# AES Impact Evaluation With Integrated Farm Data: Combining Statistical Matching and Propensity Score Matching

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Statistical Matching Background

#### 2.2. Statistical Matching and Propensity Score Matching Combined

#### 2.3. Hot Deck Technique and Distance Function Applied

**X**= $\{{X}_{1},\dots ,{X}_{l},\dots ,{X}_{L}\}$ (with ${X}_{l}^{R}$ being the vector of dimension, (${n}_{R}\times 1$) and ${X}_{l}^{D}$ the vector of dimension (${n}_{D}\times 1$)), reflecting the set of variables which is observed both in R and D. $\underset{{n}_{R}\times P}{\mathit{Z}}=\{{Z}_{1}^{R},\dots ,{Z}_{p}^{R},\dots ,{Z}_{P}^{R}\}$ (with ${Z}_{p}^{R}$ being the vector of dimension (${n}_{R}\times 1$)) and $\underset{{n}_{D}\times M}{\mathit{K}}=\{{K}_{1}^{D},\dots ,{K}_{m}^{D},\dots ,{K}_{M}^{D}\}$ (with ${K}_{m}^{D}$ being the vector of dimension (${n}_{D}\times 1$)) are two sets of variables which are observed either in R or in D, respectively. Hence, in two different data sets (R and D), we have at our disposal a set of jointly observed variables (

**X**) and two sets of variables that are exclusively observed (

**Z**and

**K**). Therefore, let {$\underset{{n}_{R}\times L}{{\mathit{X}}^{R}}$, $\underset{{n}_{R}\times P}{{\mathit{Z}}^{R}}$} be the recipient data set R and {$\underset{{n}_{D}\times L}{{\mathit{X}}^{D}}$, $\underset{{n}_{D}\times M}{{\mathit{K}}^{D}}$} the donor data set D. Finally, let the i-th and the j-th units (i.e., observations) be collected in R and D, respectively, with $i=1,\dots ,{n}_{R}$ and $j=1,\dots ,{n}_{D}$. The aim is to integrate the recipient data set with some variables of interest observed only in the donor in order to have, in the most general case, the resulting synthetic (complete) data set: {$\underset{{n}_{R}\times L}{{\mathit{X}}^{R}}$, $\underset{{n}_{R}\times P}{{\mathit{Z}}^{R}}$, $\underset{{n}_{R}\times M}{{\mathit{K}}^{D}}$}.

- R and D are two data sets containing information on two representative samples of the same target population [27].
- R ∪ D must be considered as a unique sample of the ${n}_{R}+{n}_{D}$ i.i.d. observations from the joint distribution of (
**X**,**Z**,**K**) [27]. - R and D can have any dimensionality, i.e., ${n}_{R}$ and ${n}_{D}$ must not be bounded to the condition ${n}_{R}$ ≤ ${n}_{D}$ [52].

**X**.

#### 2.4. The PSM Estimator

**X**${}_{i}^{psm}$ be a sub-set of the variables observed in the new synthetic (complete) data set generated. These variables can be chosen among all the ones originally observed in R and the ones imputed from D but the variables that have been used for the previous imputation procedure by means of the SM methodology. Hence, if the new synthetic (complete) data set is {$\underset{{n}_{R}\times L}{{\mathit{X}}^{R}}$, $\underset{{n}_{R}\times P}{{\mathit{Z}}^{R}}$, $\underset{{n}_{R}\times M}{{\mathit{K}}^{D}}$}, the ${\mathbf{X}}_{i}^{psm}$ variables can be chosen among these sets of variables with the exception of the previously used matching variables. In our application, for example, we observe both in the recipient data set R and the donor data set D several variables. Among these, the matching variables chosen for the imputation procedure by means of the SM are the farm specialization and the farm TAA, meaning that the sub-set ${\mathbf{X}}_{i}^{psm}$ could potentially consist of all the variables originally observed in R and the variables imputed from D with the exception of the farm specialization and the farm TAA (and the treatment and outcome variables selected).

- 4.
- The assignment to the treatment is independent of the potential outcomes conditional on the covariates [38]:$$({Y}_{0},{Y}_{1})\perp T|X,$$
- 5.
- The probability of the treatment assignment is bounded from 0 to 1 [38]:$$0\le Pr(T=1)\le 1,$$

**X**, i.e.:

**X**, then it is strongly ignorable given any balancing score and, at any value of a balancing score, the difference in means between treatment and control units is an unbiased estimate of the average treatment effect [16].

## 3. Empirical Application

#### 3.1. Data Description

#### 3.2. Nndc–Ms Combination Application

#### 3.3. PSM Application

## 4. Results

#### 4.1. Data Integration Results

#### 4.2. PSM Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AESs | Agri-environmental Schemes |

CAP | Common Agricultural Policy |

DID | Difference-in-Differences |

EU | European Union |

FADN | Farm Accountancy Data Network |

FSS | Farm Structure Survey |

NUTS | Nomenclature des unités territoriales statistiques |

PGs | Public Goods |

PSM | Propensity Score Matching |

PS | Propensity Score |

RDPs | Rural Development Plans |

RL | Record Linkage |

SFP | Single Farm Payment |

SM | Statistical Matching |

SUD | Statistical Up(down)scaling |

TAA | Total Agricultural Area |

UAA | Utilised Agricultural Area |

## References

- ec.europa.eu. Available online: https://ec.europa.eu/agriculture/sites/agriculture/files/policy-perspectives/policy-briefs/05_en.pdf (accessed on 12 February 2018).
- Arata, L.; Sckokai, P. The impact of Agro-environmental Schemes on farm performance in five EU Member States: A DID-matching approach. Land Econ.
**2016**, 92, 167–186. [Google Scholar] [CrossRef] - eur-lex.europa.eu. Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=COM%3A2018%3A392%3AFIN (accessed on 2 July 2018).
- ec.europa.eu. Available online: http://ec.europa.eu/transparency/regexpert/index.cfm?do=groupDetail.groupDetailDoc&id=21095&no=3 (accessed on 25 June 2018).
- Uthes, S.; Matzdorf, B. Studies on agri-environmental measures: A survey of the literature. Environ. Manag.
**2013**, 52, 1–16. [Google Scholar] [CrossRef] [PubMed] - Defrancesco, E.; Gatto, P.; Runge, F.; Trestini, S. Factors affecting farmers’ participation in Agri-environmental Measures: A Northern Ialian perspective. J. Agric. Econ.
**2008**, 59, 114–131. [Google Scholar] [CrossRef] - Pufahl, A.; Weiss, C.R. Evaluating the effects of farm programmes: Results from Propensity Score Matching. Eur. Rev. Agric. Econ.
**2009**, 36, 79–101. [Google Scholar] [CrossRef] - Chabé-Ferret, S.; Subervie, J. How much green for the buck? Estimating additional and windfall effects of French agro-environmental schemes by DID-matching. J. Environ. Econ. Manag.
**2013**, 65, 12–27. [Google Scholar] [CrossRef] [Green Version] - Viaggi, D.; Signorotti, C.; Marconi, V.; Raggi, M. Do Agri-Environmental Schemes contribute to high nature value farmland? A case study in Emilia-Romagna (Italy). Ecol. Indic.
**2015**, 59, 62–69. [Google Scholar] [CrossRef] - Sauer, J.; Walsh, J.; Zilberman, D. The identification and measurement of behavioural effects from agri-environmental policies: An empirical analysis. In Proceedings of the 14th Annual BIOECON, Kings College Cambridge, Cambridge, UK, 18–20 September 2012. [Google Scholar]
- Udagawa, C.; Hodge, I.; Reader, M. Farm Level Costs of Agri-environment Measures: The Impact of Entry Level Stewardship on Cereal Farm Incomes. J. Agric. Econ.
**2014**, 65, 212–233. [Google Scholar] [CrossRef] - Andersson, A.; Höjgård, S.; Rabinowicz, E. Evaluation of results and adaptation of EU Rural Development Programmes. Land Use Policy
**2017**, 67, 298–314. [Google Scholar] [CrossRef] - Jaraitė, J.; Kažukauskas, A. The effect of mandatory agro-environmental policy on farm fertiliser and pesticide expenditure. J. Agric. Econ.
**2012**, 63, 656–676. [Google Scholar] [CrossRef] - Rubin, D.B. Assignment to treatment group on the basis of a covariate. J. Educ. Behav. Stat.
**1977**, 2, 1–26. [Google Scholar] [CrossRef] - Liu, X.; Lynch, L. Do agricultural land preservation programs reduce farmland loss? Evidence from a Propensity Score Matching estimator. Land Econ.
**2011**, 87, 183–201. [Google Scholar] [CrossRef] - Rosenbaum, P.R.; Rubin, D.B. The central role of the propensity score in observational studies for causal effects. Biometrika
**1983**, 70, 41–55. [Google Scholar] [CrossRef] [Green Version] - Rubin, D.B. Causal inference using potential outcomes. J. Am. Stat. Assoc.
**2005**, 100, 322–331. [Google Scholar] [CrossRef] - Robbins, M.W.; Ghosh, S.K.; Habiger, J.D. Imputation in high-dimensional economic data as applied to the Agricultural Resource Management Survey. J. Am. Stat. Assoc.
**2013**, 108, 81–95. [Google Scholar] [CrossRef] - Roesch, A.; Lips, M. Sampling design for two combined samples of the Farm Accountancy Data Network (FADN). J. Agric. Biol. Environ. Stat.
**2013**, 18, 178–203. [Google Scholar] [CrossRef] - Boussard, J.M.; Foulhouze, I. The representativeness of FADN. Econ. Rurale
**1980**, 1, 29–35. [Google Scholar] [CrossRef] - San Juan Mesonada, C.; Mora, R.; de la Torre, J.E. The representativeness of the 1999 Spanish FADN survey. In LEI The Hague Report; LEI: The Hague, The Netherlands, 2003; pp. 114–140. [Google Scholar]
- Van der Meer, R.W.; van der Veen, H.B.; Vrolijk, H.C.J. Sample of Dutch FADN 2011: Design principles and quality of the sample of agricultural and horticultural holdings. In LEI Wageningen Report; LEI: Wageningen, The Netherlands, 2013; pp. 1–32. [Google Scholar]
- Prášilová, M.; Zeipelt, R. Sample representativeness verification of the FADN CZ farm business sample. Acta Univ. Agric. Silvicul. Mendelianae Brunensis
**2014**, 59, 251–256. [Google Scholar] [CrossRef] - Winkler, W.E. Overview of record linkage and current research directions. In Bureau of the Census, Report Series; U.S. Census Bureau: Washington, DC, USA, 2006; pp. 1–44. [Google Scholar]
- Blöschl, G. Statistical Upscaling and Downscaling in Hydrology. In Encyclopedia of Hydrological Sciences; John Wiley & Sons: Hoboken, NJ, USA, 2006; Chapter 9. [Google Scholar]
- Murray, J.S. Multiple Imputation: A review of practical and theoretical findings. Stat. Sci.
**2018**, 33, 142–159. [Google Scholar] [CrossRef] - D’Orazio, M.; Di Zio, M.; Scanu, M. Statistical Matching: Theory and Practice; John Wiley & Sons: Hoboken, NJ, USA, 2006. [Google Scholar]
- Conti, P.L.; Marella, D.; Scanu, M. Evaluation of matching noise for imputation techniques based on nonparametric local linear regression estimators. Comput. Stat. & Data Anal.
**2008**, 53, 354–365. [Google Scholar] - Balin, M.; D’Orazio, M.; Di Zio, M.; Scanu, M.; Torelli, N. Statistical Matching of Two Surveys with a Common Subset. In ISTAT Technical Report; ISTAT: Rome, Italy, 2009; pp. 1–14. [Google Scholar]
- Okner, B.A. Constructing a new data base from existing microdata sets: The 1966 merge file. Ann. Econ. Soc. Meas.
**1972**, 1, 325–342. [Google Scholar] - Kadane, J.B. Some Statistical Problems in Merging Data Files; Office of Tax Analysis, U.S. Department of the Treasury: Washington, DC, USA, 1978.
- Rubin, D.B. Statistical matching using file concatenation with adjusted weights and multiple imputations. J. Bus. Econ. Stat.
**1986**, 4, 87–94. [Google Scholar] - Paass, G. Statistical match: Evaluation of existing procedures and improvements by using additional information. In Microanalytic Simulation Models to Support Social and Financial Policy; Elsevier Science Pub: New York, NY, USA, 1986; pp. 401–422. [Google Scholar]
- Singh, A.C.; Mantel, H.J.; Kinack, M.D.; Rowe, G. Statistical matching: Use of auxiliary information as an alternative to the Conditional Independence Assumption. Surv. Methodol.
**1993**, 19, 59–79. [Google Scholar] - Rässler, S. Statistical Matching: A Frequentist Theory, Practical Applications, and Alternative Bayesian Approaches. In Lecture Notes in Statistics; Springer: New York, NY, USA, 2002; Volume 168. [Google Scholar]
- Andridge, R.R.; Little, R.J.A. A review of hot deck imputation for survey non-response. Int. Stat. Rev.
**2010**, 78, 40–64. [Google Scholar] [CrossRef] [PubMed] - Denk, M.; Hackl, P. Data integration and record matching: An Austrian contribution to research in official statistics. Austrian J. Stat.
**2003**, 32, 305–321. [Google Scholar] [CrossRef] - Rubin, D.B. Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol.
**1974**, 66, 688–701. [Google Scholar] [CrossRef] - Dehejia, R.H.; Wahba, S. Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. J. Am. Stat. Assoc.
**1999**, 94, 1053–1062. [Google Scholar] [CrossRef] - Black, D.A.; Smith, J.A. How robust is the evidence on the effects of college quality? Evidence from matching. J. Econom.
**2004**, 121, 99–124. [Google Scholar] [CrossRef] [Green Version] - Sianesi, B. An evaluation of the swedish system of active labor market programs in the 1990s. Rev. Econ. Stat.
**2004**, 86, 133–155. [Google Scholar] [CrossRef] - Imbens, G.W.; Wooldridge, J.M. Recent developments in the econometrics of program evaluation. J. Econ. Lit.
**2009**, 47, 5–86. [Google Scholar] [CrossRef] [Green Version] - Michalek, J. Counterfactual impact evaluation of EU rural development programmes-Propensity Score Matching methodology applied to selected EU Member States. Volume 2: A regional approach. In Joint Research Centre Technical Report; Publications Office of the European Union: Seville, Spain, 2012; pp. 1–82. [Google Scholar]
- Lynch, L.; Liu, X. Impact of designated preservation areas on rate of preservation and rate of conversion: Preliminary evidence. Am. J. Agric. Econ.
**2007**, 89, 1205–1210. [Google Scholar] [CrossRef] - Schilling, B.J.; Attavanich, W.; Sullivan, K.P.; Marxen, L.J. Measuring the effect of farmland preservation on farm profitability. Land Use Policy
**2014**, 41, 84–96. [Google Scholar] [CrossRef] - Michalek, J.; Ciaian, P.; Kancs, D. Capitalization of the single payment scheme into land value: Generalized propensity score evidence from the European Union. Land Econ.
**2014**, 90, 260–289. [Google Scholar] [CrossRef] - Kirchweger, S.; Kantelhardt, J. Improving farm competitiveness through farm-investment support: A Propensity Score Matching approach. In Proceedings of the 131st EAAE Seminar on “Innovation for Agricultural Competitiveness and Sustainability of Rural Areas”, Prague, Czech Republic, 18–19 September 2012. [Google Scholar]
- Ratinger, T.; Medonos, T.; Hruska, M. An assessment of the differentiated effects of the investment support to agricultural modernisation: The case of the Czech Republic. AGRIS On-Line Pap. Econ. Inform.
**2013**, 5, 153–164. [Google Scholar] - Willy, D.K.; Zhunusova, E.; Holm-Müller, K. Estimating the joint effect of multiple soil conservation practices: A case study of smallholder farmers in the Lake Naivasha basin, Kenya. Land Use Policy
**2014**, 39, 177–187. [Google Scholar] [CrossRef] - Datta, N. Evaluating impacts of watershed development program on agricultural productivity, income, and livelihood in Bhalki Watershed of Bardhaman District, West Bengal. World Dev.
**2015**, 66, 443–456. [Google Scholar] [CrossRef] - Shete, M.; Rutten, M. Impacts of large-scale farming on local communities’ food security and income levels: Empirical evidence from Oromia Region, Ethiopia. Land Use Policy
**2015**, 47, 282–292. [Google Scholar] [CrossRef] - D’Alberto, R.; Raggi, M. Non-parametric micro Statistical Matching techniques: Some development. In Proceedings of the Conference of the Italian Statistical Society, Firenze, Italy, 28–30 June 2017. [Google Scholar]
- Mardia, K.V.; Kent, J.T.; Bibby, J.M. Multivariate aNalysis (Probability and Mathematical Statistics); Academic Press: London, UK, 1980. [Google Scholar]
- Markatou, M.; Chen, Y.; Afendras, G.; Lindsay, B.G. Statistical Distances and Their Role in Robustness. In New Advances in Statistics and Data Science; Chen, D.G., Jin, Z., Li, Y., Liu, A., Zhao, Y., Eds.; Springer: Berlin, Germany, 2017. [Google Scholar]
- Caliendo, M.; Kopeinig, S. Some practical guidance for the implementation of Propensity Score Matching. J. Econ. Surv.
**2008**, 22, 31–72. [Google Scholar] [CrossRef] - Cerulli, G. Modelling and Measuring the Effect of Public Subsidies on Business R&D: A critical review of the Econometric Literature. Econ. Rec.
**2010**, 86, 421–449. [Google Scholar] - Abadie, A.; Drukker, D.; Herr, J.L.; Imbens, G.W. Implementing matching estimators for average treatment effects in Stata. Stata J.
**2004**, 4, 290–311. [Google Scholar] [CrossRef] - Ichino, A.; Mealli, F.; Nannicini, T. From temporary help jobs to permanent employment: What can we learn from matching estimators and their sensitivity? J. Appl. Econom.
**2008**, 23, 305–327. [Google Scholar] [CrossRef] - Capitanio, F.; Gatto, E.; Millemaci, E. CAP payments and spatial diversity in cereal crops: An analysis of Italian farms. Land Use Policy
**2016**, 54, 574–582. [Google Scholar] [CrossRef] - Sckokai, P.; Moro, D. Modeling the reforms of the common agricultural policy for arable crops under uncertainty. Am. J. Agric. Econ.
**2006**, 88, 43–56. [Google Scholar] [CrossRef] - Arata, L.; Donati, M.; Sckokai, P.; Arfini, F. Incorporating risk in a positive mathematical programming framework: A dual approach. Aust. J. Agric. Resour. Econ.
**2017**, 61, 265–284. [Google Scholar] [CrossRef] - Baumgärtner, S. The insurance value of biodiversity in the provision of ecosystem services. Nat. Resour. Model.
**2007**, 20, 87–127. [Google Scholar] [CrossRef] - Baumgärtner, S.; Quaas, M.F. Managing increasing environmental risks through agrobiodiversity and agrienvironmental policies. Agric. Econ.
**2010**, 41, 483–496. [Google Scholar] [CrossRef] - Di Falco, S.; Perrings, C. Crop genetic diversity, productivity and stability of agroecosystems. A theoretical and empirical investigation. Scott. J. Polit. Econ.
**2003**, 50, 207–216. [Google Scholar] [CrossRef] - Di Falco, S.; Perrings, C. Crop biodiversity, risk management and the implications of agricultural assistance. Ecol. Econ.
**2005**, 55, 459–466. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Integration example from a donor data set to a recipient one by means of the statistical matching (SM) methodology.

**Figure 2.**Integration from the donor data set Farm Accountancy Data Network (FADN) 2009 to the recipient data set “CAP-IRE 2009” of the variables of interest for the propensity score matching (PSM) analysis.

**Figure 3.**Graphical analysis of the variables distributions pre-and-post imputation. TAA: total agricultural area.

**Figure 5.**PS distribution between the treated and control groups both on and off the region of common support (NEW CAP-IRE 2009 data set).

T | Frequency | Percent |
---|---|---|

0 | 178 | 62.46 |

1 | 107 | 37.54 |

Total | 285 | 100.00 |

**Table 2.**Covariates used for the propensity score (PS) estimation (NEW CAP-IRE 2009 data set). Coef. = coefficients; Std. Err. = Standard Error; z = value of the test statistic; P > |z| = p-value; Conf. Interval = Confidence Interval.

T | Coef. | Std. Err. | z | P$>\left|\mathit{z}\right|$ | [95% Conf. Interval] | |
---|---|---|---|---|---|---|

owner_agri_edu | −0.476215 | 0.340462 | −1.40 | 0.162 | −1.143509 | 0.191078 |

owner_edu | 0.115175 | 0.117493 | 0.98 | 0.032 | −0.115107 | 0.345456 |

legal_status | 0.778176 | 0.303509 | 2.56 | 0.010 | 0.183310 | 1.373043 |

organic_prod | 0.920301 | 0.424769 | 2.17 | 0.030 | 0.087770 | 1.752832 |

sfp_ha | −1.015806 | 0.375366 | −2.71 | 0.007 | −1.751510 | −0.280103 |

sfp_eur | 0.002397 | 0.001040 | 2.30 | 0.021 | 0.000357 | 0.004436 |

size_esu | 0.000295 | 0.000277 | 1.06 | 0.028 | −0.000249 | 0.000838 |

uaa_irr | 0.014194 | 0.007912 | 1.79 | 0.073 | −0.001314 | 0.0297015 |

gfi | −0.000016 | 0.000008 | −2.08 | 0.038 | −0.000032 | −0.000001 |

ffi | 0.000015 | 0.000008 | 1.92 | 0.054 | −0.000000 | 0.000031 |

awu_total_input | 0.513978 | 0.183611 | 2.80 | 0.005 | 0.154109 | 0.873847 |

**Table 3.**Estimated PS in the region of common support (NEW CAP-IRE 2009 data set). Obs. = number of observations; Std. Dev. = Standard Deviation.

Percentiles | Smallest | |||
---|---|---|---|---|

1% | 0.155566 | 0.152536 | ||

5% | 0.173274 | 0.154019 | ||

10% | 0.197719 | 0.155566 | ||

25% | 0.240842 | 0.155584 | ||

50% | 0.345959 | 0.381021 | ||

Largest | ||||

75% | 0.487506 | 0.894942 | Obs. | 279 |

90% | 0.651458 | 0.899009 | Std. Dev. | 0.175115 |

95% | 0.750122 | 0.922094 | Variance | 0.030665 |

99% | 0.899009 | 0.928727 | Pseudo R${}^{2}$ | 0.1840 |

Inferior of PS Block | T | Total | |
---|---|---|---|

0 | 1 | ||

0.152536 | 15 | 6 | 21 |

0.2 | 66 | 24 | 90 |

0.3 | 43 | 33 | 76 |

0.4 | 35 | 30 | 65 |

0.6 | 10 | 8 | 18 |

0.8 | 3 | 6 | 9 |

Total | 172 | 107 | 279 |

T | Coef. | Std. Err. | z | P$>\left|\mathit{z}\right|$ | [95% Conf. Interval] | |
---|---|---|---|---|---|---|

owner_agri_edu | −0.233312 | 0.316948 | −0.74 | 0.462 | −0.854522 | 0.387897 |

owner_edu | 0.128069 | 0.110731 | 1.16 | 0.247 | −0.088961 | 0.345099 |

legal_status | 0.916068 | 0.287123 | 3.19 | 0.105 | 0.353318 | 1.478818 |

organic_prod | 0.914884 | 0.409481 | 2.23 | 0.075 | 0.112316 | 1.717453 |

ffi | −1.158031 | 0.000003 | −0.68 | 0.497 | −0.000009 | 0.000004 |

**Table 6.**Average treatment effect on treated (ATT) estimated on the land_rent_in outcome variable in the synthetic (complete) NEW CAP-IRE 2009 data set. T-stat = test statistic.

Variable | Sample | Treated | Controls | Difference | Std. Err. | T-stat |
---|---|---|---|---|---|---|

land_rent_in | Unmatched | 8.30841 | 7.18539 | 1.12302 | 2.78536 | 0.40 |

ATT | 8.35577 | 12.31989 | −3.96412 | 2.93514 | −1.35 |

**Table 7.**ATT estimated on the ghi outcome variable in the synthetic (complete) NEW CAP-IRE 2009 data set.

Variable | Sample | Treated | Controls | Difference | Std. Err. | T-stat |
---|---|---|---|---|---|---|

ghi | Unmatched | 0.18454 | 0.13551 | 0.49028 | 0.26747 | 1.83 |

ATT | 0.15188 | 0.18839 | −0.03651 | 0.05547 | −0.66 |

© 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**

D’Alberto, R.; Zavalloni, M.; Raggi, M.; Viaggi, D.
AES Impact Evaluation With Integrated Farm Data: Combining Statistical Matching and Propensity Score Matching. *Sustainability* **2018**, *10*, 4320.
https://doi.org/10.3390/su10114320

**AMA Style**

D’Alberto R, Zavalloni M, Raggi M, Viaggi D.
AES Impact Evaluation With Integrated Farm Data: Combining Statistical Matching and Propensity Score Matching. *Sustainability*. 2018; 10(11):4320.
https://doi.org/10.3390/su10114320

**Chicago/Turabian Style**

D’Alberto, Riccardo, Matteo Zavalloni, Meri Raggi, and Davide Viaggi.
2018. "AES Impact Evaluation With Integrated Farm Data: Combining Statistical Matching and Propensity Score Matching" *Sustainability* 10, no. 11: 4320.
https://doi.org/10.3390/su10114320