2.1.1. Choice Model

There are several ways to motivate the empirical strategy. Due to the nature of the survey and structure of the data, a scenario that allows for irrigators to adopt a single practice or a number of them simultaneously is needed. Hence, a model of individual practice adoption is adequate. An irrigator *i* adopts a water conservation practice *w* if the grower expects to receive a greater utility from using the practice (*Uiw*) than they would not using it (*UiNg*). The probability of adopting practice *w* is the probability that *y*∗ *iw* = *Uiw* − *UiNg* > 0 and depends on a vector of *n* identified factors *Xi*. Following Maddala [27], *y*∗ *<sup>i</sup>* is a latent, unobservable variable defined by the regression relationship:

$$y\_{iw}^{\*} = \beta^{\prime} X\_i + u\_i \tag{2}$$

where *ui* is the error term. The variable that is actually observed is whether a practice is adopted (*y* = 1) or not (*y* = 0).

From these relationships, the probability that any given practice *w* is adopted can be estimated using probit with the assumption that *ui* follows a normal distribution:

$$\Pr(y\_w = 1) = \Pr\left(\sum\_{j} \beta\_{jw} X\_j > 0\right) = \Phi\left(\sum\_{j} \beta\_{jw} X\_j\right),\tag{3}$$

where Φ(·) is the cumulative normal distribution function.

To predict the effect a change in the value of a variable would have on the probability of adopting a given practice, the marginal effects are calculated as:

$$\frac{\partial}{\partial \mathbf{x}\_{ik}} \Phi \left( \mathbf{X}\_{i}^{\prime} \boldsymbol{\beta} \right) = \boldsymbol{\phi} \left( \mathbf{X}\_{i}^{\prime} \boldsymbol{\beta} \right) \boldsymbol{\beta}\_{k\prime} \tag{4}$$

where *φ*(·) is the normal probability density function. This marginal effect is denoted as *dy*/*dx* in the results.
