and the consumer price index in country _m_ is equal to

# **B.1 Data sources and description**

This appendix provides further details about the data used in the empirical analysis. The set of developed countries included in our estimation sample is: Belgium, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Netherlands, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Sweden, United Kingdom and United States. For each of these countries, the estimation sample includes all years for which the IFR data are available during the period 1995-2015. We examine bilateral trade flows between these countries and all non-OECD countries included in BACI. Table A1 reports the final list of sectors used and their correspondence with the sectors defined in the original data sets.

**Industrial robots** : The stock of industrial robots by industry, country and year comes from the International Federation of Robotics (IFR). These data are based on yearly surveys of robot suppliers, and currently cover 75 countries (about 90 percent of the industrial robots market). The IFR measures deliveries of “multipurpose manipulating industrial robots” based on the definitions of the International Organization for Standardization. The data are disaggregated roughly at the three-digit level for manufacturing and roughly at the two-digit level for non-manufacturing. We focus only on tradable sectors, which are listed in Table A1.

To calculate a measure of the robot stock per sector, we use the perpetual inventory method assuming a depreciation rate of 10%, following Graetz and Michaels (2018).<sup>18</sup> We initialize the series using the IFR measure of the stock of robots per sector in 1993. For countries for which the 1993 sectoral breakdown of the stock of robots is not available, we initialize the series using the initial robots stock for the first year for which it is available.<sup>19</sup> The IFR data are regarded as the best source of information on industrial robots (Graetz and Michaels, 2018; Acemoglu and Restrepo, 2017b). Nonetheless, these data have some limitations. First, about 30 percent of industrial robots are not classified into any industry. Following Acemoglu and Restrepo (2017b), we allocate these unclassified robots to industries in the same proportion as in the classified data. Second, the IFR data do not cover “dedicated industrial robots”, which are defined as automatically controlled machines for only one industrial application. Third, the time coverage of the IFR data varies substantially across countries. Moreover, a detailed sectoral breakdown of the robot stock and deliveries is not always available for all years even when countries are included in the IFR, so that our panel is unbalanced.<sup>20</sup>

> 18While the IFR data contain measures of the robot stock, we prefer to use estimates based on the perpetual inventory method because the IFR measures are based on the assumption that the service lifetime of a robot is exactly 12 years, exhibiting no depreciation whatsoever for the first 12 years and losing all their functionality after the 12th year.

> 19For countries for which we have data on the aggregate (i.e. country-wide) stock of robots in years prior to having the sectoral breakdown, we deflate the initial stock per sector as follows. We first construct a deflator by dividing the sum of the IFR robot stock reported for each sector by the aggregate robot stock calculated using the perpetual inventory method. We then use this deflator to obtain the sector-specific series.

> 20Up until 2010 robots used in Mexico and Canada are reported as being used in the United States. To account for the attendant over-reporting of robots usage in the US, we first calculate what share of robots in the NAFTA area were being used in the United States in 2011 and subsequently correct the US series assuming that during the period prior to 2011 robots usage in the US, Canada and Mexico grew at equal pace.

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