Firm-embedded Productivity and Cross-country Income Differences Tables

Table A2: Estimates of sectoral elasticities β j . no controls +k n /yn + hn Coef. S.E Coef. S.E Agriculture and Mining -0.08 0.04 -0.09 0.04 Construction -0.21 0.04 -0.21 0.04 Electricity -0.12 0.02 -0.13 0.02 Food and Beverage -0.18 0.03 -0.19 0.03 Textiles, Apparel and Wood -0.26 0.05 -0.29 0.05 Chemicals, Petroleum and Plastic -0.22 0.04 -0.23 0.04 Basic Metals -0.12 0.02 -0.12 0.03 Electrical Equipment and Machinery -0.21 0.03 -0.21 0.03 Transport Equipment and Other Manufacturing -0.31 0.03 -0.32 0.03 Wholesale Trade and Retail Trade -0.18 0.05 -0.20 0.04 Transportation and Storage -0.06 0.05 -0.07 0.05 Information -0.28 0.05 -0.29 0.05 Financial and Insurance Services 0.05 0.03 0.04 0.02 Other goods Manufacturing Services Support Services -0.15 0.03 -0.15 0.02 Accommodation and Recreation -0.20 0.05 -0.22 0.04 Real Estate -0.18 0.04 -0.19 0.04 Health -0.16 0.04 -0.15 0.04 Education -0.04 0.05 -0.05 0.06 Other Sectors Notes: OLS estimates from Equation (23) by 2-digit sector. Standard errors in parentheses. 2 Table A3: Number of observations, R-squared, and mean squared errors. N R2 MSE Baseline 49,811 0.70 1.43 I. Other outcome variables Employment Value Added 41,697 27,271 0.76 0.75 1.31 1.30 II. Alternative assumption on technology transfer costs 70,353 0.72 1.46 III. Keeping MNEs with firm-sector FE belonging to: 2nd to 9th Decile 3rd to 8th Decile 4th to 7th Decile 5th to 6th Decile 38,652 27,275 16,218 6,120 0.74 0.81 0.89 0.97 1.06 0.80 0.55 0.28 IV. Keeping MNEs operating in: at least 3 countries at least 5 countries at least 10 countries 38,709 26,298 11,682 0.66 0.62 0.58 1.43 1.42 1.34 V. Other Robustness: Aggregation at 4-digit NAICS industries Excluding Real Estate, Health, and Education Excluding MNEs that do not appear in ORBIS every year between 2010-2016 Controlling for differences in GDP per-worker between source and host country Controlling for bilateral tax treaties (BTT) between source and host country Excluding gravity controls 59,088 47,584 32,396 48,955 49,811 50,649 0.63 0.70 0.72 0.70 0.70 0.70 1.54 1.43 1.34 1.43 1.43 1.44 Notes: Number of observations, R2 , and mean squared errors for the regressions presented in the paper. I. refers to alternative firm’s outcome variables. II. refers to our alternative specification in Equation (31), which includes data from parent firms. III. refers to keeping firms in the specified deciles of the distribution of the MNE-sector fixed effects. IV. refers to keeping firms that have affiliates in at least as many countries as reflected by the threshold. V. refers to the additional robutstness in Section 5.4. 3 Table A4: Contribution of aggregate firm-embedded productivity, by year. All firms Countries (#) Constant Sample 0.28 (0.15) 0.35 (0.10) 0.32 (0.09) 0.34(0.08) 0.36 (0.10) 0.35 (0.10) 0.38 (0.11) 0.28 (0.11) 0.32 (0.10) 0.33 (0.10) 0.34 (0.10) 0.34 (0.10) 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Countries (#) cov(∆yn ,∆φ̃n ) var (∆yn ) cov(∆yn ,∆φ̃n ) var (∆yn ) 15 24 25 25 25 25 25 27 27 27 27 27 0.20 (0.11) 0.24 (0.08) 0.26 (0.08) 0.31 (0.09) 0.29 (0.09) 0.31 (0.10) 0.33 (0.09) 0.34 (0.09) 0.37 (0.09) 0.39 (0.09) 0.41 (0.09) 15 24 24 24 24 24 24 24 24 24 24 Notes: Slopes of a bivariate OLS regression of ∆φ̃n on ∆yn . A country is required to have estimates of firmembedded productivity in at least 10 sectors to construct ∆φ̃n . Each sector is required to have observations of three or more foreign affiliates. The last two columns use only firms (BVDIDs) that are available in ORBIS in every year from 2010 to 2016. 4 Figure A1: Country effects: Alternative dependent variables. employment value added EE SI LV LT H R BG FI SE PT G R C Z H U D K SK AT N L R O X PL BE M B ES G IT KR FR JP D E -2 -1 0 1 2 3 sales Note: Red dots are OLS estimates of ∆An from Equation (19) using data on revenue shares. Blue and Green dots are OLS estimates of ∆An using employment and value added shares, respectively. Bars reflect 95-percent confidence intervals, clustered at the country level. 4 Table A5: Output per-worker and firm-embedded productivity, by country. Country ISO ∆yn ∆φ̃n Austria Belgium Bulgaria Czech Rep. Germany Denmark Estonia Spain Finland France (ref) UK Greece Croatia Hungary Italy Japan Korea Lithuania Latvia Mexico Netherlands Poland Portugal Romania Sweden Slovenia Slovakia AT BE BG CZ DE DK EE ES FI FR GB GR HR HU IT JP KR LT LV MX NL PL PT RO SE SI SK -0.02 -0.03 -0.93 -0.46 -0.05 -0.07 -0.61 -0.09 -0.10 0.00 -0.16 -0.43 -0.45 -0.67 -0.03 -0.21 -0.29 -0.58 -0.62 -0.85 -0.08 -0.43 -0.54 -0.50 -0.09 -0.49 -0.50 -0.20 -0.16 -0.35 -0.27 0.06 -0.32 -0.49 -0.06 -0.22 0.00 -0.02 -0.24 -0.34 -0.29 0.04 0.09 0.02 -0.48 -0.42 -0.11 -0.21 -0.13 -0.24 -0.22 -0.22 -0.37 -0.33 manu f ∆φ̃nserv -0.20 -0.15 -0.35 -0.20 0.13 -0.41 -0.53 -0.01 -0.13 0.00 0.00 -0.28 -0.38 -0.24 0.08 0.31 0.15 -0.52 -0.55 -0.02 -0.11 -0.11 -0.20 -0.20 -0.22 -0.43 -0.29 -0.18 -0.16 -0.31 -0.27 0.00 -0.27 -0.40 -0.04 -0.25 0.00 -0.05 -0.21 -0.34 -0.32 0.04 -0.05 -0.10 -0.41 -0.37 -0.15 -0.24 -0.13 -0.22 -0.17 -0.21 -0.32 -0.28 ∆φ̃n Notes: Numbers underling Figures 3 and 5. Column 3 shows the country’s output per worker relative to France, ∆yn , Column 4 shows the country’s aggregate firm-embedded productivity, ∆φ̃, and Columns 5 and 6 show the country’s firm-embedded productivity for the Manufacturing and the Service sector, respectively. 5 Figure A2: Dev. accounting: Manufacturing sectors. 0.5 NL GR DK LV SK BG HR HR HU HU LT DE SI EE SK LV CZ PL PT PT PL CZ DE LT FI FI NL MX DK SI HU BG HR LV EE LV EE GR HR GR SI PL PT RO EE PT CZ DEIT KR FR KR DEIT ES LT SK ES SK CZ LT SI PL BESE FI GB FI GB BESE NL AT DK HU RO -1.0 -1.0 BG ∆ϕ̃n: 0.36 (0.10) ∆z̃n: 0.64 (0.10) -1.0 -0.5 0.0 ∆yn -1.5 -1.5 AT NL DK RO BE SE AT ES ES KR GBFRIT KR GB BE RO AT GR SE ∆ϕ̃n, ∆z̃n -0.5 0.0 ∆ϕ̃n, ∆z̃n -0.5 0.0 0.5 1.0 Textiles, Apparel and Wood 1.0 Food and Beverage 0.5 MX BG ∆ϕ̃n: 0.13 (0.07) ∆z̃n: 0.87 (0.07) -1.5 -1.0 0.0 0.5 1.0 Basic Metals 1.0 Chemicals, Petroleum and Plastic -0.5 ∆yn GR NL BE ∆ϕ̃n, ∆z̃n -0.5 0.0 SE BG EE LV EE LV BG CZ HR CZ MX PL SI HU PT HU SK SK PT SI PL MX 0.5 LT JP FI IT AT DEKR GB GR ES FR KR RO RO GR DE FI ATJP IT SE BE NL DK LT EE LV AT NLJP DK LT ∆ϕ̃n, ∆z̃n -0.5 0.0 0.5 DK SKFI SI HR CZ BG RO PT RO HU CZ BG PT HR SI PL SKFI LV BE SE MX DEES ITES IT DE KR GB FR GB SE MX BE NLAT JP GR DK EE -1.0 ∆ϕ̃n: 0.27 (0.09) ∆z̃n: 0.73 (0.09) -1.0 -0.5 ∆yn 0.0 -1.5 -1.5 -1.0 LT 0.5 -0.5 0.0 ∆yn 0.5 1.0 0.5 0.5 JP -1.0 BG DK KR NL -0.5 ∆yn 0.0 -1.5 ∆ϕ̃n: 0.40 (0.12) ∆z̃n: 0.60 (0.12) -1.0 RO LV BG BG MX -1.5 SE JP KR ∆ϕ̃n, ∆z̃n -0.5 0.0 NL KR -1.0 ∆ϕ̃n, ∆z̃n -0.5 0.0 GR LT PL CZ HULV HR PT SK RO SI SI HR EE RO PT EE SKLV CZ GR HU LT PL BG DK DE BEAT GB FI ES SE FR FI AT SEES BE DE GB IT DK JP IT MX -1.5 -1.0 Transport Equipment and Other Manufacturing 1.0 Electrical Equipment and Machinery ∆ϕ̃n: 0.54 (0.13) ∆z̃n: 0.46 (0.13) 0.5 PT EE EE HR HR PL LT PT RO SI SI LT PL MX NL FIHU CZ SK CZ HU SK NL FI AT BE ITGB ES FR DE DE ES ITGBAT KR SE BE JP MX DK LV ∆ϕ̃n: 0.47 (0.08) ∆z̃n: 0.53 (0.08) -1.5 -1.0 ∆yn -0.5 0.0 Notes: Each circle (square) represents a country. The figures plot the decomposition in Equation (15) at j j j the sectoral level. ∆yn is plotted in the x-axis and ∆z̃n and ∆φ̃n are plotted in the y-axis for j = two-digit manufacturing sectors. 6 Figure A3: Dev. accounting: Service sectors. 1.0 Transportation and Storage 1.0 Wholesale Trade and Retail Trade 0.5 0.5 GR HU BG BG RO LV SK GR HR SK GR IT BE ∆ϕ̃n: 0.23 (0.08) ∆z̃n: 0.77 (0.08) -1.0 -0.5 0.0 ∆yn -1.5 -1.5 HR HR 0.5 IT IT ES BE AT NL GR -1.0 -0.5 0.0 ∆yn 0.5 1.0 1.0 MX EE EE KR SI HR HU HU HR BG BG SI KR SK SK GB AT CZ ES PL ES CZ GB AT FI PT DK GRFI PT DK BE RO SE DE JP IT IT FR RO SE DE BE NL LT LV -0.6 -0.4 ∆yn -0.2 FR AT KR PL HUSI IT GB DE DE GB IT PT 0.0 NL BE ES DK GR JP FI BGRO LV SK HR EE LT NL BE SE DK ES AT PLKR HUSI CZ PT SE MX CZ -1.0 -1.5 ∆ϕ̃n: 0.30 (0.07) ∆z̃n: 0.70 (0.07) -0.8 LV SKRO FI BG JP GR EE LT ∆ϕ̃n, ∆z̃n -0.5 0.0 LT LV 0.5 0.5 HR -1.0 ∆ϕ̃n, ∆z̃n -0.5 0.0 ES Financial and Insurance Services NL -1.5 LVEE MXRO CZ MXRO CZ LVEE BE AT ∆ϕ̃n: 0.16 (0.08) ∆z̃n: 0.84 (0.08) Information ∆ϕ̃n: 0.31 (0.13) ∆z̃n: 0.69 (0.13) -0.5 0.0 0.5 ∆yn 1.0 ∆ϕ̃n, ∆z̃n -0.5 0.0 LT LV MX BG BG HU PT HU LV LT 0.5 EE AT PL DK RO HRNL SE JP GR FR SI CZSK DE DE KR GB ES GB JP SE PL KR NL RO CZSK AT SI GR FI HRDK EE BE IT SI FI ∆ϕ̃n, ∆z̃n -0.5 0.0 0.5 1.0 Accommodation and Recreation 1.0 Support Services IT BE KR BG HU EE EE LT LV LT LV HU KR DK NL HR FI ROGR CZ SE GB PT DE FR JP SK PTROGR PL MX GB FI NL MX PL SKJP SE CZHR DK SI BE AT IT ES ESIT AT BE BG -1.0 -1.0 MX ∆ϕ̃n: 0.27 (0.08) ∆z̃n: 0.73 (0.08) -1.5 -1.0 -0.5 ∆yn 0.0 -1.5 -1.5 HU BG HU BG LT DK SE SI PT SK FI GBKR DE JP FR KR PL GB PL DE SE FI PT JP DK SI SK LT -1.0 LV IT NL ATSE PLMX FR MX PL ATSENL -1.0 HU RO LT FI DK EE JP GBSI ES KRDE ES KRDE JP CZ PT DK CZ PT FI SI GB LT EE NL ∆ϕ̃n, ∆z̃n -0.5 0.0 ∆ϕ̃n, ∆z̃n -0.5 0.0 BE 0.5 ∆ϕ̃n: 0.29 (0.09) ∆z̃n: 0.71 (0.09) -1.0 -0.5 ∆yn 0.0 0.5 Notes: Each circle (square) represents a country. The figures plot the decomposition in Equation (15) at the j j j sectoral level. ∆yn is plotted in the x-axis and ∆z̃n and ∆φ̃n are plotted in the y-axis for j = two-digit service sectors. 7 EE SI LV LT R BG H FI SE PT G R C Z H U D K SK AT N L R O BE M X PL B ES G IT KR FR JP D E -2 -1 0 1 2 3 4 Figure A4: Country effects: Alternative specification of the technology transfer costs. Note: Red dots are our baseline OLS estimates of ∆An . Blue dots are the OLS estimates of ∆Pn from Equation (31). Bars reflect 95-percent confidence intervals, clustered at the country level. A Data Appendix Firm level data: In this section we describe the construction of our sample using ORBIS. We start by dropping those firms with revenues below 100,000 USD. We also drop firms that only report information from consolidated accounts, as well as firms with only “limited financials” (LF) information. From the remaining sample, we exclude firms operating in “Public Administration”, "Extraterritorial Organizations", and "Activity of Households" sectors. The time span of our dataset is 2006-2017, but our baseline analysis uses information for 2016 since it is the latest year with the largest number of firms in ORBIS historical. A multinational enterprise (MNE) is defined as a company exerting above 50 percent of the control rights on affiliates located in more than one country. Crucially for our analysis, a MNE is defined within a given sector. In order to define a company as a MNE, we use the NAICS sector classification at three different levels of disaggregation, NAICS2 (18 industries), NAICS3 (99 industries) and NAICS4 (336 industries). Information on revenues, employment, and value-added are aggregated for all tax identification numbers in ORBIS belonging to the same corporate group and operating in the same country and sector. Therefore, in our analysis an affiliate is defined as a corporate group-country-sector triplet in which the country of location differs from the country where the headquarter is located, whereas a parent is defined as a triplet located at the headquarter’s country. Moreover, a MNE owning affiliates in multiple countries, but each operating in a different sector, will ultimately be excluded from our sample. Table A6 shows the number of affiliates and the number of parent firms in each NAICS2 8 Table A6: Number of affiliates and parents, by NAICS2. Foreign Affiliates Sales Emp. VA Other goods Agriculture and Mining Construction Electricity Manufacturing Food and Beverages Textiles, Apparel and Wood Chemicals, Petroleum and Plastic Basic Metals Electrical Equipment and Machinery Transport Equipment and Other Manufacturing Services Wholesale Trade and Retail Trade Transportation and Storage Information Financial and Insurance Services Support Services Accommodation and Recreation Other Sectors Real Estate Health Education Parents Sales Emp. VA 407 1,041 557 354 843 344 246 583 273 43 125 73 37 113 65 30 92 57 1,061 965 3,104 1,550 3,019 1,445 964 886 2,861 1,401 2,828 1,309 794 699 2,375 1,178 2,195 1,082 118 127 307 160 327 139 116 126 301 158 321 136 99 109 260 124 270 105 18,513 2,265 1,499 1,402 10,329 1,218 16,434 2,004 1,298 1,104 9,015 1,098 11,429 1,417 882 555 5,817 774 1,245 237 115 147 959 105 1,184 231 111 138 894 99 868 192 86 80 702 75 1,969 204 96 1,132 187 84 910 151 49 192 21 5 145 21 4 112 19 4 Notes: A foreign affiliate is a majority-owned firm by a company with operations in multiple countries within a given sector. Sectors roughly correspond to the 2-digit NAICS classification. sectors in our sample, including affiliates in “Other Goods” as well as in other sectors. Each column of Table A6 shows the number of affiliates and parents according to the availability of information on firm’s revenues, employment and value-added. Table A7 and Table A8 report the number of affiliates and the number of parents in each country in our sample, according to the available information from sales, employment and value added. The numbers are shown for manufacturing, services, and for all sectors. Aggregate firm-embedded productivity at the country level is constructed by calculating the weighted average of the sector level firm-embedded productivity, using countrysector level expenditure shares as weights. If a country has less than three foreign MNE affiliates in a particular sector, we exclude the country from that sector, and reweigh the remaining sectors accordingly to compute the aggregate ∆φ̃n for that country. Table A9 j reports the country-sector pairs for which we cannot compute an estimate of ∆φn for our baseline regression. 9 Table A7: Number of foreign affiliates, by country and sector. Country All Austria Belgium Bulgaria Czech Rep. Germany Denmark Estonia Spain Finland France UK Greece Croatia Hungary Italy Japan Korea Lithuania Latvia Mexico Netherlands Poland Portugal Romania Sweden Slovenia Slovakia 1,510 2,743 737 2,507 3,680 819 659 4,099 1,417 4,659 5,072 512 829 1,272 4,545 192 899 445 679 137 1,130 3,399 1,759 2,040 2,694 612 1,603 Sales Mfg. Services 293 536 119 656 1,046 151 99 819 258 1,075 1,259 74 102 306 1,176 48 291 69 60 51 260 833 278 424 419 108 334 1,141 1,973 536 1,602 2,378 581 502 2,933 1,045 3,267 3,402 398 634 827 2,997 141 592 324 543 72 805 2,238 1,304 1,365 2,064 460 1,102 Employment All Mfg. Services 1,219 2,555 711 2,389 3,620 703 612 3,909 1,143 3,638 4,690 502 776 1,172 4,279 180 694 439 658 52 1,003 992 1,651 1,934 2,526 567 1,537 271 526 119 652 1,040 151 94 817 219 950 1,231 74 99 302 1,166 47 256 69 60 24 249 293 275 416 411 106 332 895 1,866 522 1,555 2,337 502 476 2,825 848 2,528 3,144 393 609 774 2,883 130 426 318 533 20 710 617 1,249 1,329 1,967 427 1,070 Value Added All Mfg. Services 956 1,863 596 1,492 2,795 635 3,995 655 3,469 2,744 568 3,654 12 384 28 1,871 1,712 1,266 1,378 345 996 242 434 108 499 921 138 809 139 969 881 196 1,098 4 171 2 541 275 348 205 64 279 661 1,304 437 866 1,673 454 2,855 471 2,337 1,689 310 2,359 8 208 24 1,189 1,268 788 1,091 261 621 Notes: A foreign affiliate is defined as a corporate group-country-sector triplet where the country of operation differs from the country where the headquarter is located. 10 Table A8: Number of parents, by country and sector. Country All Austria Belgium Bulgaria Czech Rep. Germany Denmark Estonia Spain Finland France UK Greece Croatia Hungary Italy Japan Korea Lithuania Latvia Mexico Netherlands Poland Portugal Romania Sweden Slovenia Slovakia 246 218 2 54 629 156 50 248 161 715 459 18 8 34 387 418 32 18 10 8 109 40 36 2 365 13 10 Sales Mfg. Services 55 67 5 192 42 5 54 45 170 91 3 3 2 118 180 13 1 2 5 10 7 7 99 2 149 125 2 45 379 101 36 156 99 446 328 12 4 28 241 225 18 15 5 1 87 29 20 2 237 11 7 All Employment Mfg. Services 226 204 2 53 627 143 45 246 145 639 425 18 8 33 376 418 29 18 10 6 92 30 36 2 348 13 9 54 66 5 192 42 5 54 44 163 89 3 3 2 118 180 12 1 2 4 9 6 7 95 2 135 118 2 45 378 92 33 156 89 398 304 12 4 27 234 225 17 15 5 1 76 20 20 2 232 11 6 All Value Added Mfg. Services 212 185 2 44 508 136 53 62 4 174 40 125 104 2 37 288 87 - - - 243 119 647 308 53 34 167 68 154 74 401 220 - - - 23 361 208 23 1 116 137 9 20 223 65 14 - - - - 2 - - - - - 21 35 2 188 10 8 1 7 39 2 17 19 2 138 8 5 Notes: A parent is defined as a corporate group-country-sector triplet located in the source country of the MNE. 11 Table A9: Countries with less than 3 affiliates, by NAICS2. Sector Country Other goods Agriculture and Mining Construction Electricity Manufacturing Food and Beverages Textiles, Apparel and Wood Transport Equipment and Other Manufacturing Services Information Others Real Estate Health Education KR, MX JP KR, MX JP, MX JP GR MX JP DK, EE, GR, JP, LV, SI AT, CZ, DK, HU, KR, NL, PT, RO, SI, SK Notes: A foreign affiliate is a majority-owned firm by a company with operations in multiple countries within a given sector. Sectors roughly correspond to the 2-digit NAICS classification. Aggregate data: In addition to the ORBIS data, to construct sales, employment, and value-added shares, we use information from KLEMS and OECD on gross output, gross value-added, and the number of employees at the country-sector level, in million of current dollars and thousands of employees, respectively. The KLEMS dataset corresponds to the statistical national accounts from their latest release in 2019. The OECD statistics come from the Dataset for Structural Analysis (STAN) and we convert the sectoral ISIC revision 4 to the sectoral classification used in KLEMS. To maximize the number of country-sector pairs in our sample, we combine some ISIC sectors into the following categories: Agriculture and Mining; Textiles, Apparel and Woods; Chemicals, Petroleum and Plastic; Electrical Equipment and Machinery; Transport Equipment and Other Manufacturing; and Accommodation and Recreation. We use the real GDP at chained PPPs in 2016 US dollars over total employment to measure output per-worker in each country from Penn World Tables (PWT, 9.1). To construct measures of output per-worker at the sectoral level we use gross value added per-worker from the KLEMS-OECD dataset that we convert to international dollars using the PPP conversion factor for GDP, measured in units of local currency per international dollars. We obtain the GDP PPP conversion factor and the share of employees compensation in value added from PWT (9.1). Finally, we obtain aggregate information for the activity of foreign affiliates for each country-sector pair in our sample from the OECD Activity of Multinational Enterprises (AMNE) dataset and the Eurostat Foreign Affiliates Statistics (FATS), for which we harmonize the sectoral classification into the 18 sectors used in our dataset. 12 B Additional statistics: two-way fixed-effect estimation Connectivity: To identify the country-sector fixed effects in Equation (19), we should perform our estimation on the largest connected set (LCS), which corresponds to the largest sample where destination countries are connected by the MNE foreign affiliates. In our case, the LCS is comprised of all 27 countries in our sample, whether using sales or employment, NAICS2 or NAICS4 sector classification.1 Nonetheless, it is still possible that countries are poorly connected, even within the LCS, if only few MNEs link them together. When only a handful of MNEs connect countries in the sample, the variance of the fixed effects will be over-estimated and spurious negative correlations can appear between country and MNE fixed effects (Andrews et al. 2008). The literature has proposed three ways in which connectivity can be improved. The first method consists in performing the estimation on the "leave-one-out" set, which is defined as the set of countries that remain connected even after any individual MNE is removed from the sample (Kline et al. 2020). We note that all countries in our sample stay connected regardless of which MNE is dropped from the set. The second method (Andrews et al., 2008) consists of restricting the sample to countries hosting MNEs that also operate elsewhere. Since we only work with MNEs, this restriction is always satisfied in our sample. The third method (Bonhomme et al., 2019) groups destination countries using k-mean clustering based on the distribution of affiliates’ market shares. This method enhances connectivity by reducing the number of country fixed effect that must be estimated. Unfortunately, its application would defeat our purpose of estimating firm-embedded productivity for each country-sector pair. Log-linearity assumption: In Section 5.3, we show that the standardized residuals are mostly flat across the MNE-sector fixed effects and country-embedded factors decilebins. A different approach to assess the additive separability assumption comes from Bonhomme et al. (2019), where each pairing of firm and country-sector is allowed to have a differential effect. This new specification replaces the additive country and MNE-sector fixed effects with an interaction between country-group and MNE-sector fixed effect. If country-MNE “match effects” are relevant in determining the assignment of MNEs to countries, then there is a potential for bias since the error term could be correlated with the country fixed effects. Table A10 shows the share of the variance explained by the country-sector fixed effects. Our results indicate that an additive model provides a very good approximation to our data: allowing interactions between MNE and country-group yields a small increase in the R-squared (Column 3) compared to an additive model that uses individual countries (Column 1) or country groups (Column 2). Also notice that the individual contributions of MNE and country effects to the variance of MNEs market shares remain almost unchanged in the additive model that uses k-country groups relative to the additive model that uses individual countries. 1 By definition, all MNEs contribute to connecting the countries where they keep operations, overcoming the usual problem of “limited mobility bias” that plagues most two-way fixed effect exercises in the labor literature. In that literature, identification is achieved by workers who switch employers over their careers (Abowd et al., 1999). 13   j Table A10: Contribution to Var sin (ω ) . Variance Decomp. j ∆Ak δ j (ω ) R2 Baseline (1) 0.27 0.45 0.72 k-means (linear) (2) 0.26 0.45 0.70 Interaction (3) 0.76 Notes: Column 1 corresponds to the additive model using individual country-sector fixed effects (baseline). Columns 2 and 3 use country-sector-group fixed effect, with k=5. The MNE-sector and the country-sectorgroup enter additively in the second column, and multiplicatively in the third column. C Extension: Intermediate inputs This section shows how to extend our framework to allow for intermediate inputs in production. We again focus on the one-sector case to facilitate the exposition. We assume that the final good can be used as an input, and that the production function for intermediate goods is h iγ Yin (ω ) = Zin Xin (ω ) Hin (ω )1−α Kin (ω )α Min (ω )1−γ . Here, the parameter γ is the value-added share and Min (ω ) represents the intermediate inputs used by producer ω in country n. The aggregate production function is 1 1 1 1 Yn = γ γ Znγ Φnγ ρ−1 [ H̄n Ln ] 1− α [ Kn ]α . We can write cross-country differences in the log of value added per-worker as ∆yn = 1 1 ∆z̃n + ∆φ̃n . γ γ (C.1) We show next how to obtain the contribution of aggregate firm-embedded productivity to cross country differences in value added per-worker, γ1 ∆φ̃n . Note that in this economy, the revenue, employment, and the value-added shares coincide and are given by Equation (16). We can thus use Equation (19) and the procedure described in Section 3.2 to estimate ∆An , which under our baseline assumption on technology transfer costs corresponds to ∆An =−∆φn . The last step is to reestimate β ≡ [1 − α] [ρ − 1] in a way that is consistent with Equation (C.1). With intermediate inputs, Equation (23) becomes inp b ∆yn = b0 + 1 ∆An + b2 Cn + un , γ 14 inp so that the coefficients in Table 1 should be interpreted as b1 = b1 γ . The contribution of firm-embedded productivity to cross-country income differences is γ1 ∆φ̃n = b1 ∆An , which coincides with the estimate used in our baseline analysis. 15 inp b1 γ ∆An =