# **B.3 Counterfactual simulations**

## **B.3.1 Computation of production and consumption shares**

The production and consumption shares are calibrated using WIOD. The production share parameter of inputs, _αM_<sup>_m,i_,iscalculatedbydividingthestageoneexpenditurebythetotaloutput</sup> of a given industry. The labor share parameter, _αT_<sup>_m,i_,iscalibratedusingthewagebill(adjusted</sup> using equation (A14) with the equilibrium share of robots, initial wages and initial robot rental rate). The consumption share parameter, _γ_<sup>_m,i_</sup> , is calibrated using the expenditure on stage two outputs. All calibrated parameters, initial wages and robot prices are reported in Table A7.

## **B.3.2 Computation of the trade matrix**

We index South as _m_ = 1, Other as _m_ = 2 and North as _m_ = 3. We index individual countries � � with _m_ and _n_ , and country sets with _m_ and _n_ . Define _N_ 1 = 7, _N_ 2 = 1 and _N_ 3 = 9, _M_ 1 =Brazil, China, ..., _M_ 2 =Australia, Austria, ..., and _M_ 3 =Belgium, Germany, .... Let _Ys_<sup>_m,_�</sup><sup>_n,i_�</sup> denote the trade flow between _m_ � and � _n_ for industry _i_ and stage _s_ . The structure of WIOD is similar to OECD input-output tables, with multiple countries in each column and row. A row reveals how output of a given industry for a specific country is used across different columns. Take an entry from the database. If both its row and column correspond to an industry within the sector, we consider that entry as a part of the first stage output of the sector. The other entries, including those that correspond to consumption by households or government, are considered a part of second stage output. For a given entry, a country in the row is the origin country, while the country in the column is the destination country. We construct _Ys_<sup>_m,_�</sup><sup>_n,i_�</sup> for each individual country. We define the trade matrix between _m_ and _n_ as Additionally, we assume that all NT sector output is final.

## **B.3.3 Solution method**

We follow the solution methods of Caliendo and Parro (2015) and Caliendo, Dvorkin, and Parro (forthcoming), and calculate the new equilibrium after an exogenous reduction of robot prices using changes in variables from their initial values. For the purpose of the solution, we can treat first and second stage production as different industries, and impose that first stage output is only demanded by producers as intermediate inputs, while second stage output is only used for final household consumption. Our model then becomes a special case of Caliendo and Parro (2015) with additional task structure involving robots and additional fixed factors. The task structure does not affect the solution method significantly. The only difference (with regard to the solution method) is the inclusion of cost reduction variable Ω<sup>_m,i_</sup> , and the related labor demand variable, Ξ<sup>_m,i_</sup> . Given the exogenous effective robot rental rate,<sup>_<u>φ</u>_</sup> _<u>R</u>_<sup>_i_</sup> _φ_<sup>_i_</sup> _L_<sup>_wR_, it is straightforward to solve for Ω</sup><sup>_m,i_</sup> using (11). We then plug the change in the cost reduction parameter into the equation used in the solution. Similarly, we can solve for the labor demand variable Ξ<sup>_m,i_</sup> using (12). The changes in labor allocations can be easily solved jointly with the changes in equilibrium wages, productivity and cost reduction using (21b). Apart from the variables Ξ<sup>_m,i_</sup> and Ω<sup>_m,i_</sup> , the solution is similar to other papers in the literature, and therefore we omit further details.

54