90 _γk_<sup>_n_,</sup><sup>_γ_</sup> _k_<sup>_l}k_) from Table III. Additionally, we use data on crop-specific fertilizer subsidy rates (</sup><sup>_{sk}k_)</sup> and crop-district-specific prices ( _{pik}i,k_ ), production ( _{Qik}i,k_ ), and cultivated area ( _{Lik}i,k_ ). And we use district-level annual wages ( _{wi_<sup>_m, w_</sup> _i_<sup>_e}i_), and numbers of mobile workers and farmers</sup> ( _{Ni_<sup>_m_,</sup><sup>_N F_</sup> _i_<sup>_}i_).Bilateral transportation costs (</sup><sup>_{τ A_</sup> _ni,k_<sup>_}n,i,k_,</sup><sup>_{τ M_</sup> _ni_<sup>_}n,i_) are computed using the coeffi-</sup> cients estimated in Section VI.A.2.

For the RoW, we use data on 2019 crop prices ( _{pRoW,k}k_ ), production ( _{QRoW,k}k_ ), and cultivated area ( _{LRoW,k}k_ ), as well as on the 2019 wage ( _wRoW_ ). We assume that the RoW has no estate workers ( _NRoW_<sup>_e_=0) and that its tea sector uses mobile workers instead, and we rely on the</sup> measures of the number of workers ( _NRoW_<sup>_m_) and farmers (</sup><sup>_N F_</sup> _RoW_<sup>) described in Appendix A.K. All</sup> monetary variables expressed in USD are converted into LKR using the 2019 exchange rate. The international price of fertilizer, _p_<sup>_f_</sup> _RoW_<sup>=0.31 USD/kg,from our trade data (see Appendix A.B), is</sup> converted to LKR using the 2019 exchange rate.<sup>119</sup>

# **F Equivalent Variation**

Since we are interested in the welfare effects of the fertilizer import ban, we use our estimated QSM of trade and agriculture to estimate such effects in Section VII. However, to do that we must first address some difficulties that emerge when using PIGL preferences. Careful inspection of equation (12) shows that indirect utility can be negative for some combinations of prices and income.<sup>120</sup> As a result, it is not straightforward to express utility as “real income” (i.e. nominal income divided by a price index), as it is often done for other classes of preferences such as CES. Therefore, we propose an alternative welfare metric to measure changes in welfare between any two equilibria, namely, the EV.

Suppose we are comparing a given initial equilibrium to a given final equilibrium. Starting from the initial equilibrium, the EV for a given agent is defined as the change in income that would leave that agent with the same level of utility as she has in the final equilibrium if prices were held constant at their initial levels. Formally, the EV for that hypothetical agent living in region _n_ is given by: where _v_ 1 is the agent’s utility in the final equilibrium, _y_ 0 is her income in the initial equilibrium, ( _Pn,_<sup>_A_</sup> 0<sup>_, P_</sup> _n,_<sup>_M_</sup> 0<sup>)arethepricesindicesintheinitialequilibrium,and</sup><sup>_V−_1istheinverseoftheindirect</sup> utility function (12) with respect to the income argument ( _y_ ).<sup>121</sup> This formula shows that the EV

> 119See Appendix A for more details on the data that is mentioned in this section.

> 120 For example, if _ν >_ 0 and _P A > P M_ , then utility will be negative for a sufficiently small level of income _y_ .

> 121Simple algebraic manipulation shows that the inverse of the indirect utility function (with respect to the income <u>1 1</u> argument _y_ ) is: _V_<sup>_−_1</sup> ( _v_ ; _P_<sup>_A_</sup> _, P_<sup>_M_</sup> ) = _η η_ ( _v_ + _ν_ ln( _P_<sup>_A_</sup> _/P_<sup>_M_</sup> )) _η_ ( _P_<sup>_A_</sup> )<sup>_φ_</sup> ( _P_<sup>_M_</sup> )<sup>1</sup><sup>_−φ_</sup> . For definitions of the agricultural and