# Technical Efficiency in the European Dairy Industry: Can We Observe Systematic Failures in the Efficiency of Input Use?

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

## 3. Materials and Methods

#### 3.1. Methodology Used in the Study

#### 3.1.1. Input Distance Function

**w**denotes a vector of input prices. The minimisation problem provides the relation between the derivatives of the IDF and the cost function [43]. In particular, the derivative with respect to the jth input gives:

_{j,t}is a cost-share of the particular input.

_{jk}= β

_{kj.}The time trend included in the IDF allows for capturing the joint effects of embedded knowledge, technology improvements and learning-by-doing in input quality improvements [45]. Here, δ

_{t}and δ

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

_{mt}and δ

_{jt}measure the bias of technical change.

_{it}) and latent heterogeneity (μ

_{i}), and replacing $\mathrm{ln}{D}_{it}^{I}$ with inefficiency terms, persistent technical inefficiency (η

_{i}) and transient technical inefficiency (u

_{it}), that is ${\eta}_{i}+{u}_{it}=\mathrm{ln}{D}_{it}^{I}$, the IDF takes the form of a generalized true random effects model (GTRE, [33]):

#### 3.1.2. Heterogeneity in Technology

_{i}in (10). To capture the inter-sector heterogeneity, first-order parameters in (10) are expanded based on dummy variables for four major sectors in the food processing industry (namely the manufacture of dairy products, processing of meat, milling, and manufacture of bakery and farinaceous products):

#### 3.1.3. Estimation Strategy

_{i}are independent of explanatory variables. The violation of this assumption can originate from the heterogeneity bias as a kind of omitted variable bias, which is a typical problem of hierarchical data. To deal with this heterogeneity bias, the study applies Mundlak’s [49] formulation and adds group-means for each time-varying explanatory variable in the first-order level.

_{i}and ε

_{it}have zero mean and constant variance. The multistep procedure consists of three steps. In step 1, standard random effect panel regression is used to estimate β, γ, δ, α

_{m}, and theoretical values of α

_{i}and ε

_{it}, denoted by ${\widehat{\alpha}}_{i}$ and ${\widehat{\epsilon}}_{it}$. In step 2, the transient technical inefficiency, u

_{it}, is estimated using ${\widehat{\epsilon}}_{it}$ and the standard stochastic frontier technique with assumptions: ${v}_{it}\sim N(0,{\sigma}_{v}^{2}),{u}_{it}\sim {N}^{+}(0,{\sigma}_{u}^{2}).$ In step 3, the persistent technical inefficiency, η

_{i}, is estimated using and the stochastic frontier model with the following assumptions: ${\eta}_{i}\sim {N}^{+}(0,{\sigma}_{\eta}^{2}),{\mu}_{i}\sim N(0,{\sigma}_{\mu}^{2}).$ These steps are done in the SW STATA 14.0.

_{it}) that could render some lags invalid as instruments. In step 2, residuals are used from the system GMM level equations to estimate a random effects panel model employing the generalized least squares (GLS) estimator. The transient and persistent technical inefficiency is estimated in steps 3 and 4 based on the same procedure as described above. These estimates are also done in the SW STATA 14.0.

#### 3.2. Data Used in the Study

## 4. Results

_{m}≤ 0) and positive for the inputs (β

_{j}≥ 0 for j = L,K) and β

_{L}+ β

_{M}< 1, where L stands for labour and M represents material [60]. Concavity in inputs requires that the Hessian matrix of second-order derivatives of the IDF of the function with respect to the inputs is negatively semidefinite, according to Diewert and Wales [61]. This is fulfilled on the sample mean, if β

_{jj}+ β

^{2}

_{j}–β

_{j}≤ 0 j = L,M. Table 3 proves that these conditions hold for all model specifications, evaluated on the sample mean.

_{t}) has a low negative value representing the cost decrease with a decelerating rate (δ

_{tt}> 0) over the analysed period. However, the second-order time parameter (δ

_{tt}) is statistically significant only at the 10% significance level in the GMM model. The parameters of biased technical change are not statistically significant even at the 10% significance level. The rest of the second-order parameters have a similar pattern as well.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Kernel density comparison (overall technical efficiency). Source: authors’ own calculation.

**Figure 3.**Country-specific overall technical efficiency (GMM). Source: authors’ own calculation. Note: AT denotes Austria, BE denotes Belgium, CZ denotes Czechia, DE denotes Germany, ES denotes Spain, FI denotes Finland, FR denotes France, IT denotes Italy, SW denotes Sweden, UK denotes the United Kingdom.

**Figure 4.**Country-specific transient technical efficiency development (GMM). Source: authors’ own calculation. Note: AT denotes Austria, BE denotes Belgium, CZ denotes Czechia, DE denotes Germany, ES denotes Spain, FI denotes Finland, FR denotes France, IT denotes Italy, SW denotes Sweden, UK denotes the United Kingdom.

**Figure 5.**Meta-frontier technical efficiency comparison (GMM). Source: authors’ own calculation. Note: AT denotes Austria, BE denotes Belgium, CZ denotes Czechia, DE denotes Germany, ES denotes Spain, FI denotes Finland, FR denotes France, IT denotes Italy, SW denotes Sweden, UK denotes the United Kingdom.

**Figure 6.**Meta-frontier persistent technical efficiency comparison (GMM). Source: authors’ own calculation. Note: Reference line represents the sample average transient technical efficiency score; AT denotes Austria, BE denotes Belgium, CZ denotes Czechia, DE denotes Germany, ES denotes Spain, FI denotes Finland, FR denotes France, IT denotes Italy, SW denotes Sweden, UK denotes the United Kingdom.

**Table 1.**Recent studies of technical efficiency of European dairy processing industry. Source: authors.

Study | Countries | Years | Method |
---|---|---|---|

Čechura and Hockmann [8] | CZ | 2003–2012 | Stochastic frontier analysis (SFA) |

Čechura et al. [6] | AT, BE, BG, CZ, DE, DK, EE, ES, FI, FR, UK, GR, HU, IR, IT, LT, LV, NL, PL, PT, RO, SW, SL, SI, SR | 2003–2012 | SFA |

Kapelko and Oude Lansink [21] | AT, BE, FI, FR, DE, LU, NL, NO, CH, BIH, BG, HR, CZ, EE, HU, PL, RO, SR, SL, SI, IT, PT, ES | 2005–2012 | Data envelopment analysis (DEA) |

Kapelko and Oude Lankink [22] | ES | 2001–2009 | DEA |

Rezitis and Kalandzi [10] | GR | 1984–2007 | DEA |

Rudinskaya [9] | CZ | 2005–2012 | SFA |

Soboh et al. [14] | BE, DK, FR, DE, IR, NL | 1995–2005 | SFA |

Špička [11] | CZ, PL, SK | 2008–2013 | DEA |

Country | AT | BE | CZ | DE | ES | FI | FR | IT | SW | UK | Total |
---|---|---|---|---|---|---|---|---|---|---|---|

I | 15 | 40 | 58 | 80 | 114 | 36 | 211 | 97 | 22 | 62 | 735 |

N | 131 | 336 | 498 | 658 | 1108 | 285 | 1940 | 915 | 150 | 496 | 6517 |

RS1 | 48 | 40 | 43 | 32 | 41 | 84 | 33 | 58 | 54 | 60 | 48 |

RS2 | 44 | 74 | 79 | 59 | 82 | 97 | 48 | 95 | 70 | 90 | 63 |

10.5 | GTRE | GTRE with Mundlak | GMM | ||||||
---|---|---|---|---|---|---|---|---|---|

Variable | Coef. | St.Er. | P > |z| | Coef. | St.Er. | P > |z| | Coef. | St.Er. | P > |t| |

ln_y | −0.9601 | 0.0064 | 0.0000 | −0.8886 | 0.0207 | 0.0000 | −0.9801 | 0.0039 | 0.0000 |

ln_xL | 0.2976 | 0.0161 | 0.0000 | 0.3039 | 0.0230 | 0.0000 | 0.2620 | 0.0088 | 0.0000 |

ln_xM | 0.6483 | 0.0146 | 0.0000 | 0.6375 | 0.0222 | 0.0000 | 0.6864 | 0.0084 | 0.0000 |

t | −0.0074 | 0.0008 | 0.0000 | −0.0090 | 0.0009 | 0.0000 | −0.0069 | 0.0010 | 0.0000 |

ln_y_2 | −0.0032 | 0.0057 | 0.5740 | −0.0007 | 0.0053 | 0.8890 | 0.0045 | 0.0052 | 0.3920 |

ln_xL_2 | 0.0538 | 0.0072 | 0.0000 | 0.0582 | 0.0077 | 0.0000 | 0.0656 | 0.0127 | 0.0000 |

ln_xM_2 | 0.1322 | 0.0098 | 0.0000 | 0.1326 | 0.0090 | 0.0000 | 0.1472 | 0.0080 | 0.0000 |

ln_xLxM | −0.0847 | 0.0079 | 0.0000 | −0.0863 | 0.0077 | 0.0000 | −0.0949 | 0.0103 | 0.0000 |

t_2 | 0.0005 | 0.0004 | 0.1400 | 0.0000 | 0.0003 | 0.9240 | 0.0009 | 0.0005 | 0.0780 |

ln_yt | 0.0005 | 0.0005 | 0.2800 | 0.0008 | 0.0005 | 0.0950 | 0.0004 | 0.0010 | 0.6780 |

ln_xLt | −0.0001 | 0.0011 | 0.9380 | 0.0003 | 0.0011 | 0.7700 | −0.0014 | 0.0030 | 0.6390 |

ln_xMt | −0.0001 | 0.0012 | 0.9650 | −0.0004 | 0.0012 | 0.7760 | 0.0033 | 0.0026 | 0.1920 |

ln_yxL | −0.0055 | 0.0073 | 0.4570 | −0.0016 | 0.0069 | 0.8200 | 0.0008 | 0.0079 | 0.9180 |

ln_yxM | −0.0080 | 0.0059 | 0.1760 | −0.0101 | 0.0057 | 0.0750 | −0.0246 | 0.0069 | 0.0000 |

_cons | −0.0714 | 0.0136 | 0.0000 | −0.0772 | 0.0135 | 0.0000 | −0.0915 | 0.0095 | 0.0000 |

ln_y_gmean | −0.0867 | 0.0200 | 0.0000 | ||||||

ln_xL_gmean | −0.0049 | 0.0201 | 0.8080 | ||||||

ln_xM_gmean | −0.0013 | 0.0232 | 0.9550 | ||||||

t_gmean | 0.0007 | 0.0066 | 0.9110 | ||||||

Mean | Std.D. | Mean | Std.D. | Mean | Std.D. | ||||

Overall TE | 0.9553 | 0.0139 | 0.9624 | 0.0099 | 0.9200 | 0.0179 | |||

Transient TE | 0.9561 | 0.0139 | 0.9629 | 0.0099 | 0.9500 | 0.0177 | |||

Persistent TE | 0.9992 | 0.0000 | 0.9994 | 0.0000 | 0.9684 | 0.0044 |

**Table 4.**Country-specific overall technical efficiency and its decomposition (GMM). Source: authors’ own calculation.

Country | Overall Technical Efficiency | Transient Technical Efficiency | Persistent Technical Efficiency | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Std.Dev. | Min. | Max. | Mean | Std.Dev. | Min. | Max. | Mean | Std.Dev. | Min. | Max. | |

Austria | 0.7548 | 0.0541 | 0.5414 | 0.8577 | 0.8319 | 0.0438 | 0.6454 | 0.9153 | 0.9066 | 0.0300 | 0.8234 | 0.9371 |

Belgium | 0.9297 | 0.0158 | 0.794 | 0.9684 | 0.9309 | 0.0159 | 0.7949 | 0.9695 | 0.9988 | 0.0000 | 0.9988 | 0.9988 |

Czechia | 0.9121 | 0.0185 | 0.723 | 0.9686 | 0.9123 | 0.0185 | 0.7232 | 0.9688 | 0.9997 | 0.0000 | 0.9997 | 0.9997 |

Finland | 0.9028 | 0.0219 | 0.784 | 0.9635 | 0.903 | 0.0219 | 0.7842 | 0.9637 | 0.9997 | 0.0000 | 0.9997 | 0.9997 |

France | 0.9320 | 0.0243 | 0.3968 | 0.9947 | 0.9328 | 0.0243 | 0.3971 | 0.9954 | 0.9992 | 0.0000 | 0.9992 | 0.9992 |

Germany | 0.9303 | 0.0271 | 0.4859 | 0.9846 | 0.9307 | 0.0271 | 0.4862 | 0.9851 | 0.9995 | 0.0000 | 0.9995 | 0.9995 |

Italy | 0.8393 | 0.0345 | 0.5913 | 0.9398 | 0.9227 | 0.0279 | 0.6312 | 0.9783 | 0.9095 | 0.0240 | 0.8168 | 0.9620 |

Spain | 0.9267 | 0.0249 | 0.6573 | 0.9806 | 0.9269 | 0.0249 | 0.6574 | 0.9808 | 0.9998 | 0.0000 | 0.9998 | 0.9998 |

Sweden | 0.9466 | 0.0192 | 0.8194 | 0.9892 | 0.9483 | 0.0192 | 0.8209 | 0.991 | 0.9982 | 0.0000 | 0.9981 | 0.9982 |

United Kingdom | 0.9427 | 0.0266 | 0.7332 | 0.9847 | 0.9434 | 0.0266 | 0.7337 | 0.9854 | 0.9993 | 0.0000 | 0.9993 | 0.9993 |

**Table 5.**Meta-frontier overall technical efficiency and its decomposition (GMM). Source: authors’ own calculation.

Country | Overall Technical Efficiency | Transient Technical Efficiency | Persistent Technical Efficiency | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Std.Dev. | Min. | Max. | Mean | Std.Dev. | Min. | Max. | Mean | Std.Dev. | Min. | Max. | |

Austria | 0.9202 | 0.0092 | 0.8608 | 0.9392 | 0.9511 | 0.0093 | 0.8888 | 0.9682 | 0.9675 | 0.0017 | 0.9631 | 0.9701 |

Belgium | 0.9181 | 0.0200 | 0.7490 | 0.9537 | 0.9495 | 0.0155 | 0.8379 | 0.9873 | 0.9669 | 0.0101 | 0.8696 | 0.9750 |

Czechia | 0.9191 | 0.0217 | 0.6862 | 0.9639 | 0.9492 | 0.0220 | 0.7069 | 0.9894 | 0.9682 | 0.0033 | 0.9586 | 0.9832 |

Finland | 0.9212 | 0.0183 | 0.8179 | 0.9741 | 0.9498 | 0.0181 | 0.8326 | 0.9871 | 0.9699 | 0.0051 | 0.9562 | 0.9868 |

France | 0.9212 | 0.0152 | 0.5673 | 0.9715 | 0.9506 | 0.0153 | 0.5903 | 0.9963 | 0.9690 | 0.0034 | 0.9611 | 0.9844 |

Germany | 0.9185 | 0.0254 | 0.6251 | 0.9673 | 0.9494 | 0.0249 | 0.6484 | 0.9893 | 0.9674 | 0.0059 | 0.9318 | 0.9831 |

Italy | 0.9206 | 0.0139 | 0.7570 | 0.9576 | 0.9505 | 0.0141 | 0.7785 | 0.9832 | 0.9686 | 0.0027 | 0.9627 | 0.9757 |

Spain | 0.9197 | 0.0145 | 0.7566 | 0.9578 | 0.9503 | 0.0147 | 0.7784 | 0.9820 | 0.9678 | 0.0030 | 0.9591 | 0.9754 |

Sweden | 0.9171 | 0.0314 | 0.7384 | 0.9732 | 0.9454 | 0.0317 | 0.7705 | 0.9945 | 0.9700 | 0.0062 | 0.9520 | 0.9785 |

United Kingdom | 0.9190 | 0.0195 | 0.7105 | 0.9613 | 0.9495 | 0.0191 | 0.7491 | 0.9825 | 0.9679 | 0.0044 | 0.9484 | 0.9806 |

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**MDPI and ACS Style**

Čechura, L.; Žáková Kroupová, Z.
Technical Efficiency in the European Dairy Industry: Can We Observe Systematic Failures in the Efficiency of Input Use? *Sustainability* **2021**, *13*, 1830.
https://doi.org/10.3390/su13041830

**AMA Style**

Čechura L, Žáková Kroupová Z.
Technical Efficiency in the European Dairy Industry: Can We Observe Systematic Failures in the Efficiency of Input Use? *Sustainability*. 2021; 13(4):1830.
https://doi.org/10.3390/su13041830

**Chicago/Turabian Style**

Čechura, Lukáš, and Zdeňka Žáková Kroupová.
2021. "Technical Efficiency in the European Dairy Industry: Can We Observe Systematic Failures in the Efficiency of Input Use?" *Sustainability* 13, no. 4: 1830.
https://doi.org/10.3390/su13041830