# Total Factor Energy Productivity and Efficiency Changes of the Gher (Prawn-Carp-Rice) Farming System in Bangladesh: A Stochastic Input Distance Function Approach

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{15}BTU = 1.05 × 10

^{18}Joules [1]) of fossil fuel and renewable energy used every year [2], which is mainly due to population growth, urbanization and high level of resource consumption rates [1]. Future demand for energy is projected to double every 32 years in response to a doubling of population\every 50–60 years [2,3]. Developing economies with a high rate of population growth are increasingly using fossil fuel in agriculture to meet growing demand for food and fiber [1]. The global production of inorganic fertilizers, a vital input necessary for modern agriculture, has declined by 22%, and due to limited amount of fossil fuel, its availability is likely to decline further in the future [1].

## 2. Materials and Methods

#### 2.1. Data and the Study Area

#### 2.2. Analytical Framework

#### 2.2.1. Basic Energy Measures of Input-Output Ratios

^{−1}/Energy input MJ·ha

^{−1}

^{−1}/Energy input MJ·ha

^{−1}

^{−1}/Output t·ha

^{−1}

^{−1}− Energy Input MJ·ha

^{−1}

#### 2.2.2. The Stochastic Input Distance Function

_{I}

^{t}(x,y) is non-decreasing, positively linearly homogenous and concave in x, and increasing in y. The distance function, D

_{I}

^{t}(x,y), takes a value ≥1 if the input vector, x, is in the feasible input set, L

^{t}(y) [D

_{I}

^{t}(x,y) ≥ 1 if x $\in $ L

^{t}(y)]. D

_{I}

^{t}(x,y) = 1 if x is situated on the inner boundary of the input set. The input distance function is interpreted as the multi-input input-requirement function and provides a measure of technical efficiency because its reciprocal is the Farrell’s technical efficiency index [40,41].

_{k}, is given by:

#### 2.2.3. The Empirical Model

_{s}are inputs and Y

_{s}are outputs all presented in energy units. The six inputs used are: X

_{1}= energy from all machineries (i.e., power tiller for land preparation and shallow tube wells for irrigation), X

_{2}= energy from male labor input (family supplied + hired), X

_{3}= energy from female labor input (family supplied + hired), X

_{4}= energy from all type of feeds, X

_{5}= energy from all chemicals (fertilizers, pesticides and chemicals), and X

_{6}= energy from HYV rice seed and prawn and carp fingerlings. The three outputs are: Y

_{1}= energy produced by prawn, Y

_{2}= energy produced by carp, and Y

_{3}= energy produced by HYV rice and straw.

_{1}[45]:

_{1}= experience of the farmer (age in years); Z

_{2}= education of the farmer (years of completed schooling), Z

_{3}= household size (persons), and Z

_{4}= gher farm area (ha).

## 3. Results and Discussion

#### 3.1. Changes in Energy Performance of the gher Farming System over Time

#### 3.2. Drivers of Energy Productivity of the gher Farming System

_{0}: α

_{kl}= β

_{mn}= τ

_{km}= 0 for all k, l, m, and n) was conducted to choose between the restricted Cobb-Douglas versus flexible translog function, which was strongly rejected, thereby confirming that the latter is a better representation of the underlying production technology. Next, separability of inputs and outputs in the input distance function was tested by equating all the interaction terms between inputs and outputs to 0 (H

_{0}: all τ

_{km}= 0 for all k and m) [40], which was strongly rejected (p < 0.01) implying that aggregating all inputs and outputs into a single index is not permitted. The existence of inefficiencies in the model was tested by examining the value of the parameter γ, which is the ratio of error variances from Equation (10) and lies between 0 and 1. If γ = 0, technical inefficiency is not present, and if γ = 1, then there is no random noise. The value of γ is estimated at 0.30 (see lower panel Table 5) which is low but significant (p < 0.10), thereby confirming that inefficiencies exist in the model. Next we tested whether the inefficiency effects variables used in the model are appropriate (H

_{0}: δ

_{z}= 0 for all z) which was strongly rejected (p < 0.01), implying that the inefficiency distributions vary across observations [40]. Finally, we tested the impact of time trend on productivity (H

_{0}: all κ

_{k}= 0 for all k) which was strongly rejected (p < 0.01), implying that productivity improved significantly over time (Table 4).

_{Y}provides an overall measure of the incentive to increase operation size of multiple enterprises. The estimate of ε

_{Y}= −0.66 suggests presence of significant scale economies (Table 6). Rahman [44,50] also noted that increasing returns to scale exist for the diversified crop production system in Bangladesh but Rahman and Kazal [7] noted that constant returns to scale exists instead. Table 6 shows that output elasticities of all enterprises are significant (p < 0.01), implying that increasing production of any of these outputs will significantly increase energy use. The highest energy elasticity is for prawn output indicating that a 1% increase in prawn output will increase the use of energy by 0.32%. Rahman and Barmon [6] also noted highest prawn output elasticity of −0.22. Rice energy output elasticity is also substantially high, estimated at −0.26. This value is much higher than the output energy elasticity of cereals at −0.14 (i.e., rice, wheat and maize combined) reported by Rahman and Kazal [7].

_{kl}), provides information on the output jointness or complementarities. This information is reproduced in the mid-panel of Table 6. Results show that the prawn and rice enterprise as well as prawn and carp enterprise combinations are negative and significant (p < 0.05), implying competitive relationship in gher farming system. In contrast, Rahman and Barmon [6] noted significant output jointness/complementarity between rice and prawn enterprise in gher farming. Rahman and Kazal [7] also noted output jointness between cereal and oilseed enterprises but competitive relationship between pulse and jute as well as oilseed and jute enterprise combinations in Bangladesh.

#### 3.3. Total Factor Energy Productivity Change and Sources of Growth

## 4. Conclusions and Policy Implications

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Particulars | Unit | Energy Equivalent (MJ·unit ^{−1}) | References |
---|---|---|---|

A. Prawn and carp enterprise | |||

Inputs | |||

Prawn fingerling | kg | 4.40 | [6] |

Fish fingerling | kg | 4.52 | [38] |

Egg | kg | 6.20 | [38] |

Vermicelli | kg | 5.59 | [38] |

Fish meal | kg | 12.14 | [6] |

Meat of snail | kg | 3.37 | [6] |

Oilcake | kg | 14.40 | [6,38] |

Broken rice | kg | 15.28 | [38] |

Wheat bran | kg | 9.02 | [6,37] |

Flattened rice | kg | 14.40 | [38] |

Pulses | kg | 14.11 | [38] |

Male labor | hour | 1.96 | [37] |

Female labor | hour | 1.57 | [37] |

Outputs | |||

Prawn | kg | 4.40 | [6] |

Fish | kg | 4.61 | [38] |

B. HYV rice enterprise: | |||

Inputs | |||

Rice seed | kg | 15.28 | [38] |

Power tiller (land preparation) | litre | 62.20 | [6] |

Irrigation (diesel) | litre | 56.31 | [35] |

Pesticides | litre | 120.00 | [35] |

Nitrogen (N) | kg | 66.14 | [35] |

P_{2}O_{5} | kg | 12.44 | [35] |

K_{2}O | kg | 11.15 | [35] |

Sulphur (S) | kg | 1.12 | [35] |

Outputs | |||

Rice | kg | 15.28 | [38] |

Rice Bran | kg | 13.23 | [38] |

Straw | kg | 2.25 | [6,38] |

**Table 2.**Summary statistics of the input-output and socio-economic factors of the gher farming system.

Variables | Unit | Mean | Standard Deviation |
---|---|---|---|

Gher area | ha | 0.55 | 0.43 |

HYV rice area | ha | 0.34 | 0.28 |

Inputs | |||

Feed | MJ·ha^{−1} | 47,795.33 | 20,124.63 |

Chemicals | MJ·ha^{−1} | 6150.45 | 2562.13 |

Labor | MJ·ha^{−1} | 18,288.87 | 7085.77 |

Machine | MJ·ha^{−1} | 4460.24 | 1784.82 |

Seeds | MJ·ha^{−1} | 948.19 | 331.46 |

Total gher Input | MJ·ha^{−1} | 77,643.07 | 23,448.32 |

Total prawn-carp Input | MJ·ha^{−1} | 63,299.92 | 23,104.30 |

Total HYV rice Input | MJ·ha^{−1} | 14,343.14 | 3402.13 |

Outputs | MJ·ha^{−1} | ||

Gher output | MJ·ha^{−1} | 120,530.66 | 6832.39 |

Prawn-carp output | MJ·ha^{−1} | 6280.25 | 1300.85 |

HYV rice output | MJ·ha^{−1} | 114,250.41 | 6512.22 |

B. Socio-economic variables | |||

Farmer’s age | Years | 43.44 | 14.41 |

Farmer’s education | Completed years of schooling | 6.34 | 3.67 |

Household size | Number | 4.23 | 1.01 |

Number of observations | 1260 |

Enterprises | Unit | 2002 | 2005 | 2008 | 2011 | 2013 | 2015 | Growth Rate, 2002–2015 (%) |
---|---|---|---|---|---|---|---|---|

Prawn and fish enterprise: | ||||||||

Energy input | MJ·ha^{−1} | 64,536.19 | 64,430.67 | 68,102.57 | 62,381.54 | 61,465.86 | 58,421.40 | −0.10 |

Energy output | MJ·ha^{−1} | 6379.39 | 6500.11 | 6172.23 | 6215.33 | 6172.90 | 6239.80 | −0.20 |

Specific energy | MJ·kg^{−1} | 46.82 | 44.65 | 50.01 | 45.11 | 45.02 | 42.09 | −0.10 |

Energy use efficiency | - | 0.11 | 0.11 | 0.10 | 0.11 | 0.11 | 0.12 | −0.10 |

Energy productivity | kg·MJ^{−1} | 0.23 | 0.23 | 0.23 | 0.23 | 0.23 | 0.22 | −0.005 * |

Net energy | MJ·ha^{−1} | −58,156.80 | −57,930.56 | −61,930.33 | −56,166.22 | −55,292.96 | −52,181.60 | 1.30 *** |

HYV rice enterprise: | ||||||||

Energy input | MJ·ha^{−1} | 15,052.91 | 14,984.36 | 14,768.10 | 14,418.84 | 13,136.36 | 12,344.27 | −1.30 *** |

Energy output | MJ·ha^{−1} | 111,433.44 | 115,639.56 | 112,104.81 | 115,511.31 | 115,735.83 | 115,555.49 | 0.20 *** |

Specific energy | MJ·kg^{−1} | 2.17 | 2.07 | 2.11 | 1.99 | 1.81 | 1.71 | −1.50 *** |

Energy use efficiency | - | 7.94 | 8.13 | 8.01 | 8.34 | 9.17 | 9.78 | 1.50 *** |

Energy productivity | kg·MJ^{−1} | 0.50 | 0.51 | 0.51 | 0.52 | 0.58 | 0.61 | 1.50 *** |

Net energy | MJ·ha^{−1} | 96,380.53 | 100,655.20 | 97,336.71 | 101,092.47 | 102,599.47 | 103,211.23 | 0.40 *** |

Gher system as a whole | ||||||||

Energy input | MJ·ha^{−1} | 79,589.10 | 794,15.03 | 82,870.66 | 76,800.39 | 74,602.22 | 70,765.67 | −0.40 ** |

Energy output | MJ·ha^{−1} | 117,812.83 | 122,139.67 | 118,277.04 | 121,726.64 | 121,908.73 | 121,795.30 | 0.10 *** |

Specific energy | MJ·kg^{−1} | 9.49 | 9.10 | 9.82 | 8.84 | 8.59 | 8.16 | −0.50 *** |

Energy use efficiency | - | 1.63 | 1.69 | 1.57 | 1.69 | 1.70 | 1.84 | 0.50 *** |

Energy productivity | kg·MJ^{−1} | 0.18 | 0.19 | 0.17 | 0.19 | 0.19 | 0.20 | 0.40 ** |

Net energy | MJ·ha^{−1} | 38,223.74 | 42,724.64 | 35,406.37 | 44,926.25 | 47,306.52 | 51,029.63 | 1.30 *** |

Name of test | Parameter Restrictions | LR Test Statistic | Degrees of Freedom | χ^{2} Critical Value 1% | Outcome |
---|---|---|---|---|---|

Functional form test (Translog vs. Cobb-Douglas) | H_{0}: α_{kl} = β_{mn} = τ_{km} = 0 for all k, l, m, and n | 558.80 *** | 36 | 58.62 | Cobb-Douglas model is inadequate |

Input-output separability | H_{0}: all τ_{km} = 0 for all k and m | 160.12 *** | 18 | 34.81 | Aggregating output into a single index will provide inconsistent result |

Returns to scale (Scale economy if ε_{Y} < 1) | H_{0}: (Σβ_{m}) = 1 for all m | 478.23 *** | 1 | 6.64 | Significant scale economy exists |

Time trend and interactions | H_{0}: all κ_{k} = 0 for all k | 225.49 *** | 10 | 23.21 | Significant influence of time on productivity |

No inefficiency effects | H_{0}: δ_{z} = 0 for all z | 174.33 *** | 4 | 13.27 | Inefficiencies are jointly explained by these variables |

**Table 5.**Parameter estimates of the stochastic input distance function including inefficiency effects.

Variables | Parameters | Coefficients | t-Ratio |
---|---|---|---|

Production Variables | |||

Constant | α_{0} | −8.5485 | −0.77 |

ln (Female labor energy/Machine energy) | α_{2} | 0.0204 *** | 3.56 |

ln (Male labor energy/Machine energy) | α_{3} | 0.3091 *** | 18.80 |

ln (Feed energy/Machine energy) | α_{4} | 0.1059 *** | 9.95 |

ln (Chemical energy/Machine energy) | α_{5} | 0.1555 *** | 14.53 |

ln (Seed energy/Machine energy) | α_{6} | 0.1779 *** | 13.35 |

½ ln (Female labor energy/Machine energy)^{2} | α_{22} | 0.0088 *** | 2.93 |

½ ln (Male labor energy/Machine energy)^{2} | α_{33} | −0.1408 ** | −2.34 |

½ ln (Feeed energy/Machine energy)^{2} | α_{44} | −0.1087 *** | −3.95 |

½ ln (Chemical energy/Machine energy)^{2} | α_{55} | 0.0003 | 0.01 |

½ ln (Seed energy/Machine energy)^{2} | α_{66} | 0.1621 *** | 3.26 |

ln (Female labor energy/Machine energy) × ln (Male labor energy/Machine energy) | α_{23} | −0.0133 | −0.40 |

ln (Female labor energy/Machine energy) × ln (Feed energy/Machine energy) | α_{24} | −0.0866 *** | −3.19 |

ln (Female labor energy/Machine energy) × ln (Chemical energy/Machine energy) | α_{25} | 0.1009 *** | 5.22 |

ln (Female labor energy/Machine energy) × ln (Seed energy/Machine energy) | α_{26} | −0.0608 * | −1.92 |

ln (Male labor energy/Machine energy) × ln (Feed energy/Machine energy) | α_{34} | 0.4066 *** | 6.22 |

ln (Male labor energy/Machine energy) × ln (Chemical energy/Machine energy) | α_{35} | −0.0113 | −0.22 |

ln (Male labor energy/Machine energy) × ln (Seed energy/Machine energy) | α_{36} | 0.0416 | 0.77 |

ln (Feed energy/Machine energy) × ln (Chemical energy/Machine energy) | α_{45} | 0.2565 *** | 3.77 |

ln (Feed energy/Machine energy) × ln (Chemical energy/Machine energy) | α_{46} | −0.2291 *** | −2.76 |

ln (Chemical energy/Machine energy) × ln (Seed energy/Machine energy) | α_{56} | −0.1597 *** | −2.54 |

ln (Rice energy) | β_{1} | −0.2641 *** | −3.56 |

ln (Prawn energy) | β_{2} | −0.3159 *** | −11.78 |

ln (Carp energy) | β_{3} | −0.0756 *** | −10.12 |

½ ln (Rice energy)^{2} | β_{11} | −5.2921 *** | −3.61 |

½ ln (Prawn energy)^{2} | β_{22} | −0.0665 | −0.78 |

½ ln (Carp energy)^{2} | β_{33} | 0.0305 | 1.71 |

ln (Rice energy) × ln (Prawn energy) | β_{12} | −2.0371 ** | −2.27 |

ln (Rice energy) × ln (Carp energy) | β_{13} | −0.0860 | −0.35 |

ln (Prawn energy) × ln (Carp energy) | β_{23} | −0.2505 *** | −2.83 |

ln (Female labor energy/Machine energy) × ln (Rice energy) | τ_{21} | −0.0962 | −1.11 |

ln (Female labor energy/Machine energy) × ln (Prawn energy) | τ_{22} | 0.1685 *** | 4.54 |

ln (Female labor energy/Machine energy) × ln (Carp energy) | τ_{23} | −0.0419 *** | −4.47 |

ln (Male labor energy/Machine energy) × ln (Rice energy) | τ_{31} | 0.8651 *** | 3.64 |

ln (Male labor energy/Machine energy) × ln (Prawn energy) | τ_{32} | 0.1224 | 1.35 |

ln (Male labor energy/Machine energy) × ln (Carp energy) | τ_{33} | −0.1289 *** | −5.20 |

ln (Feed energy/Machine energy) × ln (Rice energy) | τ_{41} | 0.0968 | 0.60 |

ln (Feed energy/Machine energy) × ln (Prawn energy) | τ_{42} | −0.1296 ** | −1.99 |

ln (Feed energy/Machine energy) × ln (Carp energy) | τ_{43} | 0.0200 | 1.12 |

ln (Chemical energy/Machine energy) × ln (Rice energy) | τ_{51} | 0.1157 | 0.63 |

ln (Chemical energy/Machine energy) × ln (Prawn energy) | τ_{52} | −0.0920 | −1.27 |

ln (Chemical energy/Machine energy) × ln (Carp energy) | τ_{53} | 0.0541 *** | 2.90 |

ln (Seed energy/Machine energy) × ln (Rice energy) | τ_{61} | −0.9501 *** | −4.18 |

ln (Seed energy/Machine energy) × ln (Prawn energy) | τ_{62} | −0.2477 *** | −2.87 |

ln (Seed energy/Machine energy) × ln (Carp energy) | τ_{63} | 0.0930 *** | 4.03 |

Time trend and interactions | |||

Time | κ_{1} | 0.0138 *** | 12.09 |

½ (Time)^{2} | κ_{11} | 0.0021 *** | 3.71 |

Time × ln (Female labor energy/Machine energy) | κ_{12} | −0.0026 ** | −2.22 |

Time × ln (Male labor energy/Machine energy) | κ_{13} | −0.0228 *** | −6.28 |

Time × ln (Feed energy/Machine energy) | κ_{14} | 0.0015 | 0.58 |

Time × ln (Chemical energy/Machine energy) | κ_{15} | −0.0001 | −0.05 |

Time × ln (Seed energy/Machine energy) | κ_{16} | 0.0167 *** | 4.65 |

Time × ln (Rice energy) | κ_{17} | −0.0514 *** | −2.68 |

Time × ln (Prawn energy) | κ_{18} | 0.0050 | 0.76 |

Time × ln (Carp energy) | κ_{19} | 0.0074 *** | 4.09 |

Model diagnostics | |||

Gamma | γ | 0.3007 * | 1.78 |

Sigma-squared | σ_{s}^{2} | 0.0151 *** | 25.08 |

Log likelihood | 855.6781 | ||

χ^{2}_{(54,0.99)} | 19,016.51 *** | ||

Inefficiency effects function | |||

Constant | δ_{0} | 0.2053 | 0.02 |

Experience | δ_{1} | −0.0018 *** | −5.92 |

Education | δ_{2} | −0.0061 *** | −5.32 |

Household size | δ_{3} | 0.0131 *** | 3.27 |

Gher area | δ_{4} | 0.1697 *** | 11.55 |

Number of total observations | N | 1260 |

Variables | Symbol | Value | t-Ratio |
---|---|---|---|

Output energy elasticities | |||

Scale economy | ε_{Y} | −0.6556 *** | -- |

Rice energy | ε_{Y1} | −0.2641 *** | −3.56 |

Prawn energy | ε_{Y2} | −0.3159 *** | −11.78 |

Carp energy | ε_{Y3} | −0.0756 *** | −10.12 |

Input energy elasticities | |||

Female labor energy | ε_{X2} | 0.0204 *** | 3.56 |

Male labor energy | ε_{X3} | 0.3091 *** | 18.80 |

Feed energy | ε_{X4} | 0.1059 *** | 9.95 |

Chemical energy | ε_{X5} | 0.1555 *** | 14.53 |

Seed energy | ε_{X6} | 0.1779 *** | 13.35 |

Machine energy | ε_{X1} | 0.2312 | -- |

Output jointness or complementarity | |||

Rice energy × Prawn energy | ε_{Y12} | −2.0371 ** | −2.27 |

Rice energy × Carp energy | ε_{Y13} | −0.0860 | −0.35 |

Prawn energy × Carp energy | ε_{Y23} | −0.2505 *** | −2.83 |

**Table 7.**Total factor energy productivity and its components of the gher farming system, (2002–2015).

Year | Energy Efficiency Scores (MTE) | Technical Change (TC) | Energy Efficiency Change (EEC) | Total Factor Energy Productivity (TFEP) |
---|---|---|---|---|

2002 | 0.7797 | 1.0000 | 1.0000 | 1.0000 |

2003 | 0.7803 | 1.3051 | 1.0007 | 1.3061 |

2004 | 0.7803 | 1.3134 | 1.0024 | 1.3165 |

2005 | 0.7841 | 1.3149 | 1.0024 | 1.3180 |

2006 | 0.7896 | 1.3261 | 1.0070 | 1.3354 |

2007 | 0.7897 | 1.3405 | 1.0001 | 1.3407 |

2008 | 0.7888 | 1.3481 | 0.9988 | 1.3466 |

2009 | 0.7900 | 1.3468 | 1.0016 | 1.3489 |

2010 | 0.7923 | 1.3483 | 1.0029 | 1.3522 |

2011 | 0.7948 | 1.3520 | 1.0032 | 1.3563 |

2012 | 0.7952 | 1.3514 | 1.0005 | 1.3520 |

2013 | 0.7950 | 1.3459 | 0.9998 | 1.3456 |

2014 | 0.8000 | 1.3301 | 1.0063 | 1.3384 |

2015 | 0.7992 | 1.3431 | 0.9989 | 1.3417 |

Geometric mean | 0.7899 | 1.3084 | 1.0018 | 1.3107 |

Growth rate (%) | 0.1905 | 2.5700 | −0.0075 | 2.5620 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rahman, S.; Barmon, B.K.
Total Factor Energy Productivity and Efficiency Changes of the *Gher* (Prawn-Carp-Rice) Farming System in Bangladesh: A Stochastic Input Distance Function Approach. *Energies* **2018**, *11*, 3482.
https://doi.org/10.3390/en11123482

**AMA Style**

Rahman S, Barmon BK.
Total Factor Energy Productivity and Efficiency Changes of the *Gher* (Prawn-Carp-Rice) Farming System in Bangladesh: A Stochastic Input Distance Function Approach. *Energies*. 2018; 11(12):3482.
https://doi.org/10.3390/en11123482

**Chicago/Turabian Style**

Rahman, Sanzidur, and Basanta Kumar Barmon.
2018. "Total Factor Energy Productivity and Efficiency Changes of the *Gher* (Prawn-Carp-Rice) Farming System in Bangladesh: A Stochastic Input Distance Function Approach" *Energies* 11, no. 12: 3482.
https://doi.org/10.3390/en11123482