Climatic Change and Environmental Effects on Rice Productive Efficiency

This study is concerned with the productive efficiency among rice crops (Aus, Aman and Boro) and identifies the impact of climatic and environmental effects on rice production using a translog stochastic production frontier model in Bangladesh. The result shows that the translog production function fits the study better than the Cobb-Douglas production and there is a comprehensible impact on input variables of rice productive efficiency. The γ -estimate associated with the variance of the technical inefficiency effect is found large and significant (90%). The mean technical efficiency of the three types of rice during the period 1980 to 2008 is found to be 78, 71 and 80%, respectively. The loss of technical efficiency from the optimum level has occurred, because of lack of proper combination of related input variables. Among the inputs rainfall and good seed are recorded to be the most significant factor in rice production. The square effect of Area is found statistically significant with a negative value at 1% level of significance. The interaction effect of Area and Seed has been statistically significant. It is also observed that the interaction effect among the inputs and environmental factors exist in rice production. The explanatory variables are found decreasing the level of inefficiency and the climatic factors played the essence rule in rice productive efficiency in Bangladesh.


INTRODUCTION
Climate is one of the major controlling factors for well-being of the residents of the world.But climate variability and change, its impacts and vulnerabilities are growing concern worldwide.Climate and agriculture are interrelated processes, both of which take place on a global scale (Fraser, 2008).The climate in Bangladesh has been changing and it is becoming more unpredictable every year (Sikder, 2010).Global warming induced changes in temperature and rainfall are already evident in many parts of the world, as well as in Bangladesh (Ahmed and Alam, 1999).The overall effect of changing climatic condition on agriculture will depend on the balance of these effects.Assessing the effects of global climate condition change on agriculture would ensure to properly anticipate the weather extremes brought by global warming and adapt farming techniques to continue the growth of agricultural production.
Rice is a major source of livelihood of rural population in most Asian countries and there are about 4 billion people who consume over 90% of the world's rice production.Rice was selected in this study because of its prominent position in the national economy of Bangladesh.There exist few literatures in estimating stochastic frontier production and consequently dealing with technical inefficiency of rice production in Bangladesh (Rahman et al., 1999;Dev and Hossain, 1995;Banik, 1994;Rahman, 2002).Khan et al. (2010) examined the influenced of farmers' age, education and experience on technical efficiency of Boro and Aman production using Cobb-Douglas production function and they found that education was positively related to technical efficiency.However, none of these studies focused on the potential influence of climatic conditions to enhancing technical efficiency of rice production.Given this back drop, the present study assesses the effects of climatic conditions (Rainfall, Humidity and Temperature) in Bangladesh on rice productive efficiency followed by stochastic frontier model (Battese and Coelli, 1995).In spite of this, the country is languishing with food deficit and each year the country has been importing over one million metric tons of rice at the expense of hard-earned foreign currency (BBS, 2009).The government of Bangladesh usually imports additional rice every year to meet the population demands.An earlier Agricultural Research Strategy document prepared by the Bangladesh Agricultural Research Council (BARC) projected the required paddy production by 2020 at 52 million tons (34.7 million tons of rice), which would require a production growth of 2.2% per year (Azad et al., 2008).The average rice yield in Bangladesh was 2.81 tones/ha in 2008-2009(BBS, 2010)), which is much lower compared to those of other Asian countries such as China, South Korea, Indonesia, Japan and Vietnam (FAPRI, 2009).The impacts of climate change on food production are global concerns and they are very important for Bangladesh (Basak et al., 2010).Rice production in Bangladesh is a major concern in recent years due to changing climatic conditions and environmental effects because there is a significant amount of rice production may hamper for climatic change and environmental effect.A number of studies have been examined the productive efficiency in its domain of agricultural production.But a few studies of the impact of climatic change and environmental effects on rice production using translog frontier production are available in the literature.For example, Tan et al. (2010) showed the impact of land fragmentation on rice producers' technical efficiency in South-East China.But no studies are found to estimate the productive efficiency with the impact of climatic change and environmental effects considering three rice crops (Boro, Aus and Aman) except Hossain et al. (2012).
However, Hamjah (2014) conducted a study to measure the efficiency regarding the climatic and hydrological effects on cereal crop productions in Bangladesh but not in the rice crops.Baten et al. (2012) conducted a study on efficiency of rice growing farmers in selected area of Mymensingh district in Bangladesh with the environmental awareness but not considering the impact of climatic change on rice production.
Only a few studies have been carried out on the efficiency of rice production in Bangladesh, even though rice production is very important for ensuring food security considering the country's vulnerability to climate change.
Have farmers concerned the impact of climatic change on rice production?How have the policies undertaken by governments impacted rice production and a farmer's technical efficiency?So, it is important to evaluate the impact of climatic change and environmental effects on rice production in Bangladesh.This study also attempts to investigate the effect of other inputs such as area, seed and variety of fertilizer in rice production.This study may assist policy makers to design and formulate policy to increase rice production in Bangladesh.How have the policies undertaken to be aware of farmers regarding the effect of climatic conditions on rice production in Bangladesh.This study partly sought to answer of the question.This study has the following specific objectives: • To measure productive efficiency of the three types of rice crops.• To determine the effect of interaction among inputs and environmental factors in rice crops production.• To investigate the influence of climatic and environmental effects on rice productive efficiency in Bangladesh.

Sources of data:
Rice production, Seed, Area, The average daily wage rate per man without food data and The Wage rate for Bullock: Bangladesh Bureau of Statistics (BBS).
Fertilizer data for rice crops (Boro, Aus and Aman): Bangladesh Agriculture Development Corporation (BADC).Meteorological data such as rainfall, temperature and humidity: Meteorological Department in Bangladesh (BMD).
The list of variables considered in this study is shown below in Table 1.
Table 2 showed the summary statistics of output, input and explanatory variables used in this study.

Likelihood ratio test for the model selection:
The Likelihood Ratio (L-R) test is an important aspect of the process that helps to determine whether the frontier where, In [L(H 0 )] = The value of the log likelihood function for the stochastic frontier estimated under null hypothesis In [L(H 1 )] = The value of the log-likelihood function for the stochastic production function under alternative hypothesis.

Hypotheses of the L-R Test:
The following hypotheses require testing with the generalized likelihood ratio test: where L(H 0 ) and L(H 1 ) are the maximum values of the log likelihood functions under the null and alternative hypothesis, respectively.The null hypothesis is rejected when λ LR > $ .The following hypotheses will be tested: H 0 : β ij = 0, the null hypothesis identifies an appropriate functional form between the restrictive Cobb-Douglas and the Translog production function.It specifies that the second-order coefficients of the Translog frontier are simultaneously zero.H 0 : γ = 0, the null hypothesis specifies that the technical inefficiency effects in firm are zero.H 0 : γ = 0 the null hypothesis means that there is no change in the technical inefficiency effects over time.

Parametric stochastic frontier model:
Model-1: In this framework, the output (rice production) is treated as a stochastic production process and the specification of Battese and Coelli (1995) model may be expressed as: where, I = The production at the ˮ-th observation for the ˩th firm; I = The (1 X k) vector of values of known functions of inputs of production in the ˩-th firm at the tth observation, β = A vector of unknown parameters for the stochastic frontier.ˢ = Assumed to be iid N (0, $ ) random errors, independently distributed of the ˡ .ˡ = Non-negative random variables which are assumed to account for technical inefficiency in production and to be independently distributed as truncations at zero of the N(µ, $ ) distribution defined as: where, I is a (1×p) vector of explanatory variables which may influence the inefficiency of rice producing in Bangladesh, the random variable ˣ follows truncated normal distribution with mean zero and variance σ2 , such that the point of truncation is −I and δ is a (p×1) vector of parameters to be estimated.Parameters of the stochastic frontier given by Eq. ( 2) and inefficiency model given by Eq. ( 3) are simultaneously estimated by using maximum likelihood estimation method.After obtaining the estimates of ˡ the technical efficiency of the ˮ-th observation inthe ˩-th rice firm is given by:

Model-2:
A stochastic frontier production model with time-varying inefficiency used in panel data can be defined as: where, Y CH = The value of the output in the i-th firm in the t-th period X CH = The input variables in the i-th firm in the tth period β " , β C , β CD = The unknown parameters to be estimated The systematic error component, v CH , is assumed to be independently and identically distributed random error having normal distribution with mean zero and variance σ $ , i.e N(0,σ $ { and u CH stands for technical inefficiency and can be predicted by the following equation: u CH is measured as the ratio of observed output to the corresponding stochastic frontier output.It takes a value between zero and 1.The technical inefficiency effect, u CH in the stochastic frontier model ( 2) can be specified as u CH = z CH δ+w CH (4) Where, the random variable w CH is defined by the truncation of the normal distribution with zero mean and variance σ $ , such that the point of truncation is -z CH δ, i.e.w CH >-z CH δ.These assumptions are consistent with u CH being a non-negative truncation with N(z CH δ, σ J $ ) distribution ( 5).The technical efficiency of production for the i-th firm at the t-th observation is defined as:

Empirical stochastic frontier model:
Model-1: The stochastic frontier production function to be estimated is: where, i = 1, 2, 3; t = 1, 2, 3……..29 I = Production in the i-th rice (Boro, Aus and Aman) with t-th period.˓˞˗ = Area in the i-th rice with t-th period ˟˗˗ = The quantity of seed of the -th rice in the i-th rice with t-th period ˘˗ˡ = The amount of Urea is used in the i-th rice with t-th period ˘˗ˠ = The amount of TSP is used in the i-th rice with t-th period " , , , , , = Unknown parameter to be estimated ˬJ = Refers to the natural logarithm i = The number of rice (Boro, Aus and Aman) t = Time period The technical inefficiency effects are assumed to be defined by: where, ˞˓˚ = Rainfall in the it-th rice with t-the period ˠ˗H = The average temperature in the i-th rice with t-th period

RESULTS AND DISCUSSION
Maximum-likelihood estimates of the stochastic frontier model with efficiency effects on rice production: In this section, Maximum Likelihood Estimates (MLE) of the parameters was reported in the context of rice productive efficiency of Bangladesh followed by stochastic frontier Model-1 and Model-2.The estimates of parameters were obtained by grid search in the first step and then these estimates were used to estimate the maximum likelihood estimates of the parameters of stochastic frontier model.The estimates of parameters in the model were presented in the Table 3.The results showed that the maximumlikelihood estimates of the coefficients of Area and Seed input were found to be positive values and significant at 1% level of significance for Model -1 and the coefficient of Fertilizer (Urea and TSP) found to be negative at 1% and 10% level of significance respectively.For Model -2, the square effect of the input variable Area was found statistically significant with a negative value at 1% level of significance.Hence, it can be said that the square effect of Area had depressing effect on the rice production of Bangladesh.
The interaction effect of Area and Seed was observed as positive and significant at 5% level of significance.
It can be concluded that the interaction effect of Area and Seed had a positive impact on the rice production in Bangladesh.The interaction effects of Area and Fertilizer (Urea), Area and Fertilizer (TSP) and Seed and Fertilizer (Urea) were recorded with negative values and it can be realized that these three interaction effects have reverse effect on rice production in Bangladesh for Model-2.The coefficient of squared Seed and Fertilizer (TSP) were also negative and moreover Fertilizer (Urea) was found to be insignificant for Model -2 which implied that the extra seed and fertilizer actually decreased the technical efficiency in rice production.Hence, concerned rice growing households need to be aware of their rice cultivation methods regarding this outcome.For Model-1 one of the climatic factors, Rainfall was observed to be a significant inefficiency variable with positive value and also WRL was significant with a negative value at 1% level of significance.On the other hand these two inefficiency variables in Model-2 were insignificant.
In the inefficiency effect model, a positive coefficient value increases the level of inefficiency and vice-versa.In Model-1, the inefficiency variables, Temperature and WRL were found negative hence they contribute in decreasing the level of inefficiency and WRL ha d a significant effect on the level of efficiency.In Model-2, though Temperature had a positive value yet it was insignificant in increasing the level of inefficiency.For both models estimation of the effect of Humidity was statistically insignificant with positive values indicating that it contributed in increasing the level of inefficiency.On the other hand, WRL had negative values on both the models, which was found to be significant for Model-1 and insignificant in case of Model-2.The other important climatic factor Rainfall, was significant with a positive value in Model-1 but it is insignificant in Model-2.This indicate that the inefficiency level of rice production is linked with rainfall.Therefore the results suggest that Rainfall, Humidity and Temperature: these climatic factors are internally linked with other inputs affecting rice production even at a technical level.The value of γ was estimated at 0.84 and 0.99 respectively (Table 3) which was positive and significant at 1% level of significance for both the models.It can be interpreted as follows: 84% and 99% of random variation for Model-1 and Model-2 respectively, that exist in rice production can be explained through inefficiency and only one 1% due to stochastic random error.It was also observed that  Model-2 explained the maximum variation of the rice production efficiency in this study.The estimate of sigma was found significant for both models that indicated that the estimated factors are perfectly fitted for these models (Table 3 and 4).

Year-wise rice productive efficiency:
This study used two models to estimate the technical efficiency of rice production.The first model, Model-1 used rice production as a stochastic production process where technical inefficiency was estimated as a functions of the parameters of the distribution.In Model 2, timevarying inefficiency is used on the same data, making it a dynamic model that showed how technical efficiency evolved over time (Desli et al., 2002).Figure 1 show that in the last 29 years the overall rice production efficiency of the three crops increased at a steady state except for the years 1984-85, 1990-91, 1994-95 and 1997-98.In these years TE dropped from the steady trend.However, it is important to notice that since 1998-99 to 2008-2009 TE maintained an average value of 0.9 for all the rice crops (Aus 0.930, Aman0.957 and Boro 0.979).In addition, Table 5 summarizes the findings of TE for Model 1 that shows that TE of Aus and Aman rice has increased significantly over the years.
Figure 2 depicts the TE of rice production that evolved over time in Model 2, where TE was separated from fixed year specific effects that were not treated as parts of TE (Desli et al., 2002).
In this Fig. 2 the TE of rice production shows more fluctuations compared to Fig. 1.Distinctively, the TE for Aus showed a volatile trend from 1980-81 (0.76) till 2000-01(0.92).However, it reached a steady growth after that period and achieved the highest TE (0.9981) among the crops in 2008-09.The summary of Fig. 2 is compiled in Table 6.Kodde and Palm (1986) By comparing the findings of the two models (Model -1 and Model-2), it was found that on average TEis higher in Model-2 compared to Model-1.In Model-1, the minimum TEs for Aus, Aman & Boro states were at 59, 57 and 65%, repectively.On the other hand minimum TEs for Aus, Aman & Boro in model 2 are 73, 74 and 82%.However, the maximum value of TE in the three crops for both models was close to 99%.Also, the average TEs for Aus, Aman & Boro for Model-1 were 79%, 82% and 86% and for Model -2 were 85%, 88% and 93% respectively.Hence, the overall mean efficiency of Model -1 was 82% and for Model-2 was 88%.It is also important to note that the variations of TE for the three different crops were more prominent in the 1980's and 1990's.The fluctuations of TE reached a steady state after the year 2000-01 at 90% level.Hence, it is difficult to interpret the changes of environmental factors on rice production as the TE reached at highest level in the 21 st century.Hence, in this study the interaction of environmental parameters within the models describes the effect of environmental factors on rice production rather than the changes in TE.

Results of tests of hypothesis and model selection:
The null hypothesis which includes the restriction that γ is zero does not have a chi-square distribution, because the restriction defines a point on the boundary of parameter space.From Table 7, the null hypothesis, H 0 : β ij = 0 is rejected and it is in favor of the Translog production function, the second null hypothesis is H 0 : γ = 0, which is rejected and so there was a technical inefficiency effect in the model.The third null hypothesis is H 0 : η = 0, which is rejected indicating that the technical inefficiency effects varied significantly.

CONCLUSION
This study attempts to identify the impact of climatic and environmental factors on rice productive efficiency for three different rice crops of Bangladesh.The Cobb-Douglas production frontier model and the Translog Stochastic Frontier Model are formulated to see the impact of climatic and environmental effects on rice production during the time period of 1980-1981 to 2008-2009.It provides the estimates of rice productive efficiency and compares the efficiencies among three types rice crop in Bangladesh.The analysis estimated that the level of technical efficiency among the three rice crops: Boro, Aus and Amanare 0.86, 0.79 and 0.82 for Model-1 and 0.93, 0.85 and 0.882 for Model-2 respectively.In addition this study estimates the average production of the three crops considering human effort, agricultural inputs and environmental factors.The highest production in Aman is explained by its highest technical efficiency on average for the last 29 years.Also, about 84% and 99% variations in output are explained by the production's technical efficiency among three different rice crops by using the Model-1 and Model-2 in that order.Area has a direct influence to increase the level of TE for both models.The study also examined the interaction effect among the inputs factors and how they impact to the total production of output.In Model -1, FEU and FET both have negative influence to decrease the level TE while in Model-2, FEU and the square of FEU are the cause of increasing TE.In Model-1 model, Seed has direct influence to increase the TE while in Model-2 it has negative impact to decrease the level of TE.
HˡH= The average humidity in the i-th rice with t-th period ˣ˞H = In the i-th rice with t-th period the average wage rate of human labour without food ˣ˞˔ = The wage rate of bullock pair in daily in the i-th rice with t-th period" , # , $ , % , & & ' =Unknown parameter to be estimated Model-2: The formulation of the stochastic frontier Translog production model is defined as: in the i-th rice firm with tth period ˓˞˗ = The Area in the i-th rice firm with t-th period ˟˗˗ = The quantity of seed in the i-th rice firm with t-th period ˘˗ˡ = The amount of Urea is used in the i-th rice firm with t-th period ˘˗ˠ = The amount of TSP is used in the i-th rice firm with t-th period ln = Refers to the natural logarithm, β i 's = Unknown parameters is to be estimated; ˰ ~ N (0, σ 2 v ) and ˯ ~ Truncations at zero of the N (µ, σ 2 u ) distribution.

Table 3 :
Maximum-likelihood estimates of stochastic frontier Model -1 and Model -2 with rice productive efficiency effects Bangladesh

Table 4 :
Year wise efficiency of rice in Bangladesh by translog stochastic

Table 7 :
Generalized likelihood-ratio tests of hypothesis : The critical values are obtained from table of *