On the Measurement of Upstreamness and Downstreamness in Global Value Chains

Transcription

1 On the Meaurement of Uptreamne and Downtreamne in lobal Value Chain Pol Antrà Harvard & NBER Davin Chor NU Dec 2017 Antrà, Chor On the Meaurement of VC Poitioning 1 / 48

2 Overview Backdrop: Production procee are now global in nature, with intermediate input obtained from multiple countrie and indutrie along global value chain (VC). purred an increaed interet in undertanding: (i) Where are countrie and indutrie located along VC? (ii) What are the underlying determinant of country poitioning along VC? Antrà, Chor On the Meaurement of VC Poitioning 2 / 48

3 Overview Backdrop: Production procee are now global in nature, with intermediate input obtained from multiple countrie and indutrie along global value chain (VC). purred an increaed interet in undertanding: (i) Where are countrie and indutrie located along VC? (ii) What are the underlying determinant of country poitioning along VC? On (i): Recent work employing technique and concept from input-output analyi to provide decriptive anwer. (Fally 2012, Antrà et al. 2012, Antrà and Chor 2013, Alfaro et al. 2017, Miller and Temurhoev 2017, Wang et al. 2017) Antrà, Chor On the Meaurement of VC Poitioning 2 / 48

4 Overview Backdrop: Production procee are now global in nature, with intermediate input obtained from multiple countrie and indutrie along global value chain (VC). purred an increaed interet in undertanding: (i) Where are countrie and indutrie located along VC? (ii) What are the underlying determinant of country poitioning along VC? On (ii): An emerging body of general equilibrium model, though not eay to tructurally dicipline thee model. (Yi 2003, Kohler 2004, Yi 2010, Harm et al. 2012, Baldwin and Venable 2013, Cotinot et al. 2013, Antrà and Chor 2013, Fally and Hillberry 2014, Kikuchi et al. 2017, Tyazhelnikov 2017, Alexander 2017, Antrà and de ortari 2017, de ortari 2017) Antrà, Chor On the Meaurement of VC Poitioning 2 / 48

5 What we do Thi paper: Attempt to provide a bridge between thee two trand of work. 1. Review four meaure that have been ued to capture countrie and indutrie VC poitioning (that are baed on pattern of intermediate input and final-ue purchae) 2. Document how thee meaure have evolved over time in the World Input-Output Databae (WIOD). Will report everal alient pattern and puzzling correlation 3. Develop an extenion of Caliendo and Parro (2015) that can match all entrie of a WIOD (i.e., the full pattern of intermediate input purchae and final-ue expenditure) 4. Perform model-baed counterfactual to explore the role of: (i) trade cot movement; and (ii) change in final conumption hare, in explaining the evolution of VC poitioning. Antrà, Chor On the Meaurement of VC Poitioning 3 / 48

6 Roadmap for thi talk 1. Motivation and Introduction 2. Review of VC Meaure 3. The Evolution of VC Poitioning from tructural Model 6. Counterfactual 7. Concluion Antrà, Chor On the Meaurement of VC Poitioning 4 / 48

7 Meaure of VC Poitioning Antrà, Chor On the Meaurement of VC Poitioning 5 / 48

8 World Input-Output Table (WIOT) VC meaure are defined with a WIOT in mind: Unit of analyi: Indutry r in country i J countrie and indutrie/ector J by J block of intermediate-ue value J by J block of final-ue value Input ue & value added Final ue Total ue Country 1 Country J Country 1 Country J Indutry 1 Indutry Indutry 1 Indutry 1 Indutry 1 Z11 11 Z11 Z1J 1J 11 1J 1 Z F F Y Intermediate Country 1 Z11 r Z1J Indutry Z11 1 Z11 Z1J 1J 11 1J 1 Z F F Y input Zij r Fij Yi Indutry 1 ZJ1 11 ZJ1 ZJJ ZJJ FJ1 FJJ YJ upplied Country J ZJ1 r ZJJ Indutry 1 ZJ1 1 ZJ1 ZJJ ZJJ FJ1 FJJ YJ Value added V A 1 1 V A 1 V A j V A 1 J V A J ro output Y1 1 Y1 Yj YJ 1 YJ Antrà, Chor On the Meaurement of VC Poitioning 6 / 48

9 World Input-Output Table (WIOT) VC meaure are defined with a WIOT in mind: Row: Ue of output from indutry r in country i Column: Value-add and input-ue in the production of indutry in country j Input ue & value added Final ue Total ue Country 1 Country J Country 1 Country J Indutry 1 Indutry Indutry 1 Indutry 1 Indutry 1 Z11 11 Z11 Z1J 1J 11 1J 1 Z F F Y Intermediate Country 1 Z11 r Z1J Indutry Z11 1 Z11 Z1J 1J 11 1J 1 Z F F Y input Zij r Fij Yi Indutry 1 ZJ1 11 ZJ1 ZJJ ZJJ FJ1 FJJ YJ upplied Country J ZJ1 r ZJJ Indutry 1 ZJ1 1 ZJ1 ZJJ ZJJ FJ1 FJJ YJ Value added V A 1 1 V A 1 V A j V A 1 J V A J ro output Y1 1 Y1 Yj YJ 1 YJ Antrà, Chor On the Meaurement of VC Poitioning 6 / 48

10 Uptreamne from Final Ue Define the direct requirement coefficient: a r ij = Z r ij /Y j. tart from the output accounting identity: Y r i = =1 j=1 aij r Yj + Fi r. (1) Iterate to obtain: Y r i = F r i + =1 j=1 a r ij F j + =1 j=1 t=1 k=1 a r ij a t jkf t k +... (2) Antrà, Chor On the Meaurement of VC Poitioning 7 / 48

11 Uptreamne from Final Ue Define the direct requirement coefficient: a r ij = Z r ij /Y j. tart from the output accounting identity: Y r i = =1 j=1 aij r Yj + Fi r. (1) Iterate to obtain: Y r i = F r i + =1 j=1 a r ij F j + =1 j=1 t=1 k=1 a r ij a t jkf t k +... (2) imple meaure: Final ue hare in gro output F /O = F r i /Y r i (3) Antrà, Chor On the Meaurement of VC Poitioning 7 / 48

12 Uptreamne from Final Ue Richer meaure: Taking into account production-taging ditance from final ue U r i = 1 F i r + 2 Yi r =1 j=1 Yi r aij r Fj + 3 =1 j=1 t=1 k=1 Yi r a r ij a t jkf t k +... (4) Remark: U r i 1 U r i larger if ue occur on average more tage uptream from final demand Computation: Numerator = [I A] 2 F Denominator = [I A] 1 F where A i the J by J matrix of the aij r (direct requirement matrix); and F i the J by 1 vector of the Fi r. Antrà, Chor On the Meaurement of VC Poitioning 8 / 48

13 Uptreamne from Final Ue An alternative recurive formulation: Ũ r i = 1 + =1 j=1 b r ij Ũ j (5) o indutrie are uptream if they ell to indutrie that are themelve relatively uptream. Equivalence reult from Antrà et al. (2012): Ũ r i = U r i Antrà, Chor On the Meaurement of VC Poitioning 9 / 48

14 Downtreamne from Primary Factor Define: b r ij = Z r ij /Y r i. Output accounting identity from the perpective of ource of value-added: Y j = r=1 i=1 b r ij Y r i + VA j. Iterate to obtain: Y j = VA j + r=1 i=1 b r ij VA r i + r=1 i=1 t=1 k=1 b tr ki b r ij VA t k +... Antrà, Chor On the Meaurement of VC Poitioning 10 / 48

15 Downtreamne from Primary Factor Define: b r ij = Z r ij /Y r i. Output accounting identity from the perpective of ource of value-added: Y j = r=1 i=1 b r ij Y r i + VA j. Iterate to obtain: Y j = VA j + r=1 i=1 b r ij VA r i + r=1 i=1 t=1 k=1 b tr ki b r ij VA t k +... imple meaure: Value-added hare in gro output VA/O = VA j /Y j (6) Antrà, Chor On the Meaurement of VC Poitioning 10 / 48

16 Downtreamne from Primary Factor Richer meaure: D j = 1 VA j Y j + 2 r=1 i=1 b r ij VA r i Y j + 3 r=1 i=1 t=1 k=1 Yj b tr ki b r ij VA t k +... (7) Remark: D j 1 D j larger if ue occur on average more tage downtream from primary factor Computation: Numerator = [I B] 2 V Denominator = [I B] 1 V where B i the J by J matrix of the b r ij (allocation matrix); and V i the J by 1 vector of the VA j. Antrà, Chor On the Meaurement of VC Poitioning 11 / 48

17 Downtreamne from Primary Factor Alternative recurive formulation: D j = 1 + i=1 r=1 aij r D i r. (8) o indutrie are downtream if they purchae input from indutrie that are themelve relatively downtream. Reult from Fally (2012) and Miller and Temurhoev (2017): D j = D j Antrà, Chor On the Meaurement of VC Poitioning 12 / 48

18 Aggregation Four VC meaure at the country-indutry level: F /O, U, VA/O, D. Two approache to aggregate to the country level: (i) Take a O-weighted average of the country-indutry VC meaure (ii) Collape the WIOT to a country-by-country I-O table, and compute the VC meaure Both approache clearly equivalent for F /O and VA/O. Not equivalent, but very highly correlated for U and D. Antrà, Chor On the Meaurement of VC Poitioning 13 / 48

19 Aggregation Four VC meaure at the country-indutry level: F /O, U, VA/O, D. Two approache can be applied to aggregate to the world level a well: Both approache clearly equivalent for F /O and VA/O till. But at the world level, aggregate finale expenditure equal aggregate payment to primary factor, o: F /O = VA/O Far le obviou, but O-weighted U and D at the world level are alo equal (Miller and Temurhoev 2017): Ū = D Thu: At the world-level, view thee more a meaure of production complexity, rather than poitioning. Antrà, Chor On the Meaurement of VC Poitioning 13 / 48

20 VC Poitioning from (from the World Input-Output Databae) Antrà, Chor On the Meaurement of VC Poitioning 14 / 48

21 To the WIOD Data... Ue 2013 edition of the World Input-Output Databae, c.f. Timmer et al. (2015) J = 41 countrie = 35 indutrie/ector 16 year: A lot of data point! Z r ij matrix in any year: (35 41) 2 = 2, 059, 225 F r ij matrix in any year: = 58, 835 Computational detail: Apply a net inventorie correction Antrà et al. (2012) Antrà, Chor On the Meaurement of VC Poitioning 15 / 48

22 For the World a a whole... F /O and VA/O on the decline U and D on the rie Uphot: VC appear to be lengthening F/O over time (World) Year U over time (World) Year Antrà, Chor On the Meaurement of VC Poitioning 16 / 48

23 Country-level VC Meaure over Time imilar pattern preent acro different percentile of the country-level ditribution of the repective VC meaure F/O over time (country percentile) VA/O over time (country percentile) Year Year U over time (country percentile) D over time (country percentile) Year Year Antrà, Chor On the Meaurement of VC Poitioning 17 / 48

24 Country-level VC Meaure over Time (cont.) triking tability and peritence in rank order Table 1 Country-Level VC Poition by Rank (Top and Bottom Five) Rank: F/O (1995) F/O (2011) Rank: VA/O (1995) VA/O (2011) 1. China Luxembourg China China Luxembourg China Czech Rep Luxembourg lovakia Korea lovakia Korea Czech Rep Taiwan Etonia Czech Rep Ruia Czech Rep Romania Bulgaria Denmark Brazil Autria Brazil Brazil UA Turkey UA Turkey Mexico Brazil Mexico reece Cypru reece Cypru Cypru reece Cypru reece Rank: U (1995) U (2011) Rank: D (1995) D (2011) 1. Cypru reece Cypru reece reece Cypru Brazil Cypru Turkey Mexico Turkey Mexico Brazil UA reece Brazil Denmark Brazil Autria UA Ruia Czech Rep Romania Luxembourg Luxembourg Taiwan Etonia Bulgaria Czech Rep Korea lovakia Czech Rep lovakia Luxembourg Czech Rep Korea China China China China Note: Rank order baed on the repective VC meaure computed at the country-level, i.e., baed on the WIOD aggregated to a country-by-country panel of Input-Output table. The top and bottom five countrie in the rank order are reported, for both 1995 and Antrà, Chor On the Meaurement of VC Poitioning 18 / 48

25 Country-indutry VC Meaure over Time Focuing on the pure within-component of the variation: till find F /O and VA/O on the decline; U and D on the rie VCj,t Table 2 = β 1Year t + FEj + ɛ j,t. (9) Evolution of VC Meaure within Country-Indutrie over Time Dependent variable: F/O j,t F/O j,t VA/O j,t VA/O j,t (U) j,t (U) j,t (D) j,t (D) j,t (1) (2) (3) (4) (5) (6) (7) (8) Year * *** *** *** [0.0004] [0.0005] [0.0015] [0.0017] (Dum: Year=1996) [0.0025] [0.0026] [0.0083] [0.0079] (Dum: Year=1997) [0.0020] [0.0020] [0.0068] [0.0062] (Dum: Year=1998) ** *** * [0.0010] [0.0015] [0.0032] [0.0043] (Dum: Year=1999) *** *** *** [0.0004] [0.0005] [0.0010] [0.0025] (Dum: Year=2000) *** *** *** [0.0014] [0.0016] [0.0045] [0.0044] (Dum: Year=2001) *** ** *** [0.0020] [0.0021] [0.0065] [0.0053] (Dum: Year=2002) *** *** [0.0024] [0.0022] [0.0069] [0.0054] (Dum: Year=2003) *** ** *** [0.0027] [0.0022] [0.0082] [0.0059] (Dum: Year=2004) *** *** *** [0.0030] [0.0025] [0.0100] [0.0079] (Dum: Year=2005) * *** *** *** [0.0031] [0.0032] [0.0099] [0.0101] (Dum: Year=2006) ** *** *** *** [0.0033] [0.0036] [0.0117] [0.0115] (Dum: Year=2007) *** Antrà, Chor *** On the Meaurement of *** VC Poitioning *** 19 / 48

26 Correlation in VC Meaure acro Countrie In an autarkic world, aggregate F and VA would be equal a a national accounting identity. Would expect a perfect poitive correlation in F /O and VA/O acro countrie Converely, would expect that a trade cot fall and production become more fragmented, thi tight correlation between F /O and VA/O would weaken. Logic hould carry over to correlation between U and D a well, ince F /O and U are negatively correlated (a are VA/O and D) Antrà, Chor On the Meaurement of VC Poitioning 20 / 48

27 Puzzling Correlation Correlation between F /O and VA/O (a well a between U and D) how no ign of weakening! F/O (1995) CYP RC TUR BRA MLT RoWMEX DNK DEU AUT PRT EPFRA IND ITABRCAN HUN BR IRL JPN UA VN LTU IDN LVA NLD ROU TWNPOL WE ETKOR BEL AU FIN RU CZE CHN VK LUX F/O (2011) RC CYP MEX BRA UA LTU IND FRA ITA EP ROU PRT TUR DNK BR DEU CAN JPN POL VNIDN MLT LVA AUT AU HUN BEL FINET NLD RoW VK WE BR IRL CZE RU TWN KOR CHN LUX VA/O (1995) VA/O (2011) U (1995) VK CZE LUX RU FINAU BEL KOR ET NLD IDN BR HUN CAN EP AUT DEU FRA BR LVA JPNITA IND POL LTU IRL ROU WE TWN VN DNK UA MEXRoW BRA MLT PRT TUR RC CYP CHN U (2011) LUX KOR TWN RU CZE BR AU AUT ET FIN IRL WE BEL HUN CAN DEU IDN LVA MLT VK NLDPOL BR DNK RoW VN JPNITA EP LTU FRA TUR PRT ROU IND BRA MEX UA CYP RC CHN D (1995) D (2011) Antrà, Chor On the Meaurement of VC Poitioning 21 / 48

28 Puzzling Correlation Correlation between F /O and VA/O (a well a between U and D) how no ign of weakening! Correlation: F/O on VA/O Year lope coefficient: F/O on VA/O Year Antrà, Chor On the Meaurement of VC Poitioning 21 / 48

29 Puzzling Correlation Correlation between F /O and VA/O (a well a between U and D) how no ign of weakening! Correlation: U on D Year lope coefficient: U on D Year Antrà, Chor On the Meaurement of VC Poitioning 21 / 48

30 Note: The ample comprie all countrie (41), indutrie (35), and year (17) in the WIOD. tandard error are multi-way clutered by country and indutry; ***, **, and * denote ignificance Antrà, at the Chor 1%, 5%, and On 10% the level Meaurement repectively. The of VC dependent Poitioning variable are VC 22 / 48 Puzzling Correlation (at the country-indutry level) Poitive lope coefficient even in the country-indutry VC meaure F /Oj,t = β 1VA/O Table j,t 3 + FE j + FE + ɛ j,t, (10) Correlation between Country-Indutry VC Meaure (1995 and 2011) Dependent variable: F/O j,t F/O j,t F/O j,t F/O j,t F/O j,t F/O j,t (1) (2) (3) (4) (5) (6) VA/O j,t *** ** *** *** *** [0.1815] [0.1924] [0.0543] [0.1647] [0.1740] [0.0527] Country FE? N Y Y N Y Y Indutry FE? N N Y N N Y Obervation 1,417 1,417 1,417 1,414 1,414 1,414 R Dependent variable: U j,t U j,t U j,t U j,t U j,t U j,t (7) (8) (9) (10) (11) (12) D j,t *** ** *** *** *** *** [0.1640] [0.1902] [0.0604] [0.1454] [0.1698] [0.0617] Country FE? N Y Y N Y Y Indutry FE? N N Y N N Y Obervation 1,435 1,435 1,435 1,435 1,435 1,435 R

31 Two Candidate Explanation Antrà, Chor On the Meaurement of VC Poitioning 23 / 48

32 1. Trade Cot Could be that trade cot remain high in abolute level Ue the Head-Rei index to get an empirical handle on thi: τ r ij = τ rf ij = ( Z r ij Zji r Zii r Zjj r ( F r ij Fji r F r ii F r jj ) 1 2θ, and (11) ) 1 2θ. (12) (Aume either: (i) θ = 5; or (ii) ue Caliendo-Parro (2015) ectoral-level etimate.) Antrà, Chor On the Meaurement of VC Poitioning 24 / 48

33 1. Trade Cot Average τ remain high at the end of the period... However: Clear overall downward trend particularly in the earlier half of the period Iceberg τ Aume: θ=5 Input-ue mean τ Final-ue mean τ Year Antrà, Chor On the Meaurement of VC Poitioning 25 / 48

34 1. Trade Cot Decline in trade cot borne out robutly in regreion Table 4 Head-Rei Trade Cot for Intermediate Input over Time ln τij,t r = β 0Year t + FEij r + ɛ r ij,t, and (13) Dependent variable: log Trade Cot for Intermediate Input (1) (2) (3) (4) (3) (4) Indutrie: All All ood ood ervice ervice Year *** *** *** [0.0022] [0.0024] [0.0026] Dum: Year= * [0.0093] [0.0108] [0.0142] Dum: Year= *** *** *** [0.0048] [0.0075] [0.0061] Dum: Year= *** *** *** [0.0039] [0.0077] [0.0055] Dum: Year= *** *** *** [0.0048] [0.0074] [0.0063] Dum: Year= *** *** *** [0.0056] [0.0079] [0.0086] Dum: Year= *** *** *** [0.0067] [0.0093] [0.0099] Dum: Year= *** *** *** [0.0064] [0.0079] [0.0107] Dum: Year= *** *** *** [0.0100] [0.0123] [0.0154] Dum: Year= *** *** *** [0.0097] [0.0115] [0.0155] Dum: Year= *** *** *** [0.0109] [0.0147] [0.0159] Dum: Year= *** *** *** [0.0107] Antrà, Chor [0.0154] On the Meaurement of VC Poitioning [0.0152] 26 / 48

35 1. Trade Cot Decline in trade cot borne out robutly in regreion Table 5 Head-Rei ln τij,t rf Trade = Cot β 0Year for t Final-Ue + FEij r over + ɛtime r ij,t. (14) Dependent variable: log Trade Cot for Final ood/ervice (1) (2) (3) (4) (3) (4) Indutrie: All All ood ood ervice ervice Year *** *** *** [0.0039] [0.0041] [0.0051] Dum: Year= * [0.0332] [0.0278] [0.0550] Dum: Year= *** *** *** [0.0104] [0.0146] [0.0115] Dum: Year= *** *** *** [0.0099] [0.0116] [0.0168] Dum: Year= *** *** ** [0.0193] [0.0090] [0.0441] Dum: Year= *** *** *** [0.0257] [0.0162] [0.0456] Dum: Year= *** *** *** [0.0233] [0.0245] [0.0360] Dum: Year= *** *** *** [0.0179] [0.0238] [0.0359] Dum: Year= *** *** *** [0.0251] [0.0251] [0.0423] Dum: Year= *** *** *** [0.0304] [0.0303] [0.0435] Dum: Year= *** *** *** [0.0323] [0.0372] [0.0435] Dum: Year= *** *** *** Antrà, Chor [0.0307] On the Meaurement [0.0372] of VC Poitioning [0.0425] 26 / 48

36 2. ectoral Compoition Key obervation: ervice tend to feature a higher hare of output going traight to final demand, a well a a higher hare of ue of primary factor In other word: ervice are in hort chain, while good are in long chain Detail If ome countrie are more pecialized in good and other in indutrie, thi can account for the poitive cro-country correlation between F /O and VA/O (a well a between U and D) Could be conitent with a decline in trade cot, if thi decline reinforce pre-exiting pattern of pecialization Antrà, Chor On the Meaurement of VC Poitioning 27 / 48

37 2. ectoral Compoition A ecular rie over time in ervice hare of gro output... BUT: ome ign that pattern of pecialization in ervice have become more concentrated over time CHN IND IDN ROU BR TUR KOR TWN MEX IRL RoW VK POL HUN RU LTU VN FIN CZE MLT ET ITA BRA PRT CAN LVA EP DEU JPN WE BEL NLD BR AUT RC DNK FRA UA AU CYP LUX CHN KOR TWN IDN HUN IND RoW CZE MEX TUR RU POL BR IRL ROU DEU VK BRA CAN FIN LTU JPN VN WE ITA AUT NLD BEL EP FRA ET PRT AU DNK UA MLT RC LVA BR CYP LUX ervice hare of ro Output, De-meaned (1995) ervice hare of ro Output, De-meaned (2011) Antrà, Chor On the Meaurement of VC Poitioning 28 / 48

38 2. ectoral Compoition At the country-indutry level: Poitive lope coefficient between VC meaure i driven by ervice F/O VA/O ood only (2011) F/O VA/O ervice only (2011) F/O VA/O All indutrie (2011) Antrà, Chor On the Meaurement of VC Poitioning 29 / 48

39 2. ectoral Compoition At the country-indutry level: Poitive lope coefficient between VC meaure i driven by ervice U D ood only (2011) U D ervice only (2011) U D All indutrie (2011) Antrà, Chor On the Meaurement of VC Poitioning 29 / 48

40 2. ectoral Compoition hare of ervice in final expenditure ha been on the rie, while that for good ha fallen Table 6 lnfinal-ue αj,t = Expenditure β 0Year t hare + FEj over + Time ɛ j,t. (15) Dependent variable: log Expenditure hare, j (1) (2) (3) (4) (5) (6) Indutrie: All All ood ood ervice ervice Year *** [0.0025] [0.0037] [0.0025] Dum: Year= [0.0148] [0.0183] [0.0200] Dum: Year= * [0.0117] [0.0127] [0.0137] Dum: Year= *** ** [0.0081] [0.0158] [0.0059] Dum: Year= *** *** *** [0.0022] [0.0077] [0.0036] Dum: Year= *** *** [0.0060] [0.0130] [0.0086] Dum: Year= *** *** [0.0099] [0.0119] [0.0155] Dum: Year= *** ** [0.0144] [0.0104] [0.0231] Dum: Year= *** ** [0.0159] [0.0134] [0.0222] Dum: Year= *** *** [0.0185] [0.0250] [0.0212] Dum: Year= *** *** [0.0216] [0.0344] [0.0232] Dum: Year= ** ** [0.0234] [0.0396] [0.0245] Dum: Year=2007 Antrà, Chor On the Meaurement ** of VC Poitioning ** 30 / 48

41 2. ectoral Compoition hare of ervice in input purchae ha been on the rie, while that for good ha fallen Table 7 ln γj,t r Input-Ue = β 0Year hare t + over FETime j r + ɛ r j,t, (16) Dependent variable: r log Input-Ue hare, ɣ j (1) (2) (3) (4) (5) (6) Indutrie: All All ood ood ervice ervice Year ** *** [0.0031] [0.0043] [0.0031] Dum: Year= [0.0160] [0.0186] [0.0142] Dum: Year= ** [0.0134] [0.0167] [0.0131] Dum: Year= *** *** [0.0110] [0.0186] [0.0130] Dum: Year= *** *** [0.0043] [0.0087] [0.0087] Dum: Year= *** *** *** [0.0032] [0.0091] [0.0062] Dum: Year= *** *** *** [0.0119] [0.0103] [0.0157] Dum: Year= ** *** *** [0.0154] [0.0116] [0.0193] Dum: Year= *** *** [0.0183] [0.0166] [0.0209] Dum: Year= *** *** [0.0230] [0.0276] [0.0242] Dum: Year= ** *** [0.0260] [0.0372] [0.0250] Dum: Year= ** *** [0.0269] [0.0415] [0.0235] Dum: Year=2007 Antrà, Chor On the Meaurement ** of VC Poitioning *** 31 / 48

42 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Model Antrà, Chor On the Meaurement of VC Poitioning 32 / 48

43 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Recap: Caliendo-Parro (2015) eneral equilibrium model of cro-country production and trade with inter-ectoral linkage, that build on the Eaton-Kortum machinery etup: i and j denote countrie; ij ubcript indicate a hipment from i to j r and denote indutrie; r upercript indicate a hipment from r to Preference: Cobb-Dougla where C j u(c j ) = =1 ( C j ) α j (17) i a ector- compoite over a unit meaure of varietie (ee below) Antrà, Chor On the Meaurement of VC Poitioning 33 / 48

44 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Recap: Caliendo-Parro (2015) eneral equilibrium model of cro-country production and trade with inter-ectoral linkage, that build on the Eaton-Kortum machinery etup: i and j denote countrie; ij ubcript indicate a hipment from i to j r and denote indutrie; r upercript indicate a hipment from r to Production: Cobb-Dougla over labor and intermediate from all ector yj (ω ) = zj (ω ) ( lj (ω ) ) 1 r=1 γj r r=1 ( M r j (ω ) ) γ r j (18) where z j (ω ) are iid draw from a Fréchet ditribution: exp{ T j z θ }. Antrà, Chor On the Meaurement of VC Poitioning 33 / 48

45 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Recap: Caliendo-Parro (2015) eneral equilibrium model of cro-country production and trade with inter-ectoral linkage, that build on the Eaton-Kortum machinery etup: i and j denote countrie; ij ubcript indicate a hipment from i to j r and denote indutrie; r upercript indicate a hipment from r to CE aggregator for C j and M r j compoite: ( ) σ /(σ 1) Qj = qj (ω ) 1 1/σ dω (19) Iceberg trade cot: τ r ij 1. Antrà, Chor On the Meaurement of VC Poitioning 33 / 48

46 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Caliendo-Parro (2015): Equilibrium ytem πij Ti (ci τij ) θ = J k=1 T k (c k τ (20) kj ) θ c j = Υ j w 1 r=1 γj r j P r j = A r [ i=1 T r i r=1 ( c r i τij r ) θ r ( P r j ) γ r j (21) ] 1/θ r (22) =1 X j = X j = r=1 γ r j i=1 =1 i=1 X r i π r ji } {{ } Y j r X j π ij = + α j (w j L j + D j ) (23) =1 i=1 X i π ji + D j (24) Antrà, Chor On the Meaurement of VC Poitioning 34 / 48

47 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Limitation Trade hare π ij do not differ by the identity of the purchaer, i.e., whether thi i ued to meet final demand or a an intermediate input. When mapping to the data: π r ij = F r ij J k=1 F r kj = Z ij r J r k=1 Z kj for j = 1,..., J. (25) Would not be atified for a generic WIOT Why thi matter: A VC meaure are computed from final-ue and intermediate-ue hare, deirable to have a model that can match thee hare exactly Antrà, Chor On the Meaurement of VC Poitioning 35 / 48

48 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual A More Flexible Model Conider trade cot from country i to j in indutry r: Now allow thee to differ by identity of the purchaing entity. If ued a an input by another indutry : τ r ij If ued to meet final demand: τ rf ij Implie that trade hare expreion (and hence price indice) will depend on the identity of the purchaer. New equilibrium ytem: π r ij = π rf ij = Ti r (ci r τij r ) θr J k=1 T k r (cr k τ (26) kj r) θr Ti r (ci r τij rf ) θr J k=1 T k r (cr k τ (27) kj rf ) θr Antrà, Chor On the Meaurement of VC Poitioning 36 / 48

49 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual A More Flexible Model c j = Υ j w 1 r=1 γj r j [ Pj r = A r Ti r i=1 r=1 ( c r i τij r ) θ r ( P r) γ r j j (28) ] 1/θ r (29) i=1 r=1 =1 πij r γj r Y j = [ ( ) ] 1/θ r θ r Pj rf = A r Ti r ci r τij rf i=1 (30) ( ) α Pj F = Pj F /αj j (31) k=1 Y r j + w j L j = =1 π F jk α k (w k L k + D k ) + i=1 r=1 =1 πji r γi r r=1 k=1 Y r i + π r jk γ r k Y r k (32) =1 i=1 π F ji α i (w i L i + D i ) (33) Antrà, Chor On the Meaurement of VC Poitioning 37 / 48

50 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Mapping to the WIOD Recover final expenditure hare and input ue hare parameter in a tandard way: J r γj r i=1 Z ij = α j = Ỹ j (34) J i=1 F ij r=1 ṼAr j + D j (35) Antrà, Chor On the Meaurement of VC Poitioning 38 / 48

51 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Mapping to the WIOD Recover final expenditure hare and input ue hare parameter in a tandard way: J r γj r i=1 Z ij = α j = Ỹ j (34) J i=1 F ij r=1 ṼAr j + D j (35) Theoretical reult: uppoe that thee and all other underlying model parameter other than the trade cot are given. Then, there exit a unique et of value of τij r and τij rf that will exactly match the oberved Z ij r and F ij. Uphot: The more flexible model can now exactly match all entrie of a WIOT. Antrà, Chor On the Meaurement of VC Poitioning 38 / 48

52 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Counterfactual Change via the Hat Algebra Caveat: While the et of τij r and τij rf exit that fully match a WIOT, thee are computationally not eay to back out. Intead: Turn to hat-algebra technique. Re-expre the equilibrium ytem of equation in change, following Dekle et al. (2008) and Caliendo and Parro (2015). Denote change in variable X by X ; and percentage change by ˆX = X /X. To evaluate counterfactual change, need only: (i) the initial trade hare, π r ij and π rf ij ; (ii) the demand and technological Cobb-Dougla parameter γ r j and α j ; (iii) a vector of θ r. Antrà, Chor On the Meaurement of VC Poitioning 39 / 48

53 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Counterfactual Change via the Hat Algebra ĉ j ˆπ r ij = ˆπ rf ij = ( ) ĉr i ˆτ ij r θ r ˆP j r ( ĉr i ˆτ rf ij ˆP rf j = (ŵ j ) 1 r=1 γj r ˆP r j = ˆP rf j = [ i=1 [ i=1 π r ij π rf ij ) θ r r=1 (ĉr i ˆτ ij r ) θ r ) γ r (ˆP j r j ] 1/θ r (36) (37) (38) (39) ( ) ] 1/θ r θ r ĉi r ˆτ ij rf (40) Antrà, Chor On the Meaurement of VC Poitioning 40 / 48

54 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Counterfactual Change via the Hat Algebra ( ) ( ) ( Yj = πjk F (α k ) (ŵ k w k L k + D k ) + k=1 r=1 k=1 π r jk ) γ r k (Y r k ) (41) ( i=1 r=1 =1 π r ij ) γ r j ( ) Yj r + ŵj w j L j = ( ) γ r i πji r (Yi r ) (42) i=1 r=1 =1 ( ) + πji F (α i ) (ŵ i w i L i + D i ) =1 i=1 Antrà, Chor On the Meaurement of VC Poitioning 41 / 48

55 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Counterfactual Antrà, Chor On the Meaurement of VC Poitioning 42 / 48

56 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual Two exercie 1. Initialize to 1995 and holding deficit contant evaluate whether change in the τ and/or change in the α can explain oberved evolution of VC meaure 2. Initialize to 2011 holding deficit contant explore how change in the τ and/or change in the α are projected to affect the future movement in country VC poitioning Note: Not meant to be a definitive decompoition. Put aide change in the T, ince harder to dicipline thi empirically Alo: hat algebra in the current Cobb-Dougla framework not equipped to handle change in γ. Antrà, Chor On the Meaurement of VC Poitioning 43 / 48

57 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual 1. Change from 1995 to 2011 Conider ˆτ r ij and ˆτ rf ij from (from Head-Rei, for good v ervice). Conider actual change in the final-ue hare for the α. et: θ = 5. Table 8 Evaluating the Role of Change in Trade Cot and Expenditure hare A: Country-level VC meaure Mean F/O Mean VA/O Correlation F/O, VA/O Mean U Mean D Correlation U, D Real wage change (Min, Mean, Max) 1995 baeline (from data) baeline (from data) to 2011 hift Change trade cot (1.003, 1.104, 1.512) Change expenditure hare (0.993, 1.001, 1.017) Both change (1.002, 1.093, 1.434) B: Country-indutry VC meaure Regre F/O j,t on VA/O j,t (Coefficient on VA/O j,t ) Regre U j,t on D j,t (Coefficient on D j,t ) 1995 baeline (from data) *** ** *** ** *** baeline (from data) *** *** *** *** *** *** to 2011 hift Change trade cot *** *** * *** ** *** --- Change expenditure hare *** *** * *** *** *** --- Both change *** *** ** *** *** *** --- Country FE? N Y Y N Y Y --- Indutry FE? N N Y N N Y --- Note: Quantitative evaluation baed on the multi-country, multi-indutry general equilibrium model decribed in ection 5.2. Panel A report moment and correlation for the country-level VC meaure, a well a real wage change. Panel B report the partial correlation between the country-indutry level VC meaure baed on the Antrà, Chor On the Meaurement of VC Poitioning 44 / 48

58 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual 1. Change from 1995 to 2011 Oberved trade cot tend to weaken the key cro-country correlation between F /O and VA/O (a well a that between U and D) Converely, rie in importance of ervice (relative to good) move thee Table 8 correlation in the Evaluating oppoite the Role of Change direction in Trade Cot and Expenditure hare A: Country-level VC meaure Mean F/O Mean VA/O Correlation F/O, VA/O Mean U Mean D Correlation U, D Real wage change (Min, Mean, Max) 1995 baeline (from data) baeline (from data) to 2011 hift Change trade cot (1.003, 1.104, 1.512) Change expenditure hare (0.993, 1.001, 1.017) Both change (1.002, 1.093, 1.434) B: Country-indutry VC meaure Regre F/O j,t on VA/O j,t (Coefficient on VA/O j,t ) Regre U j,t on D j,t (Coefficient on D j,t ) 1995 baeline (from data) *** ** *** ** *** baeline (from data) *** *** *** *** *** *** to 2011 hift Change trade cot *** *** * *** ** *** --- Change expenditure hare *** *** * *** *** *** --- Both change *** *** ** *** *** *** --- Country FE? N Y Y N Y Y --- Indutry FE? N N Y N N Y --- Note: Quantitative evaluation baed on the multi-country, multi-indutry general equilibrium model decribed in ection 5.2. Panel A report moment and correlation for the country-level VC meaure, a well a real wage change. Panel B report the partial correlation between the country-indutry level VC meaure baed on the Antrà, Chor On the Meaurement of VC Poitioning 44 / 48

59 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual 1. Change from 1995 to 2011 Lower panel: Thee two force go ome way toward accounting for the rie in the lope-coefficient between the country-indutry VC meaure Table 8 Evaluating the Role of Change in Trade Cot and Expenditure hare A: Country-level VC meaure Mean F/O Mean VA/O Correlation F/O, VA/O Mean U Mean D Correlation U, D Real wage change (Min, Mean, Max) 1995 baeline (from data) baeline (from data) to 2011 hift Change trade cot (1.003, 1.104, 1.512) Change expenditure hare (0.993, 1.001, 1.017) Both change (1.002, 1.093, 1.434) B: Country-indutry VC meaure Regre F/O j,t on VA/O j,t (Coefficient on VA/O j,t ) Regre U j,t on D j,t (Coefficient on D j,t ) 1995 baeline (from data) *** ** *** ** *** baeline (from data) *** *** *** *** *** *** to 2011 hift Change trade cot *** *** * *** ** *** --- Change expenditure hare *** *** * *** *** *** --- Both change *** *** ** *** *** *** --- Country FE? N Y Y N Y Y --- Indutry FE? N N Y N N Y --- Note: Quantitative evaluation baed on the multi-country, multi-indutry general equilibrium model decribed in ection 5.2. Panel A report moment and correlation for the country-level VC meaure, a well a real wage change. Panel B report the partial correlation between the country-indutry level VC meaure baed on the Antrà, Chor On the Meaurement of VC Poitioning 44 / 48

60 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual 2. Forward Projection Conider a further decline in trade cot and/or the α for another 16 year, baed on per annum rate of change from earlier regreion etimate Interetingly: a decline in trade cot that i biaed toward ervice appear to induce greater pecialization in ervice for countrie with pre-exiting comparative advantage... and thi actually trengthen the correlation between F /O and VA/O (and between U and D) Table 9 Counterfactual Projection Country-level meaure Mean F/O Mean VA/O Correlation F/O, VA/O Mean U Mean D Correlation U, D Real wage change (Min, Mean, Max) 2011 baeline (from data) to 2011 hift Change trade cot (1.070, 1.207, 1.485) Change trade cot (ood only) (1.058, 1.151, 1.269) Change trade cot (ervice only) (1.010, 1.048, 1.286) Change expenditure hare (0.997, 1.000, 1.006) Change trade cot (good & ervice) and expenditure hare (1.064, 1.189, 1.456) Note: Quantitative evaluation baed on the multi-country, multi-indutry general equilibrium model decribed in ection 5.2. Moment and correlation for the country-level VC meaure, a well a real wage change, are reported. The "2011 baeline" row report ummary tatitic calculated directly from the 2011 WIOT data. Under "Change trade cot", thi imulate the effect of a decreae commencing in 2011 for ixteen more year, in which trade cot for intermediate good decline at a rate of 1.81% per year, trade cot for intermediate ervice input decline at a rate of 1.50% per year, trade cot for final good decline at a rate of 2.31% per year, and trade cot for final-ue ervice decline at a rate of 1.96% per year, thee being the rate of change etimated from Table 4 and 5. The ubequent two row imulate the effect of thi trade cot decreae, but applying the decreae to ood (repectively, ervice) indutrie only. Under "Change expenditure hare", thi imulate the effect of a decreae Antrà, Chor On the Meaurement of VC Poitioning 45 / 48

61 Extending Caliendo and Parro (2015) Mapping the Model to Data Counterfactual 2. Forward Projection Change in individual countrie VC poitioning (U and D) from a further trade cot decline: CHN LUX IRL CZE BR IND BEL NLD DNK HUN VK EP POL KOR VN ITA DEU MEX WE FRA CAN CYP AUT PRT BR MLT AU JPN UA LVA ET ROU RC TUR FIN RoW RU IDN BRA LTU TWN CHN RU BR IRL ROU AU IND BRA CAN KOR RC UA CZE TUR BR JPN RoW PRT ITA LVA POL EP CYP IDN FIN WE FRA VN DEU HUN LTU ET MEX MLT AUT VK BEL TWN NLD DNK LUX Counterfactual Projected Change (U) Counterfactual Projected Change (D) Antrà, Chor On the Meaurement of VC Poitioning 46 / 48

62 Concluding Remark Antrà, Chor On the Meaurement of VC Poitioning 47 / 48

63 Concluion Documented the evolution of VC poitioning of countrie and indutrie, in the WIOD Uncovered everal alient fact and puzzling correlation: Countrie (and country-indutrie) that are far removed from final demand alo have a high production-taging ditance from primary factor Explored the poible role of two force: (i) decline in trade cot; and (ii) the riing importance of ervice in final conumption hare. Done through the len of a model (extending Caliendo-Parro), that fully rationalize all the entrie of a WIOT, and thu provide a more flexible bai for counterfactual exercie on countrie VC poitioning. Antrà, Chor On the Meaurement of VC Poitioning 48 / 48

64 upplementary lide Antrà, Chor On the Meaurement of VC Poitioning 1 / 2

65 ummary tatitic Table A.1 Back ummary tatitic: Country-Indutry VC Meaure 10th Median 90th Mean td Dev N F/O All indutrie ,076 ood indutrie only ,105 ervice indutrie only ,971 VA/O All indutrie ,395 ood indutrie only ,152 ervice indutrie only ,243 U All indutrie ,395 ood indutrie only ,152 ervice indutrie only ,243 D All indutrie ,395 ood indutrie only ,152 ervice indutrie only ,243 Note: Baed on the country-indutry VC meaure calculated from the WIOD for ; the ample comprie all 41 countrie, 35 indutrie, and 17 year. ood indutrie are defined a primary and manufacturing indutrie, namely indutrie 1-16 in the WIOD claification. The ervice indutrie are indutrie Antrà, Chor On the Meaurement of VC Poitioning 2 / 2