay the groundwork for a series of programs designed to address the

lack of infrastructure and institutional support that had hampered the cooperatives. In

place by 1986, these programs provided cooperatives both the support and the opportunity

to develop into effective organizations.

In 1989, Christian Democrats lost the presidential elections to ARENA's candidate,

Alfredo Cristiani. Long hostile to the reform, the Christiani administration launched a new

initiative, designed, it argued, to correct deficiencies in the existing land reform. In 1991,

the government issued a decree entitled New Options (Nuevas Opciones), which gave the

members of Phase I cooperatives several options: they could continue to farm the land as

21

a cooperative; they could divide the land and obtain title to their individual parcels; or, they

could select a mixture in which they farmed individual parcels as well as collectively.

Official data for the Phase I cooperatives ceased to be available after 1991 because

the agency responsible for monitoring the cooperatives was closed. Nonetheless, ISTA

officials told us informally in 2002 that between 52 and 80 percent of the Phase I

cooperatives have altered their land tenancy arrangements, with the majority of them

opting to divide the land into parcels to which the members obtain individual title, thus

effectively ending the cooperative's existence. This parcelization has occurred despite

efforts to support cooperatives through a 1997 law that allowed them to write off their

debts.13 One possible explanation for the demise of the cooperatives, which we explore

below, is that they were unable to elicit levels of effort that would have enabled them to

compete with private farms, especially in crops where effort is a key input.

B. Data

The data were obtained from two surveys, one for Phase I cooperatives and the

other for private farms, both conducted for the 1991/1992 crop cycle. The survey for

Phase I cooperatives was conducted by the Oficina Sectorial de Planificacion

Agropecuaria (OSPA) within the Ministerio de Agricultura y Ganaderia (MAG) in

collaboration with the authors. For our purposes, a sample of 120 cooperatives was

randomly selected from the 360 cooperatives unaffected by violence and located outside

conflict zones. It is well-documented (Strasma, 1990, pp. 414-415) that cooperatives in

conflict zones, if not abandoned, often operated under a variety of burdens such as

demands that they alter their crop mix to produce more basic grains for guerilla fighters or

pay war taxes or protection money. Private-sector data were obtained from a survey of

13 The Special Law for the Extinction of Debts and the Reactivation of the Agricultural Sector was passed 10/10/1997.

22

private farms carried out by the Division de Estadisticas Agropecuarias, Direccion General

de Economia Agropecuaria, MAG. We were not provided details of the methodology used

to select the sample, but we were informed that the sampling methodology had been

developed by a team of consultants from the U.S. Department of Agriculture.

The data for private farms were more comprehensive than those for cooperatives.

For each private farm, we obtained information on location, physical output, type of crops

cultivated, area cultivated, quantity of labor and wage by activity (e.g., planting, spreading

fertilizer, etc.), and quantity and cost of various nonlabor inputs such as seeds, fertilizers,

herbicides, etc. The data for cooperatives lacked information on input prices and wages.

As proxies for these, we computed a mean private-farm input price and wage for each of

the fourteen departments (departamentos, political units like states) and applied these to

the Phase I cooperatives located within the same department. Land rent data by

department was obtained by surveying the governing board of each cooperative, as well

as OSPA officials assigned to conduct the surveys within each department. Summary

descriptive statistics of the production and cost data by crop and by type of farm are

presented in Table 2.

For each type of farm unit we were thus able to obtain or construct data on the cost

of land, labor and nonlabor inputs used in the production of three crops, coffee, corn

(maize) and sugar. Note that these three crops represented over 60 percent of the entire

agricultural sector's value added in 1990, and thus they accounted for a large part of the

economic activity of the farms in our sample. The cooperatives' larger size is evident from

the fact that the average cooperative devoted about five times as much land to the

cultivation of sugar and coffee and ten times as much land to the cultivation of corn.

23

C. The Technology of Coffee, Corn and Sugar Cultivation

The literature on agricultural institutions provides many examples of differences in

the complexity of crop production. In general, these examples are not cast in the

framework of the OR production function. Rather they are usually discussed either in the

importance of effort in the production of an individual crop or in terms of the amount of

monitoring required to obtain the requisite level of effort in cultivating a crop or undertaking

some non-crop agricultural production. That is to say, some agricultural tasks require more

judgment or care and tend to have follow-on effects on output that are characteristic of the

OR framework. It is also evident that such effort-intensive tasks are more important or

numerous in the cultivation of some crops than of others.

For example, Eswaran and Kotwal (1985a) note that “important tasks that require

judgment, discretion, and care (and are difficult to monitor) are seldom if ever assigned to

casual workers. Permanent workers, on the other hand, are often entrusted with such

responsibilities, almost as if they were family members” (p. 163). This is because obtaining

the requisite level of effort for key tasks has an important effect on the output of the entire

agricultural production process, and, presumably, in acting like family members,

permanent workers are understood to be supplying a higher level of effort for critical tasks

where effort is important for the production process. Eswaran and Kotwal conceive of

agricultural production as involving two types of tasks:

“Type 1 tasks are those that involve considerable care and judgment (such

as water resource management, the application of fertilizers, maintenance of

draft animals and machines, etc.). Such tasks do not lend themselves to

easy on–the–job supervision. Type 2 tasks are those that are routine and

menial (such as weeding, harvesting, threshing, etc.). Since they involve little

discretion, productivity on such tasks can be directly gauged from the extent

of the workers’ physical activity. In other words, Type 2 tasks are by their

very nature easy to monitor.” (p. 165)

24

There are two key points in the distinction between the two types of tasks. One is that that

the proper execution of Type 1 tasks has a O-Ring effect on output in the sense that many

Type 1 tasks, such as making decisions about irrigation, have an effect over all or some

large part of the crop, while menial Type 2 tasks do not, at least to the same extent. The

second is that different crops or agricultural technologies require different combinations of

Type1 and Type 2 tasks. Consequently, if a farm elicits a fixed level of effort from its

workers in all tasks, in the case of crops that require many Type 1 tasks, the shortfall in

production from the level achievable with no shirking will be much larger than would be the

case for crops that require largely Type 2 tasks.

Evidence for this proposition can be found from a variety of examples. Johnson and

Brooks (1983) argue that collective farms in the USSR were, ceteris paribus, as efficient

as private farms in North America in the production of wheat, a crop characterized by

many Type 2 tasks. On the other hand, in the USSR and in the socialist countries of

Eastern Europe, animal husbandry and the production of fruits and vegetables, activities

characterized by Type 1 tasks, was increasingly given over to the private plots of collective

farm members because the collective farm members had a direct financial interest in

providing the necessary level of effort. Similarly, in their examination of the effects of

export booms on the distribution of rural incomes in Latin America, Carter, Barham and

Mesbah (1995) characterize crops by their effort intensity in the following way:

“Some crops are responsive to interactive labor, meaning that the quantity or

quality of output can be notably increased when laborers make constant and

careful choices. For example, careful harvesting of snow peas requires the

laborer to decide constantly whether to harvest a particular plant and

individual pods on each plant now or later. This crop characteristic creates a

potential advantage for small family farms that supervise their own labor." (p.

40)

25

In this example, as in Eswaran and Kotwal’s typology of tasks, the emphasis on the

superiority of the family farm in producing these kinds of effort-intensive crops is precisely

due to the assumption that the family farm obtains higher levels of effort than do other

types of farm units and that effort is somehow more critical than just a measure of time

worked. Thus, Carter, Barham and Mesbah found that export booms in crops whose

production was very sensitive to the level of effort supplied tended to favor small producers

such as family farms that were able to elicit high levels of effort, but booms in crops such

as wheat and soybeans tended to help large farms and to exacerbate rural poverty

because these crops relied mainly on Type 2 tasks, thus negating the family farms’ one

advantage over large producers, the ability to extract high levels of effort.

In our empirical work we deal with three crops, maize, sugar cane and coffee. The

former two crops depend largely on Type 2 activities; both have been successfully

cultivated by large plantations or estates or even collective farms, suggesting that lack of

effort could not be offset by greater numbers of workers.14 On the other hand, the

cultivation of coffee reflects many more Type 1 activities and the OR technology stressed

in this paper. The cultivation of coffee plants is a year-round process involving many

specific activities that call for workers to exercise judgment and care in the execution of

their tasks. This gives rise to a situation in which the individual worker has considerable

latitude over the supply of the quality and quantity of his effort because both direct

monitoring and the linking of individual worker activities to the final harvest are difficult to

implement. For instance, among the many specific tasks that are vital to productivity is the

pruning of coffee trees immediately following a harvest. Removal of branches, some of

which are damaged during the harvest, is essential because it spurs the growth of buds for

next year’s crop. Because the buds are already present on the trees and vulnerable to

damage, the pruning must be done carefully. While the successful completion of this task

14 Sugar production does have on aspect where effort does play a very important role, and that is in getting the cut cane to the processing mill as soon after harvest as possible, but this is more a matter of mill capacity and location and the organization of transportation than the effort of individual workers.

26

is thus crucial to the final harvest in the way that the OR technology suggests, monitoring

of worker effort is difficult and costly because coffee is a tree crop grown in orchards, often

on hillsides or mountains and not in open, expansive fields. Monitoring of workers is also

complicated by the extended production cycle, yearlong rather than months, over which

these various activities are spread. Moreover, the participation of many workers at various

points in the production cycle makes it more difficult to assign responsibility. Thus farms

that are able to elicit higher levels of effort should enjoy much higher levels of output

relative to low-effort-eliciting farms in the cultivation of crops such as coffee while the

differences between the two types of farms should be less for crops such as sugar cane

and maize.

D. Specification and Estimation of the Model

Our statistical model, drawn from Aigner, Lovell and Schmidt (1977) and Schmidt

and Lovell (1979), consists of two sets of equations, a stochastic frontier production

function and a set of first-order conditions for cost minimization. Technical inefficiency, the

failure to achieve best-practice output with a given set of inputs, arises primarily from

factors internal to the farm and its production technology. Thus, differences in the

measured technical efficiency of productive units should reflect differences in the effort

supplied by workers and the way in which the provision of effort influences the level of

output.

The stochastic frontier production function is estimated separately for each of the

three crops, coffee, sugar and corn, and it is initially assumed to have the following log-

linear variable returns to scale form:

ln Qij = Aj + αMjln Mij + αNjln Nij + αDjln Lij + vj - uj Eq. 16

where j= coffee, corn, sugar, Qij is the output of the j-th crop by the i-th farm, Mij are

materials, i.e., seed, fuel, fertilizer, herbicides, insecticides, fungicides, etc., used to

produce the j-th crop by the i-th farm, Nij is labor used by farm i to produce crop j, Lij is the

amount of land used by farm i to grow crop j, and vj and uj are disturbance terms. Like a

traditional error term, v captures the effect on farm output of factors outside the farm's

control and is assumed to be distributed as N(0,σv). Technical inefficiency, reflected in

production below the frontier, is indicated by u, which is the absolute value of a variable

distributed as N(0,σu).

The second set of equations is derived from the first-order conditions for cost

minimization, and these allow for the possibility of both random and systematic deviations

from the cost-minimizing conditions. Random errors that cause cost minimization to fail to

hold are captured by ξ = (ξN, ξL)' distributed as N(0,Σ). ξ is assumed to be independent of

u. Systematic over or under-use of an input relative to another is modeled by forming

ratios of the first-order condition for an input, say input M , to the first-order condition of

each of the remaining inputs. Adopting a Cobb-Douglas production function, consistent

with the results of our estimations, yields:

δMpM/δkpk = αM Xk /αk XM, k, Xk = N,L Eq. 17

where δk is the ratio of input k's shadow price to its actual price. Shadow prices are not

separately identified, so we normalize by setting δM = 1 and then rearrange each equation

and place it in logarithmic form. This leads to the following specification:

, = + d + + ln = XpXp ln i

M

M M

i

LNk kkkkkk

ξβραα ⎟

⎠

⎞⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ Eq. 18

The condition ρk>0 indicates input k is underused relative to input M by ln(ρk) percent

compared to the cost-minimizing level and implies that the shadow price of input k

exceeds the input's actual price. To allow for the possibility that cooperatives face

alternative shadow prices, we introduced a dummy variable, di, which equals 1 if i is a

cooperative and 0 otherwise. Thus, for cooperatives, exp(ρk + βk) is input k's shadow price

divided by its actual price, while, for private farms, exp(ρk) is input j's shadow price divided

by its actual price.

We jointly estimated the system consisting of Equations 16 and 18 using maximum

likelihood techniques. The resulting frontier parameter estimates were used to calculate 27

28

the mean technical inefficiency across farm type, while the parameter estimates from both

sets of equations were used to derive a stochastic cost frontier that permits computation:

the mean cost of technical inefficiency and the mean cost or savings due to systematic

and random allocative inefficiency.15

Maximum likelihood estimates (MLE) and their asymptotic standard errors of the

production function and first-order cost minimization condition parameters are reported in

Table 3 along with the implied cost function parameters derived from the MLE estimates.

The results for all three crops are reasonable, with the parameter estimates of the

production function affirming the appropriateness of the Cobb-Douglas assumption.

Except for the coefficient on materials, which is insignificant in two of the three cases, all

coefficients are significant. The only surprise in the estimates is the finding that coffee and

corn production exhibit increasing returns as we reject the null hypothesis that returns to

scale are unity at the 95 percent significance level. The empirical literature (see Pryor

(1992) or Binswanger and Rosenzweig (1986)) suggests that scale economies are to be

expected for coffee and sugar, but only at the processing level, not in production. In any

case, the estimates indicate only very mild increasing returns. Finally, note the high value

of σu2 relative to σv

2, which are both imputed from the standard error of the regression (not

reported) and from λ. This is evidence of substantial technical inefficiency because it

indicates that variations in farm output below the production frontier, technical inefficiency,

far exceed the variation of the frontier across farms due to measurement error or to other

factors, such as weather, outside the farms' control.

Turning to the parameter estimates of the first-order conditions for cost

minimization, we find that none of the estimated coefficients for coffee producers are

significant, indicating that these producers do not systematically over- or under-use inputs.

However, both cooperatives and private farms overuse labor and other inputs relative to

land, that is, their labor-land ratios and materials-land ratios are higher than those

15 The formulae for the cost function and these other magnitudes are available from the authors upon request.

29

prescribed by cost-minimization.16 Given the scarcity of land in El Salvador (Seligson,

1995), which is perhaps not reflected in land rents due to the absence of an effective land

market, as well as the paucity of alternative nonfarm employment opportunities, it is not

surprising that farmers would compensate by using labor and other inputs as intensively as

possible, even going so far as employing them beyond their cost-minimizing levels.

Given the reasonableness of the estimates for the first-order conditions and the

stochastic production frontier, we have a high degree of confidence in the inferences we

draw from them regarding technical efficiency. It is to this task that we now turn.

E. Technical Inefficiency

The extent and pattern of technical inefficiency are shown in the first half of Table 4.

The first two rows list estimates of the average by which output is below the frontier by

crop and type of farm.17 Because the frontier production function for each crop is

estimated using data drawn from both private farms and cooperatives, the mean deviation

of each farm type from the production frontier is a measure of technical inefficiency relative

to best practice in both types of farms. Clearly, most farms exhibit some measure of

technical inefficiency, but there are systematic differences between private farms and

cooperatives, and these differences, all of which are statistically significant at the 95%

level, display a clear pattern across the three crops. To obtain a sense of the costliness of

this inefficiency, the estimates in the lower portion of Table 4, show the cost corresponding

to the inefficiency estimates of rows of one and two; these figures show the cost, as a

fraction of actual costs of production, of the most cost-efficient bundle of additional inputs

that would be required to replace the output lost to technical inefficiency. Thus, these cost

16 Overuse of seeds, fertilizers, pesticides, etc., relative to land is indicated by ρD > 0 for private farms and (ρD + βD) > 0 for cooperatives, while overuse of labor relative to land is indicated by ρL - ρD < 0 for private farms and (ρL + βL) - (ρD + βD) < 0 for cooperatives.

17 The computation of the mean technical inefficiency of a farm type requires the estimates of individual farm's technical inefficiency. These estimates are obtained following Jondrow et al. (1982).

30

estimates indicate the percentage increase in input expenditures that the typical farm

would have to make in order to produce the same level of output as would a farm

operating on the frontier of the production function.

Note that, for private farms, both the estimates of technical inefficiency and of its

cost are more or less the same for each crop while for cooperatives the inefficiency is

much greater for coffee, the effort-intensive crop, than it is for the two other crops. This is

consistent with the hypothesis that the family farms are able to elicit high levels of effort

across all three crops, and, thus, because of the consistently high levels of effort, the

effort-intensity or Type 1 task intensity of coffee is not evident because the level of effort is

so high. On the other hand, in the case of cooperatives, the shortfall in technical efficiency

in the case of coffee is much greater than it is for the other two crops. This suggests that,

as cooperatives evidently elicit a lower level of effort from their members for all tasks, it is

the production of coffee, the most effort-sensitive crop, whose production suffers the

highest levels of technical inefficiency. For all three corps, the technical efficiency of

private farms is higher than that of cooperatives and the productivity difference between

the two types of producers for each crop is significant at the 95% level. This result

suggests that, at least under the parameters that characterize El Salvadoran agriculture,

cooperatives elicit lower optimal levels of effort from their members than private farms elicit

from their workers.18

While the differences in technical efficiency between cooperatives and private farms

could conceivably be due to factors other than differences in the optimal levels of effort

supplied by their members or workers, respectively, the inter-crop differences in technical

efficiency support the hypothesis that the technical inefficiency that we observe is driven

largely by differences in the supply of effort in the two types of producers. Note that the

greatest inefficiency is found in the case of coffee, with average cooperative inefficiency at

75% and private farm at 30%, and it is also for coffee that we observe the largest

18 This is consistent with Carter’s (1987) finding of a “low-effort equilibrium” for Peruvian collectives as well as with Lin's (1988) critique of Chinese collectives.

31

efficiency gap between private and cooperative farms. We have argued above that. of the

three corps, coffee is the one whose cultivation best corresponds to an O-Ring

technology. On the other hand, for corn and especially for sugar, the technical efficiency of

both private farms and of cooperatives increases relative to that observed for coffee, but

the productivity difference between the two types of farms decreases. Indeed, between

coffee and sugar, the difference between the two technical efficiency gaps is significant at

the 95% level. This result is consistent with the illustrative calculations presented in Table

1. These showed that as we move from a CD technology to an increasingly complex OR

technology, for the same difference in the optimal level of effort supplied by collective and

private farm workers, the greater the difference in the two farms' volume of output, and

consequently, in the framework of our empirical model, the greater the difference in

technical efficiency. Because the effort that cooperatives and private farms elicit is

assumed to be independent of the crop being cultivated by members or workers, the

pattern of inter-crop efficiency differences reported in Table 4 is entirely consistent with the

hypothesis that the productivity differences observed stem from differences in the supply

of effort in private and cooperative farms.19

V. Conclusions

We have constructed a model of private and cooperative firms whose production

function assigns a key role to the supply of effort. We have shown that in such firms, any

differences in the supply of effort results in very large differences in productivity and costs,

but the model does not provide a priori conclusions as to whether cooperatives or private

firms are able to elicit greater effort. Using data on collective and private farms in El

Salvador, we find that the latter appear to be able to elicit higher levels of effort across all

farm activities. The differences between the technical efficiency of the two types of units

19 An alternative assumption would be that farms devise monitoring schemes that are crop specific, seeking to elicit higher levels of effort in the cultivation of crops that are more effort intensive. Note that, even if that were the case in El Salvadoran agriculture, this would tend to mitigate rather than exacerbate the differences between private and cooperative farms obtained in our results.

32

are greatest in coffee production, a result that is in line with the predictions of our

theoretical model.

More broadly, our work first of all serves to explain why some studies are able

observe very large shortfalls from potential production, even in organizations such a

Chinese collective farms where there may be severe penalties for shirking. It is possible

that relatively small deviations from maximum effort can cause large shortfalls in

production. Moreover, our work underscores the importance of organizations' ability to

elicit effort and shows how this ability to extract effort can play a very large role in

determining which forms of organization are viable in a competitive environment. It may be

that organizations do not differ much in their ability to elicit effort, implying that the

explanatory role of incentive and monitoring issues in explaining the competitiveness of

different ways of organizing production is less than commonly believed, while the effort

intensity of the production technology utilized by firms plays a key role in explaining why

different organizational forms can or cannot coexist in a competitive industry.

Table 1: Computations of Comparative Productivity: Optimal Cooperative Production Divided by Optimal Private Firm Production, (QC/QP)*

Cobb-Douglas Production Technology Cohesion Coefficient (η) (QC/QP)*

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.9 1.000 0.996 0.992 0.988 0.984 0.979 0.975 0.971 0.966 0.962 0.9570.8 1.000 0.992 0.984 0.975 0.966 0.957 0.948 0.939 0.929 0.919 0.9090.7 1.000 0.988 0.975 0.962 0.948 0.934 0.919 0.904 0.888 0.871 0.8540.6 1.000 0.984 0.966 0.948 0.929 0.909 0.888 0.865 0.842 0.816 0.7890.5 1.000 0.979 0.957 0.934 0.909 0.882 0.854 0.823 0.789 0.753 0.7140.4 1.000 0.975 0.948 0.919 0.888 0.854 0.816 0.775 0.730 0.680 0.6250.3 1.000 0.971 0.939 0.904 0.865 0.823 0.775 0.722 0.663 0.595 0.5170.2 1.000 0.966 0.929 0.888 0.842 0.789 0.730 0.663 0.584 0.493 0.3850.1 1.000 0.962 0.919 0.871 0.816 0.753 0.680 0.595 0.493 0.370 0.217

0 1.000 0.957 0.909 0.854 0.789 0.714 0.625 0.517 0.385 0.217 0.000 Needs Parameter (a) 0.0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

O-Ring Production Technology (N=2) Cohesion Coefficient (η) (QC/QP)*

1.00 1.563 1.563 1.563 1.563 1.563 1.563 1.563 1.563 1.563 1.563 1.5630.9 1.522 1.518 1.514 1.510 1.505 1.501 1.497 1.492 1.488 1.484 1.4790.8 1.479 1.470 1.461 1.452 1.443 1.433 1.424 1.414 1.404 1.394 1.3840.7 1.433 1.419 1.404 1.389 1.374 1.358 1.342 1.326 1.309 1.292 1.2750.6 1.384 1.363 1.342 1.320 1.298 1.275 1.251 1.226 1.201 1.175 1.1480.5 1.331 1.304 1.275 1.245 1.214 1.181 1.148 1.113 1.077 1.039 1.0000.4 1.275 1.239 1.201 1.162 1.120 1.077 1.031 0.984 0.934 0.881 0.8260.3 1.214 1.168 1.120 1.069 1.016 0.959 0.899 0.836 0.769 0.698 0.6230.2 1.148 1.092 1.031 0.967 0.899 0.826 0.749 0.666 0.579 0.487 0.3910.1 1.077 1.008 0.934 0.854 0.769 0.677 0.579 0.475 0.366 0.255 0.148

0 1.000 0.917 0.826 0.729 0.623 0.510 0.391 0.268 0.148 0.047 0.000 Needs Parameter (a) 0.0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Note: All computations assume β = 0.4.

Table 2. Summary Data for El Salvadoran Cooperatives and Private Farms During the 1191/1992 Crop Cycles for Coffee, Corn and Sugar

Full Sample Cooperatives Private Farms

Mean Stand. Mean Stand. Mean Stand.COFFEE Deviation Deviation Deviation Number of Observations 151 37 114Land (Mz) 97 153.18 250 231.86 47 62.00Labor Cost ($ for season) 270,512 558,297.30 660,309 964,158.70 143,999 227,378.Inputs Cost ($ for season) 82,486 169,399.20 212,594 285,53.00 40,258 69,105.44Rental per Mz ($ per year) 305 43.61 283 51.98 312 38.09Daily Wage 22.36 2.59 22.29 0.23 22.38 2.98

Weighted Input Price 74 52.50 73 7.08 75 60.35Production (QQ) 7,307 11,799.46 14,152 17,855.75 5,086 6,932.26 CORN Number of Observations 258 55 203Land (Mz) 12 34.57 46 63.77 3 6.37Labor Cost ($ for season) 11,599 37,600.74 44,203 72,074.57 2,766 6,498.43Inputs Cost ($ for season) 12,173 32,071.11 41,759 55,260.81 4,157 13,760.34Rental per Mz ($ per year) 289 58.94 284 46.20 290 61.97Daily Wage 18.31 3.08 17.65 2.17 18.49 3.26

Weighted Input Price 91 10.24 91 3.25 91 11.42Production (QQ) 514 1,295.01 1,786 2,309.33 169 383.94SUGAR Number of Observations 255 59 196Land (Mz) 61 119.72 157 173.51 33 78.23Labor Cost ($ for season) 90,421 180,827.35 249,757 254,623.05 42,457 115,388.49Inputs Cost ($ for season) 59,561 123,497.34 151,545 160,077.89 31,872 94,413.02Rental per Mz ($ per year) 292 71.57 291 43.76 293 78.11Daily Wage 23.66 3.72 22.86 1.97 23.90 4.07

Weighted Input Price 67 10.44 68 3.44 66 11.75Production (QQ) 4,141 8,936.22 10,201 12,865.37 2,317 6,350.77

Notes: Mz = Manzana; 1 Manzana ≈ 0.59 hectares ≈ 1.5 acres. $ = Colones; 8.7 Colones ≈ 1 U.S. Dollar (1991/1992). QQ= Spanish Quintal, 1 quintal ≈ 46 kg. MT = Metric Ton; 1 metric ton ≈ 2204.6 lbs.

TABLE 3: MLE Estimates of Production Function, First-Order Cost Minimization Conditions and

Derived Cost Function For Coffee, Corn and Sugar (asymptotic standard errors in parentheses)

Coffee Corn SugarProduction Function Constant 1.3100* 2.9665* 3.4646*

(0.3450) (0.2170) (0.2046)Ln (M = materials)) 0.0540 0.2376* 0.0545

(0.0696) (0.0544) (0.0522)Ln (N = labor)) 0.6625* 0.1516* 0.2181*

(0.0841) (0.0590) (0.0354)Ln (L = land)) 0.3278* 0.6481* 0.7308*

(0.1033) (0.0606) (0.0706)σ 0.5863* 0.4916* 0.4406*

(0.0512) (0.0205) (0.0131)λ=σu / σv 2.3738* 6.3356* 5.3541

(0.6610) (2.1332) (1.4410)Returns to scale 1.0443* 1.0373* 1.0034

(0.0227) (0.0159) (0.0085)First-Order Conditions ρN -1.3244* -2.5720* -2.6855*

(0.4311) (0.4546) (0.2340)βN 0.0720 -0.0760 -0.2293*

(0.1125) (0.0717) (0.0649)ρM -2.3219 -2.3583* 3.5646*

(1.4811) (0.2816) (1.0341)βM -0.2929 -0.2876* -0.1419

(0.2777) (0.0578) (0.0875)Derived Cost Function Constant -0.4489 -1.9472* -2.7322*

(0.3059) (0.2921) (0.3377)Ln (Q) 0.9576* 0.9640* 0.9966*

(0.0208) (0.0148) (0.0084) 0.0517 0.2291* 0.0543

(0.0961) (0.0633) (0.0943)Ln (PN) 0.6344* 0.1462** 0.2174*

(0.0555) (0.0796) (0.0698)Ln (PL) 0.3139* 0.6247* 0.7283*

(0.1099) (0.0324) (0.0268)Number of cooperativesa 35 53 59Number of private farmsa 105 174 59

Notes: * indicates significance at 95% level; ** indicates significance at 90% level. a. observation excluded if the value for any variable differs from the sub-sample average by more than two times the standard error.

TABLE 4: Estimates Private Farms' and Cooperatives' Technical Inefficiency and Its Costs for

Coffee, Corn and Sugar`

(Standard errors in parentheses)

Coffee Corn Sugar

Technical Inefficiency

Cooperatives 0.7509* 0.6040* 0.4508* (0.1691) (0.1945) (0.1852)

Private farms 0.3040* 0.3011 * 0.2776* (0.0194) (0.0469) (0.0396)

Difference 0.4469* 0.3029* 0.1732* (0.0708) (0.0628) (0.0581)

Cost loss due to technical inefficiency

Cooperatives 0.7191 0.5823 0.4493

Private farms 0.2911 0.2903 0.2767

Note: * indicates significance at 95% level.

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