where TFPR is the measure of productivity described above and T<sup>UP</sup> is a measure of input tariffs at the sector level, which is described below. All our specifications include firm- and time-fixed effects, and sector time trends. We also control for output tariffs (T<sup>O</sup> ), share of exports at the firm level, and lagged FDI flows in the sector. The model is estimated as a standard linear fixed effects estimator, all independent variables are lagged on period, and standard errors are clustered at the sector level.

A second specification (equation 2) considers FDI in upstream sectors. We first control for FDI in upstream manufacturing sectors, , also described below, to account for other trade<sup>,MM</sup> liberalization reforms that could potentially confound the effects of input tariffs. Second, we include TTF<sup>U</sup> a measure of FDI in upstream service sectors, , to capture vertical linkages from the openness<sup>,SS</sup> of services to FDI. We are particularly interested in the effect of this variable as listed firms are more TTF<sup>U</sup> likely to outsource services. Indeed, typical services feasible for outsourcing, such as sales, distribution, and other administrative costs, represent a significant share of production costs (11 percent) for these publicly listed firms.

where weights, _w_ , are fixed over time and constructed from the 2007 GTAP input-output (IO) table as input shares, which give a sense of the importance of each upstream sector in terms of input and service costs. Hence, the expectation is that firms using certain inputs or services more intensively benefit from the integration of these sectors. Our measures of upstream tariffs and FDI are, therefore, a form of Bartik instrument (in a reduced form setting) where IO weights reflect the differential exposure of downstream sectors to common shocks in upstream sectors. In this context, the main identification assumption is that input shares are exogenous to changes in TFPR, not to its level (Goldsmith-Pinkham et al. 2020). The use of IO table-based weights has several advantages. Weights are at the sector level and are based on both imported and domestic inputs. This reduces possible endogeneity concerns about productivity-related input adjustments at the firm level. Sectors are also aggregated at two-digit level (or higher level),<sup>13</sup> which limit input substitutability. In addition, the inclusion of both imported and domestic inputs when computing input shares ensures that weights reflect actual sector-level input requirements rather than tariff-induced input choices, which could bias results. Indeed, this latter concern is further mitigated by the use of predetermined fixed weights, i.e. before the tariff changes used in our estimations took place. When computing upstream FDI penetration, we separate manufacturing and service sectors.

# **_Endogeneity of trade policy and FDI penetration_**

> 13 For input tariffs we maintained the sector disaggregation of the original GTAP input-output table, consisting of 57 sectors. To compute upstream FDI, IO sectors were aggregated to match FDI data that were provided for 16 manufacturing sectors and 6 service sectors.

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