27 deviation of the logarithm of landholdings across farmers in district _i_ , and _μ_ ˆ _i_ as: _μ_ ˆ _i_ = ln( _Li/Ni_<sup>_F_)</sup><sup>_−_</sup> ˆ _σLi_<sup>2</sup><sup>_/_2, where</sup><sup>_Li_is total arable land (in ha) and</sup><sup>_N F_</sup> _i_<sup>the number of farmers in district</sup><sup>_i_.65</sup>

## **VI.B Step 2: Inversion to Recover Unobservables**

Equipped with estimates for the model’s parameters, we proceed to recover the remaining unobserved variables needed to fully characterize the 2019 baseline economy. We use the process commonly known as model inversion, which can be informally described as plugging observed variables into the model’s equilibrium system of equations and then solving the system to back out unobserved variables.<sup>66</sup> More formally:

**Definition 2 (Inversion)** _Given the model’s parameters, observed exogenous variables (_ **_N_**<sup>_m_</sup> _,_ **_N_**<sup>_F_</sup> _,_ **_L_** _,_ **_τ_** _,_ **_s_** _), and observed endogenous variables (_ **_w_** _,_ **_Q_** _,_ **_p_**<sup>**_A_**</sup> _,_ **_p_**<sup>**_f_**</sup> _), an_ **_inversion_** _is a set of unobserved exogenous variables (_ **_T_** _,_ **_b_** _,_ **_N_**<sup>_e_</sup> _,_ **_F_** _) and unobserved endogenous variables (t,_ **_p_**<sup>_−_</sup> _,_ **_P_** _,_ **_R_** _,_ **_E_** _,_ **_X_** _,_ **_β_** _) such that the resulting set of endogenous variables is an equilibrium of the economy with the resulting set of exogenous variables and with no QRs._

Intuitively, the inversion process picks values for unobserved variables to rationalize the data. For example, consider equation (6), which expresses equilibrium agricultural production ( _Qik_ ) as a function of productivity ( _Tik_<sup>_A_), prices, and land mass. Suppose that, at a given moment, the observed</sup> _Qik_ is “too high” in the sense that the equation’s left-hand side is larger than its right-hand side. The inversion process will then increase productivity _Tik_<sup>_A_enough to balance the equation.</sup> Appendix E provides details on the inversion procedure. We use data from 2019, which we choose as our baseline year because it precedes the 2021 fertilizer ban and other unusual events, such as the Covid-19 pandemic, and also due to household data availability.<sup>67</sup>

# **VII Counterfactuals**

In this section, we use the estimated model to investigate the GE effects of Sri Lanka’s fertilizer import ban (and of other potential alternative policies). Through counterfactual exercises, we demonstrate how government policies like import restrictions limit fertilizer access and how fertilizer subsidies in turn mediate the distributional impacts of such limitations. The counterfactuals

> 65Landholdings are defined as the total amount of land owned by a household (excluding land with housing built on top) and are measured in ha. The standard deviation is computed using only households with positive landholdings. We use 2016 HIES data because landholding data was not available in the more recent 2019 HIES. See Appendix C.C for more details on the estimation of the land distribution parameters.

> 66Alternatively, inversion consists of recovering unobserved from observed variables using the model’s structure.

> 67We include in the analysis the eight crops ( _K_ = 8) for which there is data on fertilizer intensity and district-level producer prices, namely: cinnamon, cloves, groundnut, maize, onions, potatoes, rice, and tea.