# Drivers of Productivity Change in the Italian Tomato Food Value Chain

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{th}output (y); ${S}_{j}=\frac{{w}_{j}{x}_{j}}{{{\displaystyle \sum}}_{j=1}^{J}{w}_{j}{x}_{j}}$ denotes input cost share of j

^{th}input (x); p denotes an output price and w denotes an input price.

**x**can be scaled down in order to produce a given output vector

**y**with the technology existing at a particular time t (L(y) represents the input requirement set) [46].

**x**,

**y**) belonging to the technology set, the input distance function takes a value no smaller than unity. A value of unity indicates that the input–output combination (

**x**,

**y**) belongs to the input isoquant, which represents the minimum input quantities that are necessary to produce a given output vector

**y**. In other words, the IDF provides a measure of technical efficiency [46]: $TE\left(y,x,t\right)=\mathrm{min}\left\{\theta :{D}^{I}\left(y,x,t\right)\ge 1\right\}$, where $\theta =\frac{1}{\rho}$, which is in an input-conserving orientation defined as the maximum equi-proportionate reduction in all inputs that is feasible with a given technology and outputs [47].

^{th}input as the cost share of this j-input and the derivate of the IDF with respect to m

^{th}output as the negative of the cost elasticity of m-output that informs of the importance of m

^{th}output in terms of cost. Further properties of the IDF are symmetry, monotonicity, linear homogeneity and concavity in inputs and quasi-concavity in outputs [49].

**α**,

**β, γ**and

**δ**are vectors of the parameters to be estimated; subscript i with i = 1, 2, …, I refers to a certain producer/processor and t, with t = 1, …, T refers to a certain time (year) and can capture the joint effects of embedded knowledge, technology improvements and learning-by-doing in input quality improvements [51]. Here, parameters δ

_{t}and δ

_{tt}capture the global effect of technological change on the IDF, while δ

_{mt}and δ

_{jt}measure the bias of technological change.

_{1}[52]:

_{it}. In line with the latest approach to technical efficiency investigation, the error term is composited from time-invariant (persistent) technical inefficiency (η

_{i}); time-varying (transient) technical inefficiency (u

_{it}), for which ${\eta}_{i}+{u}_{it}=\mathrm{ln}{D}_{it}^{I}$, holds, and from latent heterogeneity (μ

_{i}) and statistical error term (v

_{it}) [41]:

_{it}), which could render some lags invalid as instruments. In step 2, residuals were used from the system GMM level equation to estimate a random effects panel model employing the generalized least squares (GLS) estimator with the aim of obtaining theoretical values of ${\alpha}_{i}={\mu}_{i}-\left({\eta}_{i}-E\left({\eta}_{i}\right)\right)$ and ${\epsilon}_{it}={v}_{it}-\left({u}_{it}-E\left({u}_{it}\right)\right)$, denoted by ${\widehat{\alpha}}_{i}$ and ${\widehat{\epsilon}}_{it}$$.$ In step 3, the transient technical inefficiency, u

_{it}, was estimated using ${\widehat{\epsilon}}_{it}$ and the standard stochastic frontier technique with the following assumptions:${v}_{it}~N(0,{\sigma}_{v}^{2}),{u}_{it}~{N}^{+}(0,{\sigma}_{u}^{2}).$ In step 4, the persistent technical inefficiency, η

_{i}, was estimated using ${\widehat{\alpha}}_{i}$ and the stochastic frontier model with the following assumptions: ${\eta}_{i}~{N}^{+}(0,{\sigma}_{\eta}^{2}),{\mu}_{i}~N(0,{\sigma}_{\mu}^{2})$. The overall technical efficiency (OTE) is quantified based on Kumbhakar et al. [53] as: $OT{E}_{it}=\mathrm{exp}(-{\widehat{\eta}}_{i})\times \mathrm{exp}(-{\widehat{u}}_{it}).$ All of these estimates were done using SW STATA 14.0.

## 3. Results

#### 3.1. Technology and Production Structure

#### 3.2. Distribution of Scale Efficiency and Efficiency of Input Use

#### 3.3. Productivity Dynamics

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Variable | Parameter | Std. Err. | p-Value |
---|---|---|---|

ln_yC | −0.317 | 0.050 | 0.000 |

ln_yAOC | −0.462 | 0.054 | 0.000 |

ln_xL | 0.162 | 0.072 | 0.028 |

ln_xW | 0.283 | 0.039 | 0.000 |

ln_xK | 0.146 | 0.052 | 0.006 |

ln_yC_2 | 0.276 | 0.235 | 0.243 |

ln_yAOC_2 | 0.054 | 0.272 | 0.844 |

ln_yCyAOC | −0.150 | 0.231 | 0.519 |

ln_xL_2 | 0.045 | 0.115 | 0.697 |

ln_xW_2 | 0.062 | 0.075 | 0.408 |

ln_xK_2 | 0.036 | 0.083 | 0.661 |

ln_xLxW | −0.029 | 0.115 | 0.800 |

ln_xLxK | 0.004 | 0.101 | 0.965 |

ln_xWxK | 0.110 | 0.068 | 0.107 |

t | 0.014 | 0.008 | 0.092 |

t_2 | −0.006 | 0.003 | 0.057 |

ln_yCt | 0.025 | 0.012 | 0.042 |

ln_yAOCt | −0.022 | 0.014 | 0.123 |

ln_xLt | 0.000 | 0.013 | 0.993 |

ln_xWt | 0.004 | 0.010 | 0.661 |

ln_xKt | −0.008 | 0.010 | 0.411 |

ln_yCxL | 0.180 | 0.134 | 0.182 |

ln_yAOCxL | −0.103 | 0.166 | 0.534 |

ln_yCxW | −0.073 | 0.105 | 0.490 |

ln_yAOCxW | 0.047 | 0.120 | 0.698 |

ln_yCxK | −0.043 | 0.078 | 0.582 |

ln_yAOCxK | 0.156 | 0.094 | 0.100 |

Constant | −0.132 | 0.057 | 0.021 |

Test statistic | p-value | ||

AR(2) | −1.770 | 0.076 | |

Hansen test | 95.33 (347) | 1.000 |

Variable | Parameter | Std. Err. | p-Value |
---|---|---|---|

ln_y | −0.993 | 0.011 | 0.000 |

ln_xW | 0.194 | 0.027 | 0.000 |

ln_xM | 0.768 | 0.029 | 0.000 |

t | 0.006 | 0.006 | 0.282 |

ln_y_2 | −0.001 | 0.007 | 0.942 |

ln_xW_2 | 0.087 | 0.035 | 0.015 |

ln_xM_2 | 0.156 | 0.068 | 0.023 |

ln_xWxM | −0.123 | 0.045 | 0.008 |

t_2 | −0.001 | 0.003 | 0.762 |

ln_yt | 0.006 | 0.003 | 0.028 |

ln_xWt | 0.003 | 0.006 | 0.669 |

ln_xMt | −0.001 | 0.008 | 0.867 |

ln_yxW | 0.000 | 0.016 | 0.993 |

ln_yxM | −0.040 | 0.018 | 0.027 |

Constant | −0.031 | 0.025 | 0.225 |

Test statistic | p-value | ||

AR(2) | −1.200 | 0.228 | |

Hansen test | 79.58 (332) | 1.000 |

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**Figure 2.**Distribution of technological change; (

**a**) tomato producers and (

**b**) tomato processors. Source: authors’ calculations.

**Figure 4.**Distribution of returns to scale; (

**a**) tomato producers and (

**b**) tomato processors. Source: authors’ calculations.

**Figure 6.**Distribution of transient technical efficiency; (

**a**) tomato producers and (

**b**) tomato processors. Source: authors’ calculations.

**Figure 7.**Distribution of persistent technical efficiency; (

**a**) tomato producers and (

**b**) tomato processors. Source: authors’ calculations.

Tomato Producers | ||||

Data | Small | Medium | Large | Total |

I | 45 | 54 | 50 | 149 |

NO | 223 | 226 | 231 | 680 |

Tomato processors | ||||

Data | Small and medium | Large processors | Total | |

I | 47 | 46 | 93 | |

NO | 366 | 380 | 746 |

Producers | Processors | ||
---|---|---|---|

Output | Output | ||

Tomatoes | 0.317 (0.407) | Processed tomatoes | 0.993 |

Other output | 0.462 (0.593) | ||

Input | Input | ||

Land | 0.162 | ||

Labor | 0.283 | Labor | 0.194 |

Capital | 0.146 | Capital | 0.038 |

Materials | 0.409 | Materials | 0.768 |

Economies of scale | 1.284 | Economies of scale | 1.007 |

Level | Min. | First Q | Median | Mean | Third Q | Max. | Std. D. |
---|---|---|---|---|---|---|---|

Tomato producers | −0.090 | −0.029 | −0.014 | −0.014 | 0.001 | 0.063 | 0.022 |

Tomato processors | −0.041 | −0.012 | −0.006 | −0.006 | −0.001 | 0.024 | 0.010 |

Level | Min. | First Q | Median | Mean | Third Q | Max. | Std. D. | t-Test (H0: RTS=1) |
---|---|---|---|---|---|---|---|---|

Tomato producers | 0.814 | 1.099 | 1.281 | 1.387 | 1.591 | 2.611 | 0.389 | 25.929 (Pr(|T| > |t|) = 0.0000) |

Tomato processors | 0.866 | 0.978 | 1.011 | 1.009 | 1.040 | 1.170 | 0.045 | 5.656 (Pr(|T| > |t|) = 0.0000) |

Tomato Producers | |||||||

Min. | First Q | Median | Mean | Third Q | Max. | Std. D. | |

Overall | 0.644 | 0.790 | 0.817 | 0.812 | 0.839 | 0.903 | 0.040 |

Transient | 0.700 | 0.896 | 0.913 | 0.909 | 0.926 | 0.965 | 0.028 |

Persistent | 0.750 | 0.876 | 0.899 | 0.893 | 0.915 | 0.951 | 0.032 |

Tomato Processors | |||||||

Min. | First Q | Median | Mean | Third Q | Max. | Std. D. | |

Overall | 0.600 | 0.716 | 0.782 | 0.776 | 0.837 | 0.962 | 0.081 |

Transient | 0.605 | 0.723 | 0.789 | 0.785 | 0.845 | 0.975 | 0.081 |

Persistent | 0.954 | 0.986 | 0.990 | 0.988 | 0.992 | 0.997 | 0.006 |

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## Share and Cite

**MDPI and ACS Style**

Čechura, L.; Žáková Kroupová, Z.; Samoggia, A.
Drivers of Productivity Change in the Italian Tomato Food Value Chain. *Agriculture* **2021**, *11*, 996.
https://doi.org/10.3390/agriculture11100996

**AMA Style**

Čechura L, Žáková Kroupová Z, Samoggia A.
Drivers of Productivity Change in the Italian Tomato Food Value Chain. *Agriculture*. 2021; 11(10):996.
https://doi.org/10.3390/agriculture11100996

**Chicago/Turabian Style**

Čechura, Lukáš, Zdeňka Žáková Kroupová, and Antonella Samoggia.
2021. "Drivers of Productivity Change in the Italian Tomato Food Value Chain" *Agriculture* 11, no. 10: 996.
https://doi.org/10.3390/agriculture11100996