Yields are estimated using a linear expression: $$log y_t = \alpha + \gamma g_t + \kappa k_t + \omega w_t + \tau t$$

where $y_t$ are the yields, in crop-specific units, per acre; $g_t$ and $k_t$ are growing-degree days and extreme degree-days, with crop-specific limtis; $w_t$ is the season-cumulative water deficit; and $t$ is the year. Greek letters denote calibrated coefficients.

Currently, nation-wide coefficients for each crop are determined by a pooled regression of available data. These are then combined with county-specific for counties with observed data, according to: $$\beta \sim \mathcal{N}\left(\frac{\frac{\hat\beta}{\hat\sigma^2} + \frac{\bar\beta}{\bar\sigma^2}}{\frac{1}{\hat\sigma^2} + \frac{1}{\bar\sigma^2}}, \frac{1}{\frac{1}{\hat\sigma^2} + \frac{1}{\bar\sigma^2}}\right)$$

where $\hat\beta$ is a given county unpooled coefficient (one of $\alpha$, $\gamma$, $\kappa$, $\omega$, and $\tau$), $\hat\sigma$ is its standard error, and $\bar\beta$ and $\bar\sigma$ are the corresponding national pooled coefficients.

This will be replaced with county-specific parameters from the hierarchical method, when these are available.

The list (and order!) of crops is defined in `world.jl`

:

```
In [1]:
```crops = ["alfalfa", "otherhay", "Barley", "Barley.Winter", "Maize", "Sorghum", "Soybeans", "Wheat", "Wheat.Winter"]

```
Out[1]:
```

The key crop-specific definitions are listed in the table below.

```
In [2]:
```using DataFrames
readtable("../prepare/agriculture/cropmapping.csv")[:, [:crop, :unit, :yieldfile, :deficitfile, :eddprefix1, :eddprefix2, :gdd0, :kdd0, :notes]]

```
Out[2]:
```

In the model, the coefficients on temperature, $\gamma$ and $\kappa$ are not used, and $\tau$ is not used (but all regressions have time centered on 2000). Instead, irrigated regions are assumed to have $\bar{y}_t = e^\alpha$. Rainfed areas have yields $\ddot{y}_t = e^{\alpha + \omega (m - p_t)}$, where $m$ is the water requirement of each crop, determined as the maximum water deficit observed for that crop from Naresh's data. $p_t$ is the season-total precipitation, with seasons currently corresponding to timesteps (typically 6 months).

The water requirements by crop are below, in m.

```
In [5]:
```todata = "../data"
include("../src/Agriculture.jl")
water_requirements

```
Out[5]:
```

The total production for a county is $$q_t = \bar{y}_i \bar{a}_i + \ddot{y}_i \ddot{a}_i$$

where $\bar{a}_i$ is the area used for irrigated production, and $\ddot{a}_i$ is the area used for rainfed irrigation.

The Agriculture component also defines cultivation costs, below, as USD per acre, from some source.

```
In [6]:
``````
cultivation_costs
```

```
Out[6]:
```

```
In [ ]:
```