Bio-economic modeling of wine grape protection strategies for environmental policy assessment

Abstract

This research had two objectives. The first was to model the behaviour of wine producers, and the second was to assess the effectiveness of policies designed to reduce pesticide use in viticulture. We modeled the decisions of producers aiming to maximize their expected income while subject to a number of constraints and phytosanitary risks. We also examined the impacts of different protection strategies targeting downy mildew, the main grape disease in European Atlantic vineyards. The Vineyard model for Environmental Policy Analysis (VINEPA) model is a multi-periodic stochastic programming model based on panel data of about one hundred representative winegrowing farms from the Farm Accountancy Data Network in the Bordeaux region. The response of vines to fungicide treatments against downy mildew was simulated through the downy mildew potential system, an epidemiologic model initially developed for decision support, using data from multiple weather stations along with special plots of untreated vines, monitored weekly over a 10-year period. The VINEPA model accurately reproduced the current chemical protection strategies in the region. Simulations were then carried out for different types of taxes (ad valorem and volume based) at different rates. In addition, we analysed the effects of policies on spraying practices, along with their potential impact on investment in precision technology equipment.

Appendices

Appendix 1

The VINEPA model (expected value model)

$$ \begin{aligned} {\text{Max E}}\left( \pi \right) &= \mathop \sum \limits_{n = 0}^{N} w^{n} \hfill \\ &\quad \times \left( \begin{array}{l} \mathop \sum \limits_{a} \left( {{ \Pr }\left( a \right) \times \left( {rdtT0_{a} + \mathop \sum \limits_{t = 1}^{20} \left( {ita_{a,t} \times y_{{n,t,p_{0} }} + \left( {ita_{a,t} + ita_{a,t + 1} } \right) \times y_{{n,t,p_{1} }} } \right)} \right)} \right) \times \left( {v \times Y \times area - varCost} \right) \hfill \\ - area \times \left( {\left( {1 - \mathop \sum \limits_{e} x_{n,e} Eco_{e} } \right) \times \left( {\mathop \sum \limits_{p} productPrice_{p} \times z_{n,p} + fongiPrice} \right) + \mathop \sum \limits_{p} fuelPrice_{p} \times z_{n,p} } \right) \hfill \\ - area \times \left( {\hbox{max} \left( {0, 6 - \mathop \sum \limits_{p} z_{n,p} } \right) \times COidiumFuel + CBotrytisFuel} \right) \hfill \\ - area \times \left( {\left( {1 - r_{n} } \right) \times cdc + r_{n} \times cdm + \left( {1 - t_{n} } \right) \times chc + t_{n} \times ccs} \right) \hfill \\ + s_{n - 1} \times i + \mathop \sum \limits_{e} x_{n,e} \times maintenanceCost_{e} \hfill \\ - \mathop \sum \limits_{e} \left( {\left( {x1_{n,e} - x1_{n - 1,e} } \right) \times Cmat_{e} + x2_{n,e} \times R_{e } } \right) \hfill \\ \end{array} \right) \hfill \\ \end{aligned} $$

$$ \mathop \sum \limits_{p} y_{n,t,p} \le 1 \quad \forall n,t $$

(1)

$$ y_{n,t,p1} + \mathop \sum \limits_{p} y_{n,t + 1,p} \le 1\quad \forall n,t $$

(2)

$$ y_{n,t,p1} = 0 \quad \forall n,\forall t \in \left[ {t16,t20} \right] $$

(3)

$$ x1_{n,e} \ge x1_{n - 1,e} \quad \forall n,e $$

(4)

$$ x2_{n,e} \ge x2_{n - 1,e} \quad \forall n,e $$

(5)

$$ \mathop \sum \limits_{e} \left( {x1_{n,e} + x2_{n,e} } \right) \le 1 \quad \forall n $$

(6)

$$ x 1_{n,e} + x 2_{n,e} = x_{n,e} \quad \forall n,e $$

(7)

$$ z_{n,p} = \sum _{t} y_{n,p,t} \quad \forall n,p $$

(8)

$$ s_{n} \le { \hbox{max} }(0, s_{n - 1} \times \left( {1 + i} \right) + \pi_{n - 1} - minCons - \mathop \sum \limits_{e} \left( {x1_{n,e} - x1_{n - 1,e} } \right) \times Cmat_{e} )\quad \forall n $$

(9)

$$ x1_{n,e} \le x1_{n - 1,e} + { \hbox{max} }(0, 1 + s_{n - 1} \times \left( {1 + i} \right) + \pi_{n - 1} - minCons - Cmat_{e} )\quad \forall n $$

(10)

$$ x_{n,e } , x1_{n,e } , x2_{n,e} , y_{n,t,p} , r_{n} ,t_{n} \in \left\{ {0,1} \right\}\quad \forall n,t,p,e $$

(11)

$$ z_{n,p} \in \left[ {0,20} \right] \quad \forall n, t $$

(12)

$$ s_{n} \ge 0\quad \forall t $$

(13)

1.1 Indices

$n = 0, \ldots ,N$ :

Years included in the planning period, where t = 0 is the present and t = N is the terminal period,

$t = 1, \ldots ,20$ :

Weeks included in a crop year,

$a \in \left\{ {gp1,gp2,gp3} \right\}$ :

Levels of disease pressure

$p \in \left\{ {p0, p1} \right\}$ :

Type of treatment which can be chosen by the winegrower, where p₀ is a contact treatment and p₁ a systemic treatment,

$e \in \left\{ {B, C^{ - } , C, C^{ + } , D} \right\}$ :

Different PT equipments

1.2 Parameters

$w$ :

Discount rate,

$\text{Pr}(a)$ :

Probability for level of disease pressure a,

$rdtT0_{a}$ :

Percentage of the objective yield obtained if any treatment are realized for the level of disease pressure a,

$ita_{a,t}$ :

Percentage of the objective yield earned if a contact treatment is realized in the week t for the level of disease pressure $a$,

$v$ :

Production value,

$Y$ :

Objective yield of the winegrower,

$area$ :

Size in hectare of the winegrowing farm,

$varCost$ :

Variable costs which depend on income,

$opc$ :

Sum of other products, subsidies and expenses,

$Eco_{e}$ :

Percentage of plant protection products savings (or losses avoided),

$productPrice_{p}$ :

Cost per hectare of the p treatment products (copper at the end of the period),

$fuelPrice_{p}$ :

Cost per hectare of the fuel used for the p treatment,

$fongiPrice$ :

Cost per hectare of the other fungicide products (powdery mildew, grey rot),

$COidiumFuel$ :

Cost per hectare of the fuel used for the powdery mildew treatments,

$CBotrytisFuel$ :

Cost per hectare of the fuel used for the Grey rot treatment,

$cdc$ :

Cost per hectare of a chemical weeding program,

$cdm$ :

Cost per hectare of a mechanical weeding program,

$chc$ :

Cost per hectare of an insecticide program,

$ccs$ :

Cost per hectare of a sexual confusion program,

$i$ :

Saving rate,

$maintenanceCost_{e}$ :

Repair and maintenance costs for equipment e,

$minCons$ :

Household consumption of the year,

${Cmat}_{{e}}$ :

Initial purchase cost for equipment $e$,

$R_{e} = \frac{{{\text{Cmat}}_{\text{e}} \times {\text{tx}} \times (1 + {\text{tx}})^{\text{N}} }}{{(1 + {\text{tx}})^{\text{N}} - 1}}$ :

Reimbursement cost of the loan made for purchasing equipment e

1.3 Decision variables

x _n,e , x1 _n,e , x2 _n,e :

Binary investment variables: x _n,e  = 1 if the winegrower invests in the equipment e the year n or if he has already invested in this equipment a previous year and 0 otherwise, x1 _n,e  = 1 if the winegrower purchase the equipment e without borrowing the year n (or a previous year), 0 otherwise and x2 _n,e  = 1 if the equipment e is bought with a loan

y _n,t,p :

Binary treatment decision variables: y _n,t,p  = 1 if the winegrower realizes a p treatment in the t week of the year n

z _n,p :

Number of p treatments realized the year n

r _n :

Binary variables: r _n  = 1 if the winegrower doesn’t use any herbicide (mechanical weeding) the year n and 0 otherwise

t _n :

Binary variables: t _n  = 1 if the protection against moths is carried out by sexual confusion the year n and 0 if it is by insecticides

s _n :

Savings realized the year n

Appendix 2

See Tables 7, 8 and 9.

Table 7 FADN data (averages by sub-region with standard deviation in italic characters)

Table 8 Pesticide average practices and related pesticides costs within the Bordeaux region

Table 9 Characteristics of the main active ingredients used in Bordeaux

Appendix 3

See Figs. 9 and 10.