Estimating Technical Ef�iciency and its Determinants in the Coconut Plantations: The Case of Kurunegala Plantations Limited, Sri Lanka

This study estimated the Technical Ef�iciency (TE) of coconut production in Sri Lanka using the stochastic frontier production function procedure. Data on inputs and coconut production recorded by Kurunegala Plantations Limited from 2000 – 2018 were used for the analysis. The stochastic production frontier in Cobb-Douglas form and the inef�iciency model were estimated by single-step Maximum Likelihood method using STATA 14 computer software package treating coconut yield as the dependent variable and fertilizer, rainfall, labor, chemicals, tractor hours, mulching harrowing/plowing, agro-ecological zones, education level of the managers and bearing coconut extent as independent variables. Results revealed that TE of coconut production ranged from 81-98%, with an average of 88%, indicating that there is scope for increasing the production by as much as 12% without increasing inputs and simply using a higher technology level. The outcome of the analysis shows that inorganic fertilizer, rainfall, labor, tractor hours, and mulching are kind positive and signi�icant. In contrast, agro-chemicals such as weedicides, fungicides and pesticides and plowing/harrowing did not show a signi�icant contribution to coconut production. In respect of the farm and farmer-speci�ic characteristics, the size of the estate has a positive relationship with technical inef�iciency, meaning that smaller estates are more ef�icient than larger estates. It also shows that the agro-ecological zones and educational level have no signi�icant effect on the ef�iciency of coconut production. The results highlight the need for government and private sector assistance in improving the ef�iciency of smallholders and promoting access to productive inputs.


INTRODUCTION
Coconut, one of the major plantation crops in Sri Lanka, plays a vital role in sustaining the national economy, food security, and people's livelihood. Coconut cultivation occupies 20% of the total agricultural land in the country (DCS, 2014) while contributing to GDP and export earnings around 0.7% and 5.1%, respectively (CBSL, 2019). This sector employs around 135,000 people in production and industry and provides a livelihood for 698,168 smallholders (DCS, 2012). The annual average coconut production is about 2,800-3,000 million nuts, of which approximately 70% is utilized for domestic culinary purposes and the balance is divided among value-added coconut-based processing industries (CDA, 2019). Over the years, the country's coconut production remains stagnant while the demand for coconut for culinary nuts and industrial use is increasing. Coconut supply has been uncertain due to many reasons such as the impact of climate change, price �luctuation, high cost of production, pests and diseases, fragmentation of coconut lands, scarcity of labor, etc. Limitation of increasing of coconut supply is attributed by availability and opportunity cost of suitable land for the cultivation, a constraint of capital, declining production of old senile coconut palms. Since, there is a limited scope to increase the coconut supply either by expanding the area under the coconut or increasing the use of costly inputs such as labor and fertilizer, exploring the ways and means to obtain the maximum gains from the more ef�icient use of existing technology with given inputs is justi�ied.
Coconut is grown under various agroecological zones and other characteristics such as availability of inputs and different management practices. Therefore, the performance of these production units is diverse. There are various measures to assess the performance of a production unit, and among them, productive ef�iciency is an important measurement of producer performance. Technical ef�iciency (TE) measurement is one of the most commonly used methods for measuring the production performance of an economic unit. The TE determines the level of ef�iciency of an economic unit which will enable the identi�ication of the factors by which improvements can be made while providing useful information for policy formulation. Since there is little empirical evidence of the technical ef�iciency of coconut production, it necessitates an analysis of the production ef�iciency of the major coconut producers to determine the magnitude of gains arising from minimizing inef�iciencies while helping in formulating policy measures to reduce the production constraints. Hence, the objectives of this study were to estimate the technical ef�iciency by using stochastic frontier analysis (SFA) of coconut production, identify the key determinants of inef�iciency, and rank the estates according to the TE.

METHODOLOGY
Technical ef�iciency in crop production can be de�ined as a farmer's ability to maximize outputs under a given set of inputs and technology (Mango, et al., 2015). The degree of technical inef�iciency re�lects an individual farmer's failure to attain the highest possible output level given the set of inputs and technology used. The highest possible output, using available input and technology, is represented by the production frontier. The distinction between technological change and technical ef�iciency is important. The technological change re�lects a shift of the production frontier, as new technologies enable output per unit of input to increase (Bravo-Ureta, 2007). Technical ef�iciency, on the other hand, explains the difference between potential and observed yield for a given level of technology and inputs.

Theoretical framework
Theoretically, the productive ef�iciency of a �irm consists of two components: technical ef�iciency, which re�lects the ability of a �irm to obtain maximal output from a given set of inputs, and allocative ef�iciency, which re�lects the ability of a �irm to use the inputs in optimal proportions, given their respective prices. These two measures are then combined to measure total economic ef�iciency or productive ef�iciency (Farrell, 1957). These measures can be input or output orientation. Later, this has been evolved to develop a stochastic frontier approach for parametric function such as Cobb-Douglas form or non-parametric piecewiselinear technology and evolved to Data Envelopment Analysis (DEA) approach. The estimation of frontier function and ef�iciency can be completed either in one stage or in two stages. The two-stage analysis of explaining the level of technical ef�iciency (or inef�iciency) was criticized by Battese and Coelli (1995) as being contradictory in the assumption made in the separate stages of analysis. This study follows the Battese and Coelli (1992) approach of modeling both the stochastic and technical inefficiency effect in the frontier using maximum likelihood in a single-step analysis in Cobb-Douglas form to assess the stochastic production frontier of coconut production at the estates level.
The stochastic frontier models introduce a disturbance term representing statistical noise, measurement error, and exogenous shocks beyond the control of the production unit, which would otherwise be attributed to technical inef�iciency and provides the basis for conducting statistical tests of hypothesis regarding the production structure and the degree of inef�iciency. This model is composed of an error structure comprising a two-sided symmetric term and a one-sided component. The two-sided error captures random effects outside the control of the plantations, including the weather conditions, measurement errors, or other random disturbances typical of empirical data, while the one-sided non-negative component re�lects the technical inef�iciency. The stochastic production frontier model was speci�ied as: Where y i denotes the output of single farm i, ƒ(.) is the production frontier, x i represents a vector of the inputs used on the i th farm, is a vector of unknown coef�icients to be estimated, v i is the two-sided error and u i is the one-sided error representing technical inef�iciency (TIE). The two-sided error v i is assumed to be independently and identically distributed as N (0,σ v 2 ), while u i is assumed to have a half-normal distribution, i.e. a non-negative truncation of the N (o,σ 2 ) distribution. The outputs can either be measured as quantities for a single crop or more than one crop. The measure of technical ef�iciency (TE) relative to the production frontier are de�ined as: The TE of the production for the ith farm was de�ined as the ratio of observed production to the maximum feasible production as the following equation: Battese and Coelli (1988) suggest that TE should be predicted using its conditional expectation, given the composed random error, v i -u i , evaluated at the maximum-likelihood estimates of the equation (2). In the case of a production frontier, TEi will be valued between zero and one, therefore, Technical inef�iciency = 1 -TE i According to Battese and Corra (1977), the variance ratio parameter γ, which is related to the γ = σ 2 u / σ 2 where, σ 2 = σ 2 u + σ 2 v So that 0 ≤ γ ≤ 1 When γ is close to 0, the difference between yield and ef�icient yield is entirely due to statistical noise. On the other hand, if the γ is close to 1, the difference is attributed to the growers' less ef�icient use of the technology.
To estimate the factors that contribute to TIE, we applied the model which was proposed by Battese and Coelli (1995), speci�ied as: Where Z is a (1×M) vector of explanatory variables affecting TIE, δ is an (M×1) vector of coef�icients to be estimated, and are unobservable random errors de�ined by the truncation of the normal distribution.
The TE of the production for the i th farm was defined as the maximum feasible production as the following equation TE ƒ ; ƒ ; exp Battese and Coelli (1988) suggest that TE should be predicte given the composed random error, vi-ui, evaluated at the m equation (2). In the case of a production frontier, TEi will therefore, Technical inefficiency = 1-TEi According to Battese and Corra (1977), the variance ratio par When γ is close to 0, the difference between yield and efficie noise. On the other hand, if the γ is close to 1, the differen efficient use of the technology.
To estimate the factors that contribute to TIE, we applied the m and Coelli (1995), specified as: Where z is a (1 M) vector of explanatory variables affect coefficients to be estimated, and are unobservable random the normal distribution. N (0, ), such as that In this study, we use the panel data. Pitt and Lee (1981) speci Aigner, Lovell and Schmidi (1977) half -normal model as fol lnyit = ƒ(xit; β) + vit + uit i= 1.,2,…N, t= 1,2…..T Where ƒ(.) denotes a suitable functional form, in this study w form using maximum likelihood estimation (ML).

Empirical model
In this study, we use the panel data. Pitt and Lee (1981) speci�ied a panel data version of the Aigner, Lovell and Schmidi (1977) halfnormal model as follows: Where ƒ(.) denotes a suitable functional form, in this study we use Cobb-Douglas functional form using maximum likelihood estimation (ML).

Empirical model
The stochastic production frontier in Cobb-Douglas form and the inef�iciency model were estimated by single-step Maximum Likelihood method using STATA 14 computer software package treating coconut yield as the dependent variable and fertilizer, rainfall, labor, chemicals, tractor hours, mulching harrowing/plowing as independent variables in the stochastic frontier model while agro-ecological zones, education level of the managers and bearing coconut extent as independent variables in the inef�iciency model. The empirical models for both the stochastic frontier model and the inef�iciency model are stated in equations 6 and 7. A range of factors, including estate level characteristics and socio-economic, environmental, and non-physical, are likely to affect the ef�iciency of coconut growers. According to past studies, the responsiveness of coconut production to some inputs such as fertilizer and rainfall has proven the presence of lag effects. Therefore, two years lag for fertilizer (De Silva, 1972) and one-year lag for the rainfall were used in the model where it is necessary to represent the characteristic nature of the coconut cultivation.

Data collection and analysis
Secondary panel data available in nine area estates belonging to Kurunegala Plantations Ltd. over nineteen years from 2000-2018 were used for the analysis. The estates are Attanagalla, Dambadeniya, Dodangaslanda, Hiriyala/ Wariyapola, Dhathusenapura, Katugampola, Mahayaya, Narammala and Kurunegala. These estates are situated in Kurunegala and Gampaha districts that cover the major coconut growing area of Sri Lanka. The company has maintained records of input used, output, and other management practices.

Descriptive statistics of the sample
The summary statistics of the variables used in the stochastic frontier model and inef�iciency model are presented in Table 1. In terms of socio-economic characteristics, since the Kurunegala Plantations Limited (KPL) is a fully government-owned plantation management company, a lot of guidelines have been issued for the management of the estates; thereby, farmer-speci�ic characteristics are controlled. However, the bearing coconut extent and two dummy variables, namely agroecological zones, and the management's education levels were considered to analyze the inef�iciency model. In the agro-ecological zones, the majority of the sample, 68%, belongs to the Intermediate Zone while 32% belongs to the Wet Zone. Among the managers of the estates, while 62% have basic educational quali�ications 38% have obtained higher educational quali�ications (Diploma and above). Table 2 shows the maximum likelihood estimates of the stochastic frontier production function model and inef�iciency model with the determinants of the technical ef�iciency de�ined by equations 6 and 7. As shown in Table 2, the estimate of γ is 0.59, which indicates that only 59% of the total variation in coconut output was due to technical inef�iciency. Therefore, the difference between coconut yield and efficient yield in the KPL is mainly due to technical inef�iciency. This value is lower than the values recorded by Mangika et al. (2009) andSelvam et al. (2018). They have recorded an estimate of 0.85 and 0.84 for γ in a study conducted for assessing the technical ef�iciency of smallholder coconut growers in Sri Lanka and the Coimbatore District in India, respectively. However, in both studies, the focus was on smallholder coconut growers.

Results of the stochastic frontier model
The ML estimates of inorganic fertilizer, rainfall, labor, tractor hours, and mulching are positive and signi�icant at 1% signi�icant level. The estimated ML coef�icients of agrochemicals and plowing/harrowing did not show a signi�icant contribution to coconut production. The positive signi�icant coef�icient of inorganic fertilizer application of 0.16 indicates that a one-unit Source: Author's estimates increment of fertilizer application will increase coconut output by 0.16. This �inding is in line with Selvam et al. (2018) and Omar and Fatah (2021). However, it is noteworthy that most of the studies (Mangika et al., 2009;Nor et al., 2020), which assessed the technical ef�iciency among coconut smallholder farmers, have reported that the application of fertilizer has no signi�icant effect on coconut production. Rainfall has a positive signi�icant coef�icient of 0.43, indicating that a oneunit increment in rainfall will realize a 0.43 increment in coconut output. Labor input is also positive and signi�icant in the estimated model. The plantation sector has employed skilled laborers, and they are continuously supported with necessary training. Hence, the positive effect of labor on coconut output is justi�ied. Tractor hours have a positive signi�icant coef�icient of 0.30, indicating that one-unit increment in tractor hour will realize a 0.30 increment in coconut output. Mulching of the coconut trees with fronds had an elasticity of 0.26 indicates that a 1% increase in mulching (one coconut tree) would lead to a 0.26% increase in coconut output. A minimum of 12 fronds fall annually from a coconut tree, and growers use these to thatch the bases of the coconut trees. Mulching can conserve moisture and provide an organic source of fertilizer and thereby enhance the output of coconut. The analysis of the returns to scale can be done based on the estimates of the stochastic frontier production function in Table 2. Determining the scale bene�it of coconut production can be done by summarizing the input coef�icients other than the agrochemicals and harrowing/plowing factors. The sum of the coef�icients is 1.34, which implies that the coconut production system in KPL operates at increasing returns to scale.
The effect of farm and farmer-speci�ic factors on inef�iciency was estimated together with the production frontier. The estimated coef�icients of the inef�iciency model are shown in Table 2. Accordingly, only the size of the estate denoted by bearing coconut extent is the key factor affecting the technical ef�iciency of coconut plantations. The other variables; viz. agro-ecological zone and the manager's education level, are not statistically signi�icant. Table 3. Illustrates the mean, minimum and maximum technical ef�iciency of all the estates belonging to KPL. According to Table 3 mean, minimum, and maximum technical ef�iciency of the estates belonging to KPL are 88%, 58%, and 99%, respectively, which indicates that there is a 12% scope of increasing the production of coconut in KPL without incurring any additional cost.

Ranking of the estates according to the technical ef�iciency
Ranking the estates according to the mean technical ef�iciency is important to identify the best performer and to develop strategies to improve the productivity levels of the estates. The distribution of mean technical ef�iciency of the estates calculated by weighted average from the pooled data output is illustrated in Figure 1. Accordingly, the Attanagalla estate shows the highest technical ef�iciency of 98%. In contrast, Katugampola estate shows the lowest technical ef�iciency of 81%. The mean technical ef�iciency of other estates varies in between, indicating that there is a potential to increase the estates' technical ef�iciency.

CONCLUSION AND POLICY IMPLICATION
This study used the stochastic production frontier method to estimate technical ef�iciency and identify the determinants of technical ef�iciency of coconut plantations. The results revealed that the mean technical ef�iciency of coconut plantations belonging to KPL estimated using Cobb-Douglas production frontier is 88% indicating that 12% of the maximum potential

Ranking of the estates according to the technical efficiency
Ranking the estates according to the mean technical efficiency is important to identify the best performer and to develop strategies to improve the productivity levels of the estates. The distribution of mean technical efficiency of the estates calculated by weighted average from the pooled data output is illustrated in Fig.1. Accordingly, the Attanagalla estate shows the highest technical efficiency of 98%. In contrast, Katugampola estate shows the lowest technical efficiency of 81%. The mean technical efficiency of other estates varies in between, indicating that there is a potential to increase the estates' technical efficiency. productivity is lost due to technical inef�iciency of the estate-speci�ic characters. Moreover, this indicates that there is a scope for further increasing the output by 12% with a given level of technology and without increasing the level of inputs. The outcome of the analysis suggests that increment application of fertilizer, labor, tractor hours, mulching, and experience of rainfall will signi�icantly increase coconut production. The agrochemicals and plowing/harrowing did not show a signi�icant contribution to coconut production. From the farm and farmer-speci�ic characters, the size of the estate has a positive relationship with technical inef�iciency, suggesting that larger estates are less ef�icient than smaller estates.
The policy implications of these �indings are that the technical ef�iciency of coconut estates could be increased by 12% on average through better use of available resources such as fertilizer, labor, tractor hours, mulching, and supplementary irrigation, given the current state of technology. This could be achieved through awareness programs. The small-scale coconut plantations have more technical ef�iciency indicating that government and private sector assistance is necessary to improve the productivity of the small-scale coconut plantations. Continuous improvement of the technical ef�iciency of coconut production could promote income growth and pro�itability of the plantations. However, this study could only assess technical ef�iciency in large-scale coconut plantations, which could be extended to smallholders to suit them. The analysis contributes to government policy to expand the small-scale coconut plantation on abounded paddy �ields and current debate on the banning of inorganic fertilizer.