How Differently Do Farms Respond to Agri-environmental Policies? A Probabilistic Machine-Learning Approach

Silvia Coderoni; Roberto Esposti; Alessandro Varacca

doi:10.3368/le.100.2.060622-0043R1

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Figure 1
Estimated Individualized Average Treatment Effects: (a) Treatment Group T₂ (Farmers Implementing Agri-environmental Measures); (b) Treatment Group T₁ (Farmers Not Fulfilling Conditionality Restraints or Implementing Agri-environmental Measures)
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Figure 2
Shallow Regression Tree Fitted to the Maximum a Posteriori (MAP) Individualized Average Treatment Effects: (a) Treatment Group T₂; (b) Treatment Group T₁
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Figure 3
Individualized Average Treatment Effects Differentials for the Two Versions of T₂

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Table 1

Policy Treatments Set

Treatment	Agri-environmental Policy	Total Farms (2015–2018 FADN Balanced Sample)
T₁	None	512
Control group	Only those implied by the pillar 1 direct payments	2,841
T₂	Those implied by both pillar 1 direct payments and pillar 2 agri-environmental measures	648

Note: FADN = Italian Farm Accountancy Data Network.

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Table 2

Elementary Indicators Used to Assemble the Outcome Variable (FADN-AFI)

Environmental Issue	Assessment Criterion	Indicator	Measurement Unit	Weight
Natural resources protection	Intensity crop husbandry / livestock production	Fertilizer cost of UAA	€/ha	−1
		Crop protection costs UAA	€/ha	−1
		Average number of livestock units	LU/ha	−1
	Energy consumption	Energy costs UAA	€/ha	−1
		% UAA irrigated	Share	−1
Biodiversity and land use	Land use diversity	Crop diversity (Shannon diversity) index (BI_it)	Index (0–1)	+1
	Provision woodland habitats	% total farm area that is woodland	Share	+1
Climate change mitigation	GHG emissions	GHG at farm level	kg CO_2eq	−1

Note: AFI = agri-environmental footprint index; FADN = Italian Farm Accountancy Data Network; UAA = utilized agricultural area.

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Table 3

Covariates Used in Analysis

	Unit of Measure	Component	Reference
Economic characteristic
Total arable land	ha	V_it	(1), (2), (3), (4), (6), (7), (8)
Share of rented land	%	V_it	(2), (3), (4), (7), (8)
Farm revenue	€ per ha	V_it	(4), (7), (8)
Farm fixed costs	€ per ha	V_it	New
Farm variable costs	€ per ha	V_it	(4)
Fertilizer expenditure	€ per ha	V_it	(2), (4), (7)
Pesticides expenditure	€ per ha	V_it	(2), (4), (7)
Livestock density	Units per ha	V_it	(2), (5), (6), (8)
Family labor	Count	S_i(*)	(2), (3), (4), (8), (9)
Nonfamily labor	Count	V_it	(2), (3), (4), (9)
Share of most important crop	%	V_it	(5), (6)
Share of second most important crop	%	V_it	(5), (6)
Share of grassland	%	V_it	(4), (7), (8)
Machinery horsepower	Kw per ha	V_it	(3)
Machinery value	€ per ha	V_it	(3)
Machinery endowment	Units per ha	V_it	(3)
Farm specialization	Categorical	S_i	(3), (6), (7), (8)
Sociodemographic characteristic
Farmer’s age	Years	S_i(*)	(1), (3), (5), (6), (7), (8), (9)
Farmer’s gender	Categorical	S_i	New
Farmer’s education	Categorical	S_i(*)	(1), (3), (8)
Experience with previous AEPs	Categorical	S_i	(6), (7)
Environmental/geographical characteristic
Disadvantaged area	Categorical	S_i	(5), (7), (8)
Latitude and longitude	Degrees	S_i	(6), (7)
Average altitude	Meters	S_i	(9)

Note: These characteristics are not strictly time invariant, but we assume they are approximately so (V_it ≈ S_i) for the period 2015–2018. The references are (1) Vanslembrouck, Van Huylenbroeck, and Verbeke (2002); (2) Pufhal and Weiss (2009); (3) Pascucci et al. (2013); (4) Arata and Sckokai (2016); (5) Zimmerman and Britz (2016); (6) Bertoni et al. (2020); (7) Uehleke, Petrick, and Hüttel (2022); (8) Wąs et al. 2021; (9) Varacca et al. (2023).

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Table 4

Individualized Average Treatment Effects Estimates for Model [6]

Treatment	0 ∉ CrI	MAP > 0	MAP < 0	ATE > 0	ATE < 0	ATE	CrI ATE
Treatment	0 ∉ CrI	MAP > 0	MAP < 0	ATE > 0	ATE < 0	ATE	Lower	Upper
All Observations
	(%)	(%)	(%)	(%)	(%)	(AFI)	(AFI)	(AFI)
T₂	72.3	100	0	100	0	0.55	0.31	0.79
T₁	15.3	28.5	71.5	0.5	99.5	−0.42	−0.73	−0.08
Observations with 0 ∉ CrI
T₂	1	100	0	100	0	0.61	0.364	0.86
T₁	1	0	100	0	100	−0.85	−1.02	−0.46

Note: 0 ∉ CrI = proportion of IATE CrI that do not include zero; MAP > (<) 0 = proportion of IATE with MAP > (<) than zero; ATE > (<) 0 = posterior probability that ATE (as defined in equation [4]) is > (<) than zero; CrI ATE = 95% CrI for ATE. AFI = agri-environmental footprint index; ATE = average treatment effect; CrI = credible interval; MAP = maximum a posteriori.