# Technological Differences, Theoretical Consistency, and Technical Efficiency: The Case of Hungarian Crop-Producing Farms

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Heterogeneity in Production Frontiers Models

#### 2.2. Theoretical Consistency

**H**can be written in the following form,

**A**refers to the second derivatives of the production function with respect to inputs, and

**a**represents the vector of first derivatives of the production function. The Cholesky factorization of $\left[{B}_{kk}+\mathit{a}{\mathit{a}}^{\prime}-\mathit{a}\right]$ is

**L’DL [34]**. The matrix

**D**represents the Cholesky factors d

_{ii}for i = 1,4, and

**L**is a lower triangular matrix with element l

_{ij}, for i, j = 1,4 and l

_{ii}= 1.

#### 2.3. Data

## 3. Results

#### 3.1. Comparison of TRE and RPM

^{-u}, u > 0.3), the share of farms that operate at low efficiency is reduced to a marginal fraction in the second model. Given that farms are operating in a homogeneous institutional environment, this wide range of efficiencies is difficult to justify. Thus, we conclude that the RPM depicts inefficiency more appropriately than the TRE model.

#### 3.2. The Effect of Constraints

**B**that determines whether the results are theoretically consistent. This concerns not only the pure absolute value of the estimated parameter but also, in many cases, the sign.

_{kk}#### 3.3. The Effect of Heterogeneity on Production and the Connection between Farms’ Economic and Natural Conditions and Unobserved Heterogeneity

## 4. Conclusions

^{−u}, u > 0.3), the share of farms with low efficiency is reduced to a marginal fraction in the RPM. Given that farms are operating in a homogeneous institutional environment, the very wide span of inefficiencies is difficult to justify.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

- Abdulai, A.; Tietje, H. Estimating technical efficiency under unobserved heterogeneity with stochastic frontier models: Application to northern German dairy farms. Eur. Rev. Agric. Econ.
**2007**, 34, 393–416. [Google Scholar] [CrossRef] - Bauer, P.W.; Berger, A.N.; Ferrier, G.D.; Humphrey, D.B. Consistency Conditions for Regulatory Analysis of Financial Institutions: A Comparison of Frontier Efficiency Method. J. Econ. Bus.
**1998**, 50, 85–114. [Google Scholar] [CrossRef] [Green Version] - Chang, C.-H.; Wu, K.-S.; Chang, B.-G.; Lou, K.-R. Measuring Technical Efficiency and Returns to Scale in Taiwan′s Baking Industry—A case study of the 85 °C Company. Sustainability
**2019**, 11, 1268. [Google Scholar] [CrossRef] [Green Version] - Lazikova, J.; Lazikova, Z.; Takac, I.; Rumanovska, L.; Bandlerova, A. Technical efficiency in the Agricultural Business—The case of Slovakia. Sustainability
**2019**, 11, 5589. [Google Scholar] [CrossRef] [Green Version] - Tsionas, E.G. Stochastic frontier Models with Random Coefficients. J. Appl. Econom.
**2002**, 17, 127–147. [Google Scholar] [CrossRef] - Huang, H.-C. Estimation of Technical Inefficiencies with Heterogeneous Technologies. J. Product. Anal.
**2004**, 21, 277–296. [Google Scholar] [CrossRef] - Eberhardt, M.; Teal, F. No Mangoes in the Tundra: Spatial Heterogeneity in Agricultural Productivity Analysis. Oxf. Bull. Econ. Stat.
**2013**, 75, 914–939. [Google Scholar] [CrossRef] [Green Version] - Eberhardt, M.; Teal, F. Econometrics for Grumblers: A New Look at the Literature on Cross-Country Growth Empirics. J. Econ. Surv.
**2011**, 25, 109–155. [Google Scholar] [CrossRef] [Green Version] - Eberhardt, M.; Vollrath, D. The Effect of Agricultural Technology on the Speed of Development. World Dev.
**2018**, 109, 483–496. [Google Scholar] [CrossRef] - Kuenzle, M. Cost Efficiency in Network Industries: Application of Stochastic Frontier Analysis. Ph.D. Thesis, Swiss Federal Institute of Technology Zurich, Zürich, Switzerland, 2005. [Google Scholar]
- Farsi, M.; Filippini, M.; Kuenzle, M. Unobserved heterogeneity in stochastic cost frontier models: An application to Swiss nursing homes. Appl. Econ.
**2005**, 37, 2127–2141. [Google Scholar] [CrossRef] - Cillero, M.; Thorne, F.; Wallace, M.; Breen, J. Technology heterogeneity and policy change in farm-level efficiency analysis: An application to the Irish beef sector. Eur. Rev. Agric. Econ.
**2019**, 46, 193–214. [Google Scholar] [CrossRef] - Alvarez, A.; del Corral, J. Identifying different technologies using a latent class model: Extensive versus intensive dairy farms. Eur. Rev. Agric. Econ.
**2010**, 37, 231–250. [Google Scholar] [CrossRef] - Baráth, L.; Fertő, I. Heterogeneous technology, scale of land use and technical efficiency: The case of Hungarian crop farms. Land Use Policy
**2015**, 42, 141–150. [Google Scholar] [CrossRef] [Green Version] - Hsiao, C. Analysis of Panel Data, 3rd ed.; Cambridge University Press: New York, NY, USA, 2014; pp. 1–539. [Google Scholar]
- Belyaeva, M.; Hockmann, H. Impact of regional diversity on production potential: An example of Russia. Stud. Agric. Econ.
**2015**, 117, 72–79. [Google Scholar] [CrossRef] [Green Version] - Cechura, L.; Grau, A.; Hockmann, H.; Levkovych, I.; Kroupova, Z. Catching up or falling behind in European agriculture: The case of milk production. J. Agric. Econ.
**2017**, 68, 206–227. [Google Scholar] [CrossRef] - Wang, X.; Hockmann, H.; Bai, J. Technical efficiency and producers’ individual technology: Accounting for within and between regional farm heterogeneity. Can. J. Agric. Econ.
**2012**, 60, 561–576. [Google Scholar] [CrossRef] - Lachaud, M.; Bravo-Ureta, B.E.; Ludeña, C. Agricultural productivity in Latin America and the Caribbean in the presence of unobserved heterogeneity and climatic effects. Clim. Chang.
**2017**, 143, 445–460. [Google Scholar] [CrossRef] - Njuki, E.; Bravo-Ureta, B.E.; O’Donnell, C.J. Decomposing agricultural productivity growth using a random-parameters stochastic production frontier. Empir. Econ.
**2018**, 57, 1–22. [Google Scholar] [CrossRef] - Julien, J.; Bravo-Ureta, B.E.; Rada, N. Assessing farm performance by size in Malawi, Tanzania, and Uganda. Food Policy
**2019**, 84, 153–164. [Google Scholar] [CrossRef] - Sauer, J. Economic theory and econometric practice: Parametric efficiency analysis. Empir. Econ.
**2006**, 31, 1061–1087. [Google Scholar] [CrossRef] [Green Version] - Láng, I.; Csete, L.; Harnos, Z. The Agro-Ecopotential of the Hungarian Agriculture at the Turn of 2000; Mezőgazdasági Kiadó: Budapest, Hungary, 1983; pp. 1–266. [Google Scholar]
- Agrell, P.J.; Brea-Solís, H. Stationarity of Heterogeneity in Production Technology using Latent Class Modelling. Core Discuss. Pap.
**2015**, 47, 1–21. [Google Scholar] - Pitt, M.; Lee, L. The measurement and sources of technical inefficiency in Indonesian weaving industry. J. Dev. Econ.
**1981**, 9, 43–64. [Google Scholar] [CrossRef] - Schmidt, P.; Sickles, R. Production frontiers with panel data. J. Bus. Econ. Stat.
**1984**, 2, 365–374. [Google Scholar] - Greene, W. Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. J. Econom.
**2005**, 126, 269–303. [Google Scholar] [CrossRef] - Alvarez, A.; Arias, C.; Greene, W. Accounting for unobservables in production models: Management and inefficiency. Working Paper. Fund. Cent. Estud. Andal. Ser. Econ.
**2004**, E2004/72, 1–18. [Google Scholar] - Train, K. Halton Sequences for Mixed Logit. Economics Working Papers E00-27; Department of Economics, University of California: Berkeley, CA, USA, 2000; pp. 1–18. [Google Scholar]
- Terrell, D.; Dashti, I. Incorporating Monotonicity and Concavity Restrictions into Stochastic Cost Frontiers. In Proceedings of the Midwest Econometric Society Meeting, Columbus, OH, USA, May 1997; pp. 1–31. [Google Scholar]
- Sauer, J.; Hockmann, H. The Need for Theoretically Consistent Efficiency Frontiers. In Proceedings of the XIth EAAE Congress, Copenhagen, Denmark, 24–27 August 2005. [Google Scholar]
- Henningsen, A.; Christian, H.C.A. Henning. Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure. J. Product. Anal.
**2009**, 32, 217–229. [Google Scholar] [CrossRef] [Green Version] - Coelli, T.J.; Prasada Rao, D.S.; Q′Donnell, C.J.; Battese, G.E. An Introduction to Efficiency and Productivity Analysis, 2nd ed.; Springer: Boston, MA, USA, 2005; pp. 1–349. [Google Scholar]
- Lau, J.L. Testing and imposing monotonicity, convexity and quasi-convexity constraints. In Production Economics: A Dual Approach and Application to Theory and Application, 1st ed.; Fuss, M., McFadden, D., Eds.; North Holland Publishing Company: New York, NY, USA, 1978; Volume 2, pp. 1–360. [Google Scholar]
- Keszthelyi, S.; Pesti, C. A Tesztüzemi Információs Rendszer 2008. évi Eredményei. Agrárgazdasági Inf.
**2009**, 3, 1–45. [Google Scholar] - Herlemann, H.H.; Stamer, H. Produktionsgestaltung und Betriebsgröβe in der Landwirtschaft unter dem Einfluss der wirtschaftlich-technischen Entwicklung. Kiel. Stud.
**1958**, 44, 353–354. [Google Scholar] - Hayami, Y.; Ruttan, V.W. Agricultural Development: An International Perspctive, 2nd ed.; Johns Hopkins University Press: Baltimore, MD, USA, 1971; pp. 1–367. [Google Scholar]
- Bakucs, L.Z.; Latruffe, L.; Fertő, I.; Fogarasi, J. The impact of EU accession on farms’ technical efficiency in Hungary. Post-Communist Econ.
**2010**, 22, 165–175. [Google Scholar] [CrossRef] - Nemes-Zubor, A.; Fogarasi, J.; Molnár, A.; Kemény, G. Farmers’ responses to the changes in Hungarian agricultural insurance system. Agric. Financ. Rev.
**2018**, 78, 275–288. [Google Scholar] [CrossRef] - Latruffe, L.; Fogarasi, J.; Desjeux, Y. Efficiency, productivity and technology comparison for farms in Central and Western Europe: The case of field crop and dairy farming in Hungary and France. Econ. Syst.
**2012**, 36, 264–278. [Google Scholar] [CrossRef] - Jondrow, J.; Knox, C.A.; Materov, I.S.; Schmidt, P. On the Estiamtion of Technical Inefficiency in the Stochastic Frontier Production Function Model. J. Econom.
**1982**, 19, 233–238. [Google Scholar] [CrossRef] [Green Version]

**Figure 3.**Joint impact of the variance of heterogeneity and efficiency. Source: authors’ estimation.

**Figure 4.**Development of relative land productivity by region (2004–2009). Source: authors’ calculations.

**Figure 5.**Partial productivities and the man-land ratio in Hungarian grain production 2005–2008, according to region. Note: Y/A land productivity; Y/B land productivity; B/A land-man ratio; all variables are normalized using the geometric average of the total sample. Source: authors’ calculations.

Symbol | Mean | Standard Deviation | Minimum | Maximum | |
---|---|---|---|---|---|

Output (EUR) | Y | 40,097.8 | 84,487.8 | 128.51 | 931,774.0 |

Labor (AWU) | A | 3.73 | 8.30 | 0.01 | 100.09 |

Land (ha) | L | 237.41 | 428.57 | 3.68 | 3787.0 |

Capital (EUR) | K | 17,309.6 | 42,077.1 | 5.53 | 339,055.0 |

Variable Inputs (EUR) | V | 28,224.6 | 60,186.5 | 323.26 | 657,902.0 |

TRE | M_Alvarez | ||||

Constant | 0.273 | *** | 0.241 | *** | |

Neutr TF | T | 0.006 | ** | 0.028 | *** |

TT | 0.009 | *** | 0.018 | *** | |

Inputs-first order | A | 0.054 | *** | 0.074 | *** |

L | 0.158 | *** | 0.177 | *** | |

K | 0.132 | *** | 0.142 | *** | |

V | 0.664 | *** | 0.571 | *** | |

Biased technical change | A*T | −0.001 | 0.000 | ||

L*T | −0.006 | 0.000 | |||

K*T | 0.008 | ** | 0.007 | * | |

V*T | −0.004 | −0.009 | |||

Second order | AA | 0.038 | ** | 0.010 | |

LL | 0.052 | 0.126 | ** | ||

KK | 0.067 | *** | 0.071 | *** | |

VV | 0.023 | 0.023 | |||

AL | −0.107 | *** | −0.077 | *** | |

AK | 0.017 | * | 0.010 | ||

AV | 0.046 | ** | 0.051 | ** | |

LK | 0.015 | −0.008 | |||

LV | 0.002 | −0.057 | |||

KV | −0.082 | *** | −0.051 | ** | |

Unobserved heterogeneity | AM | 0.181 | *** | 0.179 | *** |

AM_T | - | 0.018 | *** | ||

AM_A | - | 0.027 | *** | ||

AM_L | - | 0.015 | ** | ||

AM_K | - | −0.001 | |||

AM_V | - | −0.070 | *** | ||

Auxiliary para-meters | SV | 0.167 | *** | 0.167 | *** |

SU | 0.395 | *** | 2.083 | *** | |

($\lambda $) | 2.368 | 2.232 | |||

RTS | 1.008 | 0.964 | |||

Model selection | Log L | −1011.391 | −853.328 | ||

AIC | 2070.782 | 1764.656 | |||

BIC | 2109.190 | 1811.065 |

Mono-Tonicity | Quasi-Concavity | Consistent | Binding Restrictions | ||
---|---|---|---|---|---|

Linear | Nonlinear | ||||

RPM without constraints | 88% | 75% | 73% | ||

RPM with constraints | 97% | 93% | 92% | 7 | 3 |

RPM without Constraints | RPM with Constraints | Difference (%) ^{+} | ||||

Constant | 0.2412 | *** | 0.2513 | *** | 4.0% | *** |

T | 0.0283 | *** | 0.0288 | *** | 1.7% | *** |

TT | 0.0176 | *** | 0.0176 | *** | 0.0% | |

A | 0.0735 | *** | 0.0750 | *** | 2.0% | *** |

L | 0.1768 | *** | 0.1748 | *** | −1.1% | *** |

K | 0.1423 | *** | 0.1397 | *** | −1.9% | *** |

V | 0.5711 | *** | 0.5716 | *** | 0.1% | |

A*T | 0.0001 | 0.0007 | 85.7% | *** | ||

L*T | −0.0003 | 0.0021 | 114.3% | *** | ||

K*T | 0.0073 | * | 0.0070 | ** | −4.3% | *** |

V*T | −0.0092 | −0.0116 | ** | 20.7% | *** | |

AA | 0.0102 | 0.0087 | −17.2% | *** | ||

LL | 0.1263 | ** | 0.0882 | ** | −43.2% | *** |

KK | 0.0713 | *** | 0.0481 | *** | −48.2% | *** |

VV | 0.023 | −0.0147 | 256.5% | *** | ||

AL | −0.0771 | *** | −0.0592 | *** | −30.2% | *** |

AK | 0.0104 | 0.0082 | −26.8% | *** | ||

AV | 0.0512 | ** | 0.0416 | ** | −23.1% | *** |

LK | −0.0075 | −0.0063 | −19.0% | *** | ||

LV | −0.0569 | −0.0324 | −75.6% | *** | ||

KV | −0.0507 | ** | −0.0300 | *** | −69.0% | *** |

AM | 0.179 | *** | 0.1746 | *** | −2.5% | *** |

AM_T | 0.0178 | *** | 0.0173 | *** | −2.9% | *** |

AM_A | 0.0267 | *** | 0.0240 | *** | −11.3% | *** |

AM_L | 0.0148 | ** | 0.0155 | *** | 4.5% | *** |

AM_K | 0.0006 | 0.0025 | 76.0% | *** | ||

AM_V | −0.0697 | *** | −0.0714 | *** | 2.4% | *** |

SV | 0.1671 | *** | 0.1681 | *** | 0.6% | *** |

SU | 2.0828 | *** | 2.1287 | *** | 2.2% | *** |

$\lambda $ | 2.232 | 2.211 | 0.9% |

© 2020 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**

Baráth, L.; Fertő, I.; Hockmann, H.
Technological Differences, Theoretical Consistency, and Technical Efficiency: The Case of Hungarian Crop-Producing Farms. *Sustainability* **2020**, *12*, 1147.
https://doi.org/10.3390/su12031147

**AMA Style**

Baráth L, Fertő I, Hockmann H.
Technological Differences, Theoretical Consistency, and Technical Efficiency: The Case of Hungarian Crop-Producing Farms. *Sustainability*. 2020; 12(3):1147.
https://doi.org/10.3390/su12031147

**Chicago/Turabian Style**

Baráth, Lajos, Imre Fertő, and Heinrich Hockmann.
2020. "Technological Differences, Theoretical Consistency, and Technical Efficiency: The Case of Hungarian Crop-Producing Farms" *Sustainability* 12, no. 3: 1147.
https://doi.org/10.3390/su12031147