Analysis of Production Efficiency of Mexican Coffee-Producing Districts

AAEA Annual Meetings, Selected Paper #134280 Providence, RI July 2005

Gabriela Cardenas,

Dmitry Vedenov

and

Jack Houston

Corresponding author: Dmitry Vedenov 315C Conner Hall Dept. of Ag. and Applied Economics University of Georgia Athens, GA 30602 Voice: (706) 542-0757 Fax: (706) 542-0739 E-mail: [email protected]

Cardenas is a former M.S. student (graduated 2004), Vedenov is an assistant professor, and Houston is a professor at the Department of Agricultural and Applied Economics, University of Georgia.

© Copyright 2005 by Cardenas, Vedenov, and Houston. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

Keywords: distance function, production systems, stochastic frontier, technical efficiency, coffee production, Mexico. Analysis of Production Efficiency of Mexican Coffee-Producing Districts

Introduction

The theory of economic growth recognizes the fundamental role of increases in agricul-

tural outputs in achieving rural advancement (Ohkawa and Rosovsky, 1960; Johnston and

Mellor, 1961; Johnston and Nielsen, 1966; Johnson, 2000). However, agricultural production in

various regions of the world is often affected by price fluctuations at the global level. In particular, if market changes were to depress prices of the main cash crop, the households that lack easy access to financial and factor markets might respond to these conditions by shifting production towards food crops as a self-insurance mechanism (DeJanvry, Fafchamps and Saudolet, 1991).

On the other hand, households that have easier access to input and financial markets and produce high quality commodities might increase their efficiency by using the best production practices,

thus exploiting their comparative advantage. In addition, their reliance on subsistence cropping

may diversify towards commercially-oriented crops driven by the market demand.

According to International Coffee Organization (ICO), the world indicator price for cof-

fee in 1984 was as high as 1.4463 USD/lb paid to producer countries (ICO, 2004). Governmental

support for coffee production in the 1980s drove farmers in lesser-developed countries to in-

crease plantings of this commodity. In the subsequent years, various forms of supports intended

to increase coffee productivity resulted in oversupply of coffee that exceeded demand by 13 mil-

lion bags1 by 2000 (ICO, 2004). As a result, an average price of coffee paid to producer countries

in 2000 dropped to 0.3797 USD/lb.2

1 One bag is about 60kg or 132 lb of coffee. 2 in 1984 dollar equivalent.

1 In Mexico, the Instituto Mexicano del Café (INMECAFE) provided support to coffee producers since 1973 in the form of machinery, technical packages, and price floors, along with marketing and organizational structures (Salazar, Nolasco, and Olivera, 1992). However, all of these support mechanisms have been shown to be a contributing factor in misallocating resources such as land in the distorted markets (Saudolet and De Janvry, 1995; Helberger and Chavas,

1996). One of the consequences of these distorting policies was that many small landowners, mainly in south Mexico (Chiapas, Veracruz, Oaxaca), devoted most of their land to coffee production, even though environmental conditions were not suitable to grow quality coffee. Simul- taneous production of high- and low-quality coffee resulted in a practice of mixing coffee of different grades that gave Mexico a bad reputation as a producer (Lopez, 2002).

In the early 1990s, there was a push to deregulate agriculture particularly in developing countries. In Mexico, this process was accelerated with the signing of the North American Free

Trade Agreement (NAFTA). One of the objectives of the market reform was to transition to free determination of market equilibrium, thus avoiding damaging distortions in factor markets and their prices. These changes combined with elimination of ICO production quota system in 1989 left Mexican coffee producers to face a free market that can either boost economic growth or suppress it.

There are four main producing regions of coffee in Mexico —Chiapas, Veracruz, Oax- aca, and Puebla — accounting for 85 percent of the country’s coffee production. 3 In 2000, coffee

in Mexico ranked second among the highest currency earning agricultural products. Eighty five percent of coffee production were exported generating $613.8 million in export revenues and representing 14.5 percent of the total agricultural exports (Mexico/CMC, 2004). However, for-

3 Based on data from Mexico/ASERCA, 2002.

2 eign currency earned from coffee production at the national level has followed a negative trend, declining from 150 million USD in 1998 to 42 million USD in 2001 in real prices.

Coffee production is highly fragmented, providing income for 700,000 family households in Mexico on which approximately 3 million people are directly dependent (Mexico/ASERCA,

2002). In 2000, the southeastern state of Veracruz, which will be a subject of closer analysis of this paper, was the second largest producer of coffee in Mexico, with coffee representing the third most planted agricultural product after corn and sugar cane. The most recent figures for Ve- racruz report 67,227 small land holders owning 152,457 hectares with an average of 2.2 hectares per producer (Mexico/CMC, 2004). The revenue from coffee production has followed the declining national trend, with a typical cherry coffee producer in Veracruz receiving $27.10 per metric ton (mt) of coffee4 in 1998 compared to $14.72/mt in 2002 (in real prices).

This study attempts to analyze the production system of coffee producers in 24 mu- nicipios5 in Veracruz, Mexico, during 1997 through 2002 growing period. The municipios included in the study comprise 54 percent of the total land planted to coffee in the state. The region experienced rapid expansion of coffee production in 1970s and 1980s. Most of this growth was promoted by government-introduced technologies and government subsidies. However, this support declined during the 1990s due to changes in agricultural strategies of the Mexican government. Along with disappearance of national and international institutions supporting coffee production and increasing international supply of the commodity, this created uncertain environment for coffee producers and impacted their technology, input use, and output production. Thus the production system is analyzed during a period when governmental support has been significantly

4 One metric ton is equivalent to 2,204.62 pounds. 5 A municipio is a unit of local administration in Mexico similar to a county or district in other countries.

3 reduced and decoupled, and the pressure of decreasing international prices also burdened rural producers.

Recent studies on production efficiency and agricultural growth in developing countries include Umetsu, Lekprichakul, and Chakravorty (2003) who estimated an input-oriented

Malmquist index for the 13 rice producing regions in the post-Green Revolution (1971-1990)

Philippines. Coelli and Fleming (2003) studied the role of cash crops (coffee) vs. subsistence production in Papua New Guinea by using an input distance function and estimating technical efficiency. Gilligan (1998) tested for relationship between farm size and productivity present in the sample of Honduras small coffee planters by estimating a non-parametric input-output distance function for a sample of 409 farmers during 1993–1994. A Tobit regression was used to find the relationship between technical efficiency and size returns. The studies in both developing and developed countries suggest that the economic productivity might be better explained by incorporating variables other than those related solely to production. Existing market imperfec- tions and involvement of public services in some productive areas have also to be considered

(Umetsu, Lekprichakul and Chakravorty, 2003).

The general goal of the present study is to characterize the system of production by inputs and outputs used by the coffee producers in Veracruz, Mexico. A distance function stochastic frontier approach is used in order to accommodate three outputs: coffee, subsistence crops and alternative (nontraditional) cash crops. The specific objectives are to: (1) measure the change of efficiency in agricultural production; (2) assess the existence of economies of diversification or complementarity between coffee and other crops, in order to identify products that could bring more growth to the region; (3) identify municipio-specific characteristics (e.g. access to markets

4 or higher altitude) that may provide comparative advantage in coffee production, and determine

to what extent these factors impact efficiency.

The rest of the paper is organized as follows. The second section outlines the modeling

methodology including discussion of input distance function for the production model, stochastic

frontier approach to estimation of technical inefficiency, and incorporation of inefficiency fac-

tors. The third section describes the data set and specifications of the model to be estimated. The

fourth section presents and discusses the empirical results. The last section contains concluding

comments.

Modeling Methodology

An input distance function characterizes the production technology by treating the output

vector y as given and looking at the minimal contraction of the input vector x that the producer

can achieve while still producing the given output vector (Shephard, 1953; Färe and Primont,

1995). One of the main characteristics of a distance function is that it allows for multiple outputs

and inputs to be considered within the same modeling framework. A general-form input distance

function is given by

D(y, x) = min{λ > 0 : (xλ) ∈ L(y)} (1)

where for a given output vector y, the input set L(y) includes all feasible input vectors (x) that

can produce y. The distance function in (1) can be shown to be non-decreasing, homogeneous of degree one, concave, and continuous in x, and decreasing in y (Färe and Primont, 1995). The dis-

tance function may also include a time trend in order to capture technological changes in produc-

tion system (Hattori, 2002).

Technical efficiency can be defined as a condition D(y,x) = 1. Given available inputs, the most efficient producer will determine an efficiency boundary from which the producers not us-

5 ing the best management practices will deviate. The degree of technical inefficiency of individ-

ual producers can be then evaluated by measuring these deviations from the efficiency frontier.

For estimation purposes, the distance function in (1) is replaced by a stochastic frontier distance

function εD(y,x) = 1, where ε is a random disturbance. The latter can be further decomposed so

that ε = v – u, where the random term u > 0 measures the degree of inefficiency and is producer-

specific, while the second error term v allows for measurement errors and impact of various

events, such as weather, that affect productivity but are outside of producer’s influence (Battese

and Coelli, 1995; Hattori, 2002).

Following Battese and Coelli (1995), we assume that the producer-specific random terms

+ 2 ui are drawn from a truncated normal distribution N (μi, σ ) with the mean μi expressed as a lin-

ear function of a vector of explanatory variables zi so that μi = δizi. In the rest of the paper, we

refer to these additional variables as inefficiency variables as they help to explain deviations of

individual producers from the efficiency frontier. The estimation of a distance function also pro-

vides coefficients and elasticities that describe the production process.

The transcendental logarithmic (or translog) function is a commonly used functional form

for the input distance function. It does not impose restrictions on substitution elasticities and is

more flexible than Cobb-Douglas specification (Christensen, Jorgenson and Lau 1973; Fuss,

McFadden and Mundlak, 1978). Therefore, we use the translog function in order to represent a

multi-output technology that allows for direct estimation of cross-output elasticity. A general-

form translog distance function for K inputs and M outputs can be written as

M 1 M M K ln D(y,x) = α + β ln y + β ln y ln y + α ln x + 0 ∑ m m 2∑∑mn n m ∑ k k m m n k (2) 1 K K K M ∑∑α kl ln xk ln xl + ∑∑χ km ln xk ln ym + ε 2 k l k m

6 The parameters of the translog function can be constrained as to satisfy the homogeneity and symmetry conditions:

∑α k = 1, ∑α kl = 0 k = 1,2,..., K k l

∑ χ km = 0 m = 1,2,..., M k

β mn = β nm m,n = 1,2,..., M α kl = α lk k,l = 1,2,...K

As suggested by Lovell et al. (1994), the homogeneity condition imposed on (2) can be used to normalize the distance function with respect to an arbitrary input. In this paper, we use

* the hectares planted to coffee as the normalizing input, define a new input vector x = (xk / xK ), k

* −1 = 1,…,K – 1, and rewrite the distance function asD'(y,x ) = xK D(y,x ) . The final model to estimate is then given by:

M 1 M M K −1 − ln x* + ln D'(y,x* ) = α + β ln y + β ln y ln y + α ln x* + 0 ∑ m m 2∑∑mn n m ∑ k k m m n k (3) K −−11K K − 1M 1 * * * ∑∑α kl ln xk ln xl + ∑∑χ km ln xk ln ym + v − u 2 k l k m

* Note that the efficiency condition D(y,x) = 1 now impliesxK = D'(y,x ) , and the random term u again measures the degree of deviation from the efficiency frontier. Therefore, the techni-

th cal efficiency for the i producer can be calculated as the conditional expectation of exp(ui) given the composite error εi = vi – ui (Hattori, 2002):

TEi = E{exp(−ui )ε i }. (4)

In addition, we are interested in cross-output elasticities

∂ 2 ln D' = β mn = β nm , (5) ∂ ln ym∂ ln yn

7 which can be calculated from (3). These elasticities measure the change of input shares when the outputs m and n are produced together and reflects output complementarity (Coelli and

Fleming, 2003). Whenever this measure is positive, output complementarity exists in the sense that production of the two outputs simultaneously increases efficiency due to a decrease in input use.

Data Specification and Expected Outcomes

Data used in this study were collected from the statistical yearbooks published by the

Secretary of Finance and Economics (SFE) in the state of Veracruz, Mexico (Mex- ico/COVERCA). The yearbooks provide information on the value of outputs produced and inputs used, as well as environmental and socio-demographic information at the municipio level.

However, the data do not include costs of inputs and are highly aggregated for certain variables.

Due to data limitations, the analysis at the household level was not possible. The smallest unit of aggregation available in the data set, and thus chosen for analysis, was a municipio (a district), which is a basic unit of local administration.

A total of 24 municipios were included in the sample, accounting for 54 percent of the total area planted under coffee in Veracruz. The demographic characteristics of the municipios as well as area planted for coffee are presented in table 1. The available data for each municipio includes use of machinery, fertilizers, and land, value of all outputs produced, and demographic variables. Table 2 provides descriptions of the variables included in the model and their sample statistics. The SFE database included data for five growing seasons, namely 97/98, 98/99, 99/00,

00/01, and 01/02. Therefore, a total of 120 observations were used in a pooled cross-section, time-series analysis.

8 The model in (3) was estimated with three outputs and five inputs. The outputs are corn, coffee, and “other crops”. Traditionally, corn is the main staple crop produced in Mexico and is considered separately in order to account for self-consumption agriculture. Corn output is measured as constant value of production6 by each municipio in an agricultural year. Coffee is the main cash crop of interest in this study. Coffee output is also measured as constant value of production in an agricultural year. Finally, “other crops” variable accounts for all cash crop production other than coffee, which varies widely across municipios, but mainly includes export- oriented crops, such as mango, passion fruit, lime, tangerine, banana, oranges and pineapple. The output of “other crops” is also measured as constant value of production in an agricultural year.

The input variables included areas planted to coffee, corn, and other cash crops as well as fertilizer use and machinery use. The fertilizer variable is measured in kilograms of fertilizer used per agricultural year and includes both organic and chemical fertilizers. Machinery use is measured as total number of hectares per agricultural year where machinery has been used.

Machinery here refers to both tractors and all other mechanized tools used in production.

Inefficiency Variables

In order to account for differences in technical efficiency of production across municipios, four variables are introduced in the model — rural population density, roads, ratio of other crops planted to coffee, and altitude.

The variable for rural population working in the agricultural sector is introduced to capture some of the effects that the labor may play in the production efficiency. In the area studied, the agricultural production is labor intensive and hence we expect that an increase in the

6 Consumer Price Index base 1997

9 rural population working in the agricultural sector would impact positively the technical efficiency of production.

In order to capture how mobility and access to markets impacts efficiency of production, the variable “roads” is used. This variable is measured in kilometers of paved roads in the municipio. Availability of road network affect efficiency in two ways. On the one hand, road infrustructure facilitates trade as the municipios have easier access to markets and can sell agricultural products in wider area. On the other hand, increased mobility allows for diversification into other economic activities. Since the model presented does not account for economic activities other than agricultural production, we expect that the sign of roads variable to depend on how market-oriented agriculture is affected by access to markets.

The ratio of cash crops produced to coffee is the variable that captures diversification of municipios toward production of export-oriented crops other than coffee. The variable is included in the model in order to find how such diversification affects technical efficiency of municipios.

Finally, the altitude of the coffee plantations is used in the model as a proxy to coffee quality. Growing high-quality arabica species of coffee usually require the altitude of 800 km or higher above the sea level, while production at lower elevations is typically associated with robusta variety used in soluble mixes. Therefore, altitude in the model is a dummy variable that has a value of one for altitudes greater than 800 km and 0 otherwise. Using altitude as an approximation to quality is consistent with the most commonly used approach to classify high quality coffee (de Graaff, 1986). This criterion is also used in Mexico in order to distinguish high- and low-quality producers (Mexico/COVECA, 2004).

10 Empirical Results

For estimation purposes, a simple time trend term has been added to the translog function

2 specification in (3). The error terms v were assumed to be normally distributed N(0,σ v ) with

2 zero mean and variance σv , while the distribution of error terms ui was assumed to be truncated

+ 2 2 normal N (μ,σ ) with variance σ and the mean μi = δizi represented as a linear combination of four inefficiency variables described in the previous section. The resulting model was estimated using the maximum likelihood technique presented in Battesse and Coelli (1995). The maximum

2 2 2 likelihood function, which is expressed in terms of the variance parameters σ ε = σ v + σ

2 2 andγ = σ /σ ε , and measures of technical efficiency were calculated using the FRONTIER 4.1 software (Coelli, 1996).

The translog distance function with the time trend and inefficiency variables was estimated for the data set comprised of five annual observations in each of 24 municipios, or 120 total observations. Estimated coefficients of interest and their p-values are presented in table 3.7

The results suggest that increases in fertilizer use and area planted under coffee increase distance function, i.e. have positive effect on efficiency. On the other hand, increases in machinery use and areas planted under corn and other cash crops decrease the distance function and thus negatively affect efficiency. However, the coefficient by fertilizer use is not significantly different from zero and the coefficient by area planted under cash crops is significant only at 90% confidence level. Coefficients by the other three input variables are all significant at 99.9% confidence level.

On the output side, increase in corn production have a positive effect on efficiency, while increase in coffee production results in a strong negative effect on efficiency. The effect of other

7 Full estimation results are available from authors upon request.

11 cash crops is not significantly different from zero. The time coefficient is also not significantly different from zero, which suggests that the productivity of the municipios did not change sub- stantially during the period considered.

Specification tests were performed on the estimated model using generalized likelihood ratio approach. The first test was performed in order to find out if the Cobb-Douglas production function offered a better representation of the data. The hypothesis tested was that all coefficients by input-output cross terms are zero. The second test was to determine if the inefficiencies are deterministic. The hypothesis tested was that the variance of the error term ui is zero or, equiva- lently, γ = 0 (Battese and Coelli, 1995). The parameter γ equal to zero indicates that the frontier deviations from efficiency are non-stochastic, and thus the model can be efficiently estimated by a simpler procedure (e.g. OLS). The third test determines whether the explanatory variables zi introduced to explain the mean technical inefficiencies ui enhance the explanatory power of the model. The null hypothesis is that the coefficients by all the introduced factors (except for the intercept) are zero. The results of the three maximum likelihood-ratio tests confirm that at a 95 percent confidence level the stochastic frontier translog model with technical inefficiencies rather than random shocks explains the production system observed in Veracruz municipios (table 4). Overall, the tests emphasize the importance of accounting for technical inefficiencies in order to explain the technological relations in Mexican crop production system. They also dem- onstrate the need for including explanatory variables zi.

Technical Efficiency

Technical efficiency as defined in (4) is a measure that ranges from 0 to 1, with all municipios compared to the most technically efficient municipio in the sample. Higher measures of technical efficiency (closer to 1) mean more efficient municipios, while lower values (closer to

12 zero) indicate possibility for improvement in the input use. The calculated measures of technical efficiency are shown in table 5. Note that these results reflect technical efficiency relative to the best practice used in this sample.

The results show that technical efficiency on average increased from 1997 to 2002 by

1.04 percent from 0.9586 to 0.9720. During the 1997/98 growing period (first period in the sample), inefficiencies8 among individual villages ranged from 0.09 percent (most efficient) to 16.6 percent (least efficient). During the 2001-2002 growing period (last period in the sample), the inefficiencies among individual villages ranged from 0.04 percent (most efficient) to 11.0 percent (least efficient). While this represents a positive trend in efficiency, the producers in the least efficient municipio (Misantla) could still decrease their input usage by 11 percent during the

2001-2002 growing period to produce at the best practice frontier. Note also that the relative efficiency of individual municipios changed over time, as no municipio consistently remained the most or least efficient during the five growing periods included in the sample.

Complementarity

The cross-output elasticities calculated according to (5) are reported in table 6. These coefficients indicate the degree of complementarity among outputs resulting in increase in efficiency. The results show existence of strong diseconomies of complementarity between coffee and corn. In other words, during the time period considered, the producers planting only the traditional crops (coffee and corn) had lower efficiency due to higher input shares used in production. In particular, one percent increase in corn production by coffee producers resulted in 0.37 percent decrease in efficiency due to an increase in inputs use.

8 Inefficiency is defined as the difference between the maximum efficiency of one and the calculated measures reported in table 5.

13 Production of other cash crops resulted is small diseconomies of complementarity (negative cross-elasticity) when planted together with coffee and small economies of complementarity

(positive cross-elasticity) when planted together with corn. However, neither of these cross- elasticities was significantly different from zero (table 3).

Inefficiency Variables

The explanatory variables included in the model in order to explain mean inefficiencies of individual municipios were rural population density, roads, share of other crops to coffee, and altitude. The estimated coefficients for these variables are presented in table 7. All explanatory variables are significant at 99% confidence level. Note that the signs of the coefficients reflect the effect of explanatory variables on the mean inefficiency, so that negative sign actually means positive effect on efficiency, and vice versa.

The coefficient by rural population is negative, i.e. an increase in rural population density decreases mean deviation from the efficiency frontier and thus increases efficiency. This result was expected as municipios under consideration are characterized by labor-intensive agricultural production. This is also consistent with other studies that find that an increase in population positively affects efficiency of agricultural production (Johnson, 2000).

The availability of roads turned out to be negatively related to agricultural productivity.

While the magnitude of the effect was relatively small, it was significantly different from zero.

This result was somewhat unexpected as road availability and thus access to markets was hy- pothesized to increase efficiency. One possible explanation is that the roads variable was measured in total lengths of paved roads in the municipio and thus might have not accounted well for proximity to local markets.

14 The municipios producing a higher ratio of cash crops to coffee were found on average to be more technically efficient. This finding is consistent with the significant negative cross- elasticity of simultaneous corn and coffee production discussed earlier. These results suggest that a shift towards crop combinations different from the traditional corn/coffee rotation may increase efficiency of production. Such shift may provide a way to diversify away from heavy depend- ence on coffee production especially at the times when coffee prices are low or volatile.

Finally, the altitude variable, which was used as a proxy to coffee quality, showed a significant and negative impact on the mean inefficiency, i.e. the technical efficiency was on average higher in the municipios located at altitudes above 800m. This is consistent with the docu- mented fact that coffee producers in higher-altitude locations in Mexico exhibit more commercially-oriented behavior in comparison with their lower-altitude counterparts because they know that the markets will pay a premium for their high quality coffee (Altobello and Valdivia, 2000).

Another important phenomenon that may be captured by the altitude variable is a longer family history of cultivating coffee in municipios with better environmental conditions and perhaps better land quality, which would allow for better methods of production and organization.

Conclusion

The production system in the state of Veracruz, Mexico, was analyzed for a five-year period for 24 coffee-producing municipios by estimating a stochastic frontier translog distance function with five inputs and three outputs. The results show that overall technical efficiency increased only marginally during the period considered despite of coffee price fluctuations in the global market. Efficiency of individual municipios changed over time but no consistent pattern was revealed. Analysis of cross-output elasticities demonstrated existence of strong diseconomies of complementarity between coffee and staple crops represented by corn. On the other

15 hand, simultaneous production of cash crops other than coffee and staple crops resulted in higher overall efficiency of production.

Higher population density, higher altitude, and higher proportion of cash crops to coffee were shown to be factors positively contributing to efficiency of production. The coefficient by roads variable, though very small, was significant, but did not have the expected sign, which might be a consequence of the way the variable was measured.

The measure of producer efficiency in this study is based on total production, i.e. quality and differentiation of products are not explicitly considered. Additional data on off-farm activities and longer data series could also improve the analysis. Nevertheless, studies on productivity at local level have not been conducted for agricultural production in many Mexican regions. Col- lection of data for micro-regions in Mexico is a recent effort, so further opportunities may be ex- ploited as more data become available. The findings obtained in this work can be then considered a part of an effort that can be extended to contribute to creation of suitable policies focused at a regional level.

The modeling approach developed here can serve as a framework for analysis of agricultural production comparing different coffee producers within Mexico or around the world. In- formation on types of farm organization, types of coffee, specific cash crops, human capital and value produced can be used in order to find a better measure of efficiency and its determinants.

The analysis can also be enriched by using later developments that introduce risk management to the frontier analysis of production process.

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19 Table 1. Coffee-Producing Districts: Demographic Data Rural Pop. Area Planted % Rural Municipio Area, km2 Population Density per under Coffee, Population km2 ha Alto Lucero 725.48 27,188 63.7% 23.86 1,626.86 Atoyac 171.09 22,619 27.3% 36.10 3,001.54 Atzalan 543.70 48,179 94.4% 83.65 5,048.61 Chumatlan 36.19 3,438 100.0% 95.00 199.40 Coatepec 255.81 73,536 19.9% 57.34 9,578.86 Comapa 319.97 17,094 74.6% 39.86 2,907.91 Coxquihui 86.37 14,423 74.8% 124.88 550.09 Coyutla 312.56 21,105 63.2% 42.66 800.10 Emiliano 394.82 44,580 67.9% 76.63 5,264.37 Zapata Jilotepec 72.38 13,025 49.7% 89.51 1,438.34 Misantla 537.90 60,771 62.6% 70.69 4,182.53 Naolinco 123.38 18,097 55.4% 81.26 772.00 Omealca 225.37 22,085 83.1% 81.41 605.48 Soteapan 528.07 27,486 43.6% 22.72 2,243.44 Tenampa 69.92 5,900 100.0% 84.38 2,082.70 Teocelo 54.29 14,900 39.2% 107.53 2,796.40 Tepatlaxco 99.53 7,844 100.0% 78.81 2,510.08 Tezonapa 351.00 51,006 82.5% 119.90 13,972.22 Tlachichilco 291.18 11,067 100.0% 38.01 2,678.21 Tlaltetela 266.50 13,339 69.5% 34.79 3,208.11 Tlapacoyan 142.30 51,877 32.8% 119.70 1,873.74 Xico 176.85 28,762 26.7% 43.35 3,388.81 Yecuatla 74.03 12,500 75.0% 126.57 2,998.40 Zongolica 347.33 39,841 84.2% 96.56 5,969.94

Note: Population data are for 2000.

20 Table 2. Variables Description and Sample Statistics

Variable Description Units Mean Std.Dev.Min. Max. Inputs Corn_H Planted area, corn hectares 2,620.67 2,825.43 111 11,643 Cof_H Planted area, coffee hectares 3,333.02 2,933.16 200 15,000

Ocro_H Planted area, other cash crops hectares 7,477.30 6,477.89 1 30,918 Fert Area fertilized hectares 7,464.75 7,558.03 625 30,918 Area using machinery input (tractors and Mac hectares 1,239.00 2,185.00 1 10,683 other powered tools) Outputs

Corn Constant value of corn production 000 of pesos 1.135 1.257 0.256 51.516

Coffee Constant value coffee production 000 of pesos 26.175 35.948 0.513 218.633

Constant value of other cash crops Ocro 000 of pesos 35.935 74.381 4.309 466.350 production Inefficiency Variables Density Rural population density persons/km2 74.0 33.0 22.7 126.6 Roads Roads km 65.7 48.12 2.0 175.7 MIX Ratio of cash crops to traditional crops percent 2.22 5.18 0.0072 23.01 1 for altitudes above 800 m Altitude Altitude 0.58 0.49 0 1 0 otherwise

21 Table 3. Selected Estimation Results

Parameter Variable Estimate P-value

α0 Intercept 1.292 0.0001

αt Time –0.002 0.2115 Inputs

αk Cof_H 0.391 0.0001 Corn_H –1.365 0.0001 Ocro_H –0.109 0.0807 Fert 0.175 0.2338 Mac –0.093 0.0011 Outputs

βm Corn 0.880 0.0001 Coffee –2.966 0.0001 Ocro 0.012 0.7124 Output-Output

2 βmn Corn 0.065 0.2662 Coffee2 1.104 0.0001 Corn×Coffee –0.369 0.0001 Corn×Ocro 0.019 0.2835 Coffee×Ocro –0.015 0.4737

Table 4. Specification Tests

Log Likelihood ML Critical Value Hypothesis Outcome Statistic α = 0.05 H0 H1

χ km = 0 ∀ k,m 172.19 306.84 269.30 51.00 Reject H0

γ = 0 264.57 306.84 84.54 11.90 Reject H0

δ1 = δ 2 = δ 3 = δ 4 = 0 273.88 306.84 65.92 9.49 Reject H0

22 Table 5. Technical Efficiency of Individual Municipios, 1997-2002

Growing Period Municipio 97/98 98/99 99/00 00/01 01/02 Alto Lucero 0.9213 0.9122 0.9428 0.9464 0.9758 Atoyac 0.9533 0.9825 0.9807 0.8976 0.9995 Atzalan 0.9948 0.9612 0.9257 0.9719 0.9408 Chumatlan 0.9699 0.9586 0.9881 0.9822 0.9968 Coatepec 0.9404 0.9645 0.9269 0.9871 0.9723 Comapa 0.9696 0.9987 0.9678 0.9551 0.9996 Coxquihui 0.9881 0.9866 0.9910 0.9943 0.9996 Coyutla 0.9818 0.9793 0.9654 0.9737 0.9910 Emiliano Zapata 0.8728 0.9697 0.9127 0.9176 0.9017 Jilotepec 0.9893 0.9698 0.9901 0.9855 0.9858 Misantla 0.9077 0.9273 0.8861 0.9167 0.8899 Naolinco 0.9919 0.9730 0.9661 0.9978 0.9994 Omealca 0.9887 0.9995 0.9895 0.9705 0.9988 Soteapan 0.8989 0.8809 0.8924 0.8862 0.9237 Tenampa 0.9810 0.9947 0.9906 0.9889 0.9938 Teocelo 0.9784 0.9939 0.9781 0.9883 0.9868 Tepatlaxco 0.9893 0.9995 0.9934 0.9845 0.9966 Tezonapa 0.8341 0.9075 0.8169 0.8441 0.9269 Tlachichilco 0.9666 0.9638 0.9587 0.9801 0.9795 Tlaltetela 0.9486 0.9984 0.9971 0.9787 0.9478 Tlapacoyan 0.9933 0.9975 0.9944 0.9994 0.9839 Xico 0.9991 0.9829 0.9969 0.9837 0.9806 Yecuatla 0.9793 0.9936 0.9711 0.9878 0.9802 Zongolica 0.9691 0.9824 0.9280 0.8406 0.9776 Average 0.9586 0.9699 0.9563 0.9566 0.9720 Inefficiency, min 0.0009 0.0005 0.0029 0.0006 0.0004 Inefficiency, max 0.1659 0.1191 0.1831 0.1594 0.1101 Note: Inefficiency is measured as the difference between one and the efficiency reported in the table.

23 Table 6. Cross-Output Elasticities

Corn Other crops

Coffee –0.369*) –0.015 Other crops 0.019

*) significant at 99.9% confidence level

Table 7 Factors Explaining Mean Inefficiency for Veracruz Municipios, 1997-2002

Dens. of Intercept Rural Roads MIX Altitude Population Coefficient 0.1420 –0.140 0.001 –0.003 –0.063 p-value (0.0001) (0.0001) (0.0001) (0.0059) (0.0001)

Note: See table 2 for description of individual variables.