flows of FDI. For example, the automobile industry in the United States may have adopted more robots over time, but it may also have experienced other shocks such as government bailouts. To address this possibility of reverse causality, as well as biases caused by omitted variables or measurement error, we adopt an instrumental variables approach. In doing so, we follow Artuc, Bastos, and Rijkers (2019) in using industry-level trends in robot adoption in other countries with similar levels of income as instrument for a given country’s robotization. Specifically, robot intensity is instrumented with robotization in the two most similar countries in terms of GDP per capita. This strategy follows closely that adopted by Acemoglu and Restrepo (2017) in their analysis of the local labor market impacts of robotization in the United States as well as subsequently by Artuc, Bastos and Rijkers (2019). Though not a panacea for all sources of omitted variable bias, this strategy allows us to focus on the variation that results solely from industries in which the intensity of robot use has been concurrent in the most similar economies. Further, we use the square of robot intensity in other countries with similar levels of income as an additional instrumental variable for the robots-squared term which is also potentially endogenous. We cannot formally test for the exogeneity of our instruments because the model is exactly identified. We can, however, test for instrument relevance through tests for under identification and weak identification. The instruments pass these tests in that they have explanatory power in predicting robotization.

Furthermore, both the positive linear and negative non-linear effects of robots per 1,000 workers engaged in HICs on FDI from HICs to LMICs remain intact (table 5). In fact, the quantitative impacts are somewhat larger. At the mean level of robots per 1,000 employees in the sample, the quadratic terms offsets about two-thirds of the linear effect whereby a 10 percent increase in the intensity of robot use increases the growth of FDI by 1.4 percent. While this could reflect possible measurement error, it is consistent with a large stock of FDI in a lower wage location providing a disincentive to automate at home. Now, the maximum impact of automation on the growth in FDI is at about 7.8 robots per 1,000 employees<sup>7</sup> and less than one-third of observations in the estimating sample are beyond this threshold. For much of the sample even here, therefore, further automation results in a diminishing rate of the growth of FDI, but not a decline. Beyond the threshold of 62 robots per 1,000 employees<sup>8</sup> is when the overall effect of additional automation results in a decline in FDI, but is met by less than 5 percent of the sample.<sup>9</sup> The sign and statistical significance of the coefficients remains the same when the transportation equipment sector is dropped from the estimation as well as when China is included as a source country but excluded as a destination country. These results remain qualitatively similar when robot intensity is instrumented with robotization in the four most similar countries in terms of GDP per capita (table 6).

> 7 2.06 in natural logarithm terms.

> 8 4.12 in natural logarithm terms.

> 9 These largely comprise the manufacture of transportation equipment in European countries such as Germany, France, Spain, Belgium, and Italy.

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