Structural Transformation of Occupation and Industry Employment

Transcription

1 Structural Transformation of Occupation and Industry Employment Georg Duernecker University of Mannheim Berthold Herrendorf Arizona State University July 21, 2015 Duernecker and Herrendorf

2 Motivation Structural Transformation (ST) As economies develop, labor is reallocated across broad sectors: agriculture shrinks industry first grows and then shrinks ( hump shape ) services grow. Duernecker and Herrendorf 1

3 Historical Employment Shares for 10 Countries (from Herrendorf, Rogerson, Valentinyi, Handbook Chapter, 2014) 0.9 Agriculture 0.9 Industry Share in total employment Share in total employment GDP per capita (1990 international $) GDP per capita (1990 international $) Share in total employment Services GDP per capita (1990 international $) BEL ESP FIN FRA JPN KOR NLD SWE GBR USA Duernecker and Herrendorf 2

4 Large literature: ST crucial force behind important economic issues Aggregate hours worked Aggregate labor productivity Urbanization Pollution This literature focuses on broad categories of industries ( sectors ). Duernecker and Herrendorf 3

5 Alternative perspective on structural transformation: occupations Occupations play key role for many important economic issues Wages Human capital Technical progress... Occupations not affected by outsourcing Janitorial labor employed by car manufacturer counted as industry employment Janitorial labor purchased by car manufacturer counted as service employment Janitor is a service producing occupation in both cases Thus, focusing on occupations rules out that ST is just relabelling. Surprisingly little evidence on ST of occupation employment. Duernecker and Herrendorf 4

6 Our contribution Provide new evidence on ST of occupation and sector employment Representative census data from IPUMS International. Many rich and many poor countries and large part of world population. Information about both occupations and sectors. Establish new stylized facts Standard patterns of ST hold for BOTH sector and occupation employment. The employment share of service occupations rises in ALL sectors. This suggests a broader notion of ST between both sectors AND occupations. Build a model of ST with sectors AND occupations, which is consistent with the old and new stylized facts of ST; allows us to study the forces behind ST of sector and occupation employment. Duernecker and Herrendorf 5

7 Outline Data Stylized Facts Model Results Applications Conclusion Duernecker and Herrendorf 6

8 Data Censuses for with sector and occupation information IPUMS International: 169 census observations from 64 countries (21 American/Carribean, 18 African, many Sub saharan ones, 14 European, 11 Asian). Large part of the world population More than 3/4 of the world population in At least one observation for seven of the ten most populous countries in 1990 (1. China, 2. India, 3. U.S.A., 4. Indonesia, 5. Brazil, 8. Pakistan, 10. Nigeria). Countries of all income levels including the very poorest ones More than 2/3 of world output in 1990 in 1990 international $ s. GDP per capita difference of more than a factor fifty: 30, 491$ in 2010 US versus 544$ in 1983 Guinea in 1990 international $ s. Duernecker and Herrendorf 7

9 Available census observations Argentina (1970, 1980); Austria (1971, 1981, 1991, 2001); Bolivia (1976, 1992, 2001); Brazil (1960, 1970, 1980, 1990, 2000, 2010); Burkina Faso (1996); Cambodia (1998, 2008); Cameroon (2005); Canada (1971, 1981, 1991, 2001); Chile (1960, 1970, 1982, 1992, 2002); China (1982, 1990); Colombia (1964, 1973); Costa Rica (1973, 1984, 2000); Domenican Republic (1960, 1970, 1981); Ecuador (1962, 1982, 1990, 2001, 2010); Egypt (2006); El Salvador (1992); France (1962, 1968, 1975, 1982, 1990, 1999, 2006); Germany (1970, 1987); Ghana (2000, 2010); Greece (1971, 1981, 1991, 2001); Guinea (1983); Haiti (1982, 2003); Hungary (2001); India (1983, 1987, 1993, 1999, 2004); Indonesia (1971, 1976, 1980, 1985, 1990, 1995); Iran (2006); Ireland (1971, 1981, 1991, 1996, 2002, 2006, 2011); Italy (1997); Jamaica (1982, 1991); Kyrgistan (2004); Liberia (2008); Malawi (1987, 1998, 2008); Malaysia (1970, 1980, 1991, 2000); Mali (1987, 1998, 2009); Mexico (1970, 1990, 1995, 2000, 2010); Mongolia (2000); Morocco (1982, 1994, 2004); Netherlands (2001); Nicaragua (1971, 1995, 2006); Nigeria (2008, 2009, 2010); Pakistan (1973); Panama (1960, 1970, 1980, 1990, 2000, 2010); Peru (1993, 2007); Philippines (1990); Portugal (1981, 1991, 2001); Puerto Rico (1990, 2000, 2005); Romania (1992, 2002); Rwanda (2002); Senegal (1998); Sierra Leone (2004); Slovenia (2002); South Africa (2007); Spain (1981, 1991, 2001); Sudan (2008); Switzerland (1970, 1980, 1990, 2000); Tanzania (2002); Turkey (1985, 1990, 2000); Uganda (2002); U.K. (1991, 2001); Uruguay (1963, 1996, 2006); U.S.A. (1960, 1970, 1980, 1990, 2000, 2010); Venezuela (1981, 1990, 2001); Vietnam (1999, 2009); Zambia (1990, 2000, 2010). Duernecker and Herrendorf 8

10 Definition of sectors Agriculture sector: agriculture, fishing, and forestry. Industry sector: construction; electricity, gas and water; manufacturing; mining. Goods sector: agriculture + industry sector. Service sector: education; financial services and insurance; health and social work; hotels and restaurants; other services; private household services; public administration and defense; real estate and business services; transportation and communications; wholesale and retail trade. Duernecker and Herrendorf 9

11 Definition of occupations Agriculture occupations: elementary agricultural occupations; skilled agricultural and fishery workers. Industry occupations: elementary industry occupations; crafts and related trades workers; plant and machine operators and assemblers. Goods occupations: Agriculture + industry occupations. Produce tangible value added. Related, but not equal, to blue collar or brawn intensive occupations. Service occupations: elementary service occupations; armed forces; clerks; legislators, senior officials and managers; professionals; service workers and shop and market sales; technicians and associate professionals. Produce intangible value added. Related, but not equal, to white collar or brain intensive occupations. Duernecker and Herrendorf 10

12 Examples Service occupation which is also in the goods sector Legislators, senior officials and managers E.g., manager of manufacturing plant. Goods occupation which is also in the service sector Crafts and related trades workers E.g., licensed electricians who works as contractor. Duernecker and Herrendorf 11

13 Stylized Facts (SF) Employment for the working age population (age 15 64): IPUMS International. GDP per capita in 1990 international $ s: Maddison s Groningen database. First pass at the data: three categories. Second pass at the data: two categories. Duernecker and Herrendorf 12

14 Sector ST for Three Categories 1 Employment Share in Agriculture Sector 1 Employment Share in Industry Sector GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Services Sector GDP per capita (1000) Duernecker and Herrendorf 13

15 Occupation ST for Three Categories 1 Employment Share in Agriculture Occupations 1 Employment Share in Industry Occupations GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Services Occupations GDP per capita (1000) Duernecker and Herrendorf 14

16 US Sector ST in comparison (black diamonds are US observations) 1 Employment Share in Agriculture Sector 1 Employment Share in Industry Sector GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Services Sector GDP per capita (1000) Duernecker and Herrendorf 15

17 US Occupation ST in comparison (black diamonds are US observations) 1 Employment Share in Agriculture Occupations 1 Employment Share in Industry Occupations GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Services Occupations GDP per capita (1000) Duernecker and Herrendorf 16

18 SF s between two Categories Goods production: agriculture and industry Services. Duernecker and Herrendorf 17

19 SF s for goods versus services 1 Employment Share in Goods Sector 1 Employment Share in Goods Occupations GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Services Sector 1 Employment Share in Services Occupations GDP per capita (1000) GDP per capita (1000) Duernecker and Herrendorf 18

20 Summary statistics sectors and occupations Goods sector GDP per capita (1,000 of int. $ s) < >20 employment share of goods occupations services occupations Services sector GDP per capita (1,000 of int. $ s) < >20 employment share of goods occupations services occupations The goods sector is intensive in the goods occupation. The service sector is intensive in the service occupation. Each sector s share of service occupation employment increases with GDP. Duernecker and Herrendorf 19

21 Two important implications of our evidence 1. ST does not follow systematically different patterns in currently poor countries Bah (Emerging Markets, Finance, and Trade, 2011) ST in some poor countries seems to follow different patterns. ST in some poor countries happens without GDP growth. Prominent deviations from standard patterns India is all but skipping industrialization, jumping right to services. South Korea industrialized much more strongly than other countries. We find no evidence that poorer countries follow systematically different patterns. We do find a lot of unsystematic variation in the service and industry shares. Duernecker and Herrendorf 20

22 Figures for Africa and Latin America separately... Duernecker and Herrendorf 21

23 2. Outsourcing is not a quantitatively important force behind ST Reallocation of resources may reflect relabeling due to outsourcing, as opposed to fundamental shifts of economic activity across sectors. This is a worrying prospect for the ST literature. Our findings imply quantitatively outsourcing cannot be main force behind ST. Occupation employment not affected by outsourcing (janitors employed by car manufacturers and cleaning firms are both janitors) If outsourcing was main force behind ST, then no increase in service occupation employment in goods sector little increase in total service occupation employment. Instead, we find service occupation employment increases in both sectors in the aggregate (and by at least as much as service sector employment; see on next page). Thus, to the extent that outsourcing drives service sector employment, there are other forces which offset it (see model to follow for details). Duernecker and Herrendorf 22

24 1 Employment Share in Agriculture Sector 1 Employment Share in Agriculture Occupations GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Industry Sector 1 Employment Share in Industry Occupations GDP per capita (1000) GDP per capita (1000) 1 Employment Share in Services Sector 1 Employment Share in Services Occupations GDP per capita (1000) GDP per capita (1000) Duernecker and Herrendorf 23

25 Much stronger conclusion than in the literature Herrendorf, Rogerson, Valentinyi (AER, 2013) Outsourcing does not affect the composition of final expenditure; There is ST in final expenditure, so not all ST is due to outsourcing. Berlingieri (Manuscript, 2014) Changes in input output structure increase service employment by 36%. Outsourcing of business services crucial for changes in input output structure. The above evidence is indirect and for the postwar US; in contrast, our evidence is direct and covers 169 censuses from around the world. Duernecker and Herrendorf 24

26 Model General remarks The purpose of the model is to highlight the features that are crucial for the patterns of employment in occupations and sectors. We will write down the most simple version with an AK investment sector. In addition, there are two sectors producing consumption goods and services and two occupations used by both sectors. Duernecker and Herrendorf 25

27 We want the model to match seven patterns that unfold as economies develop Four SF s from above 1. labor is reallocated from goods sector to service sector; 2. total labor is reallocated from goods occupations to service occupations; 3. sectoral labor is reallocated from goods to service occupations; 4. service occupations have larger employment share in service sector; goods occupations have larger employment share in goods sector. Three SF s from the literature 5. the expenditure share of services increases and that of goods decreases; 6. the price of services relative to goods increases; 7. labor productivity increases more in the goods than the service sector. Note Our model won t match the patterns of real shares. This is a common problem of ST models with CES preferences. See Boppart (ECMA, 2014) and Comin et. al. (2015) for recent solutions. Duernecker and Herrendorf 26

28 Environment Time discrete and runs forever. Three commodities in period t investment good X t ; consumption goods C Gt ; consumption services C S t. In each period, the investment good is the numeraire. Duernecker and Herrendorf 27

29 Investment sector technology Y Xt = A X K Xt (1) where A X is the (constant) TFP of producing investment goods from capital K X. Advantage of using AK: labor reallocated only between consumption sectors. Duernecker and Herrendorf 28

30 Consumption sector technologies where Y Jt = ( K Jt ) θ ( AJt L Jt ) 1 θ (2) L Jt = [ (α J ) σ(a 1 gt N Jgt ) σ 1 σ + (1 α J ) σ(a 1 st N Jst ) σ 1 ] σ σ σ 1 (3) and J {G, S } indexes sectors and j {g, s} occupations (so N J j denotes the labor in sector J from occupation j); A J is sector labor augmenting technical progress; A j is occupation labor augmenting technical progress; σ (0, ) is the elasticity of substitution (σ 0 Leontief, σ = 1 Cobb Douglas, σ perfect substitutes). Duernecker and Herrendorf 29

31 Continuum (of measure one) of identical households. Present discounted sum of lifetime utility where β (0, 1) is the discount factor C t is a consumption aggregator β t log(c t ) (4) t=0 C t = [ (α U ) 1 ε(c Gt ) ε 1 ε + (1 α U ) 1 ε(c S t ) ε 1 ] ε ε ε 1 (5) Duernecker and Herrendorf 30

32 Endowments Positive initial capital stock K 0 > 0. One unit of labor in each period. Capital and labor can be supplied to both sectors. Labor can be supplied to both occupations. Remark The last assumption will have to change if we want to study wage differences. Duernecker and Herrendorf 31

33 Resource constraints and market clearing conditions K t+1 = (1 δ)k t + X t (6) K t = K Xt + K Ct = K Xt + (K Gt + K S t ) (7) N Jt N Jgt + N Jst (8) N jt N G jt + N S jt (9) 1 = N t = N Gt + N S t = N gt + N st (10) Y Xt = X t. Y Gt = C Gt, Y S t = C S t (11) Duernecker and Herrendorf 32

34 Solving for the equilibrium Two step version of the household problem Intertemporal problem: max β t log(c t ) s.t. C t P t + K t+1 = (1 + r t δ)k t + w t (12) {K t+1,c t } t=0 t=0 Period problem: [ max (αu ) 1 ε(c Gt ) ε 1 ε {C Gt,C S t } + (1 α U ) 1 ε(c S t ) ε 1 ] ε ε ε 1 s.t. P Gt C Gt + P S t C S t = C t P t (13) where P t = [ α U (P Gt ) 1 ε + (1 α U )(P S t ) 1 ε] 1 1 ε Duernecker and Herrendorf 33

35 FOCs to the household problem lim t C t+1 P t+1 C t P t = β(1 + r t+1 δ) (14) β t C t P t K t+1 = 0 (15) P S t C S t P Gt C Gt = 1 α U α U ( PS t P Gt ) 1 ε (16) Remark (16) establishes the link between expenditure shares and relative prices. Ngai Pissarides (AER, 2007): ε < 1 required to match patterns in the data. Duernecker and Herrendorf 34

36 FOC to firm problem in the investment sector r t = A X (17) Remark AK is convenient here because it implies a constant real interest rate. Duernecker and Herrendorf 35

37 Implications of FOC s to firm problems in the consumption sectors K Ct N t = K Gt = K S t (18) N Gt N S t Y Gt /N Gt Y S t /N S t = ( ) 1 θ AGt L Gt /N Gt (19) A S t L S t /N S t Y Gt /N Gt = P S t (20) Y S t /N S t P Gt N Jst N Jgt = 1 α J α J N S st N Gst = 1 α S 1 α G ( Agt A st ( LS t L Gt ) 1 σ (21) ) 1 σ ( ) σ NS t (22) N Gt Remarks (20) establishes link between relative productivities and relative prices. (21) is about reallocation of labor within sectors (22) is about reallocation of labor between sectors. Duernecker and Herrendorf 36

38 Results Generalized balanced growth path (GBGP) Since our model features reallocation of labor between sectors and occupations, ratios won t be constant and imposing BGP would be too strong. We focus on GBGP, which only requires that the real interest rate be constant. That is trivially the case here because of the AK technology in the investment sector. Duernecker and Herrendorf 37

39 Proposition 1 There is a unique GBGP. Along the GBGP, capital, capital in consumption sectors, capital in investment sector, and consumption expenditure all grow at factor γ β(1 + A x δ). Duernecker and Herrendorf 38

40 Proposition 2 If the parameters satisfy (i) (v), then the GBGP is consistent with SF s 1 7. (i) 0 < α S < α G < 1 the service sector is more intensive in the service occupation the goods sector is more intensive in the goods occupation (ii) 0 σ < 1 inputs into the production function are complements (iii) 0 ε < 1 inputs into the utility function are complements (iv) A gt /A st increases technical progress is faster in the goods than the service occupation (v) A Gt /A St increases technical progress is faster in the goods than in the service sector Duernecker and Herrendorf 39

41 Note 1: necessary versus sufficient While (i) (v) are sufficient, only (i) (iv) are necessary. (v) is not necessary because as long as A gt /A st increases strongly enough, all SF s may hold even if A Gt /A S t decreases. Note 2: possible identification procedure Identify A g /A s from N s j /N g j. Given A g /A s, identify A G /A S from N s /N g. The levels are not identified, so we need to normalize one of them, e.g., A s = 1. Duernecker and Herrendorf 40

42 Intuition for Proposition 2 The relative price of services increases for two reasons: sector labor augmenting technical change grows more slowly in the service sector; occupation labor augmenting technical change grows more slowly in the service occupations the service sector is intensive in the service occupations. Since goods are complements in the utility function, the increase in the relative price of services implies that expenditures and labor get reallocated from the goods to the service sector. Since occupations are complements in the production function, the slower labor augmenting technical change in the service occupations implies that labor gets allocated from goods to service occupations in each sector. Labor gets allocated from goods to service occupations in the whole economy because not only does that happen in each sector but also does labor get reallocated to the service sector which is intensive in service occupations. Duernecker and Herrendorf 41

43 In other words, two forces generate reallocation of labor to service occupations: substitution between occupations within each sector (this results from uneven technological progress at the occupation level and it would take place with fixed sectoral employment); substitution of labor between sectors (here this also results from uneven technological progress but it could also result form even technological progress and nonhomothetic preferences, see Kongsamut, Rebelo, and Xi, REStud, 2001). This suggests broader notion of ST than just reallocation of sectoral employment. Duernecker and Herrendorf 42

44 Applications of the Model 1. Increase in female labor force participation in rich countries Women have a comparative advantage in service occupations (Rendall, Manuscript, 2010). ST implies the reallocation of labor from goods to service occupations. Structural transformation leads to the increase in female labor force participation. Ngai and Petrongolo (Manuscript, 2015) build a Roy model in which that is the case. Duernecker and Herrendorf 43

45 2. Job polarization Job polarization is the decrease in the employment share of the middle wage occupations and the increase in the employment shares of the low wage and high wage occupations. Service occupations tend to be both low wage and high wage occupation whereas goods occupations tend to middle wage occupations. ST increases the employment of service occupations and decreases the employment of goods occupations. Job polarization is a consequence of structural transformation. Barrany Siegel (Manuscript, 2014) build a Roy model in which that is the case. Duernecker and Herrendorf 44

46 3. Changes in the degree of unionization In the US, labor unions tend to be occupation specific and the degree of unionization is higher in goods than in service occupations. ST accounts for the decline in the rate of unionization in recent decades. Note that over the last century the degree of unionization in the US is hump shaped. The share of industry occupations in total employment follows a similar pattern. Duernecker and Herrendorf 45

47 Discussion Our model captures that ST causes compositional changes of occupation employment. In the three examples, these have consequences for economic issues of interest. Our model cannot speak to changes in relative wages because we assumed that everyone can supply every occupation. The next step on our agenda is to break this assumption (for example, there may be an entry cost into each occupation). Duernecker and Herrendorf 46

48 Conclusion We have: provided new evidence on ST from international census data; shown that the standard facts of ST hold for both sector and occupation employment; modeled the link between sector and occupation employment; used the model to shed light on important issues related to occupations. We plan to generalize this model in at least two dimensions: have more than two sectors/occuatpions; include entry costs into the occupations. Duernecker and Herrendorf 47

49 Appendix: Additional Tables and Figures Duernecker and Herrendorf 48

50 Detailed summary statistics sectors and occupations Goods-producing sector GDP per capita (1000) < >20 Legislators, senior officials, managers Professionals Technicians, associate professionals Clerks Service workers, shop, market sales Skilled agricultural, fishery workers Crafts and related trades workers Machine operators and assemblers Elementary occupations Armed forces Services sector GDP per capita (1000) < >20 Legislators, senior officials, managers Professionals Technicians, associate professionals Clerks Service workers, shop, market sales Skilled agricultural, fishery workers Crafts and related trades workers Machine operators and assemblers Elementary occupations Armed forces Duernecker and Herrendorf 49

51 Legend ARG AUT BFO BOL BRA CAM CAN CHL CHN CMO COL CRI DOM ECU EGY ESP FRA GER GHA GRE GUI HTI HUN IDO IND IRE IRN ITA JAM KYR LIB MEX MLI MLW MOG MOR MYS NED NIC NIG PAK PAN PER PHI PRI PRT ROM RWA SAF SAL SEN SLO SRL SUD SUI TUR TZA UGA UK UGY USA VEN VIE ZAM Duernecker and Herrendorf 50

52 Differences between sector and occupation employment shares Employment Share Difference (Sec Occ): Agriculture Employment Share Difference (Sec Occ): Industry GDP per capita (1000) GDP per capita (1000) 0.5 Employment Share Difference (Sec Occ): Services GDP per capita (1000) Duernecker and Herrendorf 51

53 Differences between sector and occupation employment shares 0.5 Employment Share Difference (Sec Occ): Goods 0.5 Employment Share Difference (Sec Occ): Services GDP per capita (1000) GDP per capita (1000) Duernecker and Herrendorf 52

54 FOC s to the Firm Problem Appendix: Proofs We need to show (18) (22). We drop the time indexes when this does not cause confusion. Raw FOC s for profit maximization: ( r = θp J KJ θ 1 (A J L J ) 1 θ KJ = θp J N J w = (1 θ)p J KJ θ A1 θ J L θ w = (1 θ)p J KJ θ A1 θ J L θ 1 1 σ 1 J L σ J α σ J A σ g 1 J L σ J (1 α J) 1 σa ) θ 1 ( ) 1 θ AJ L J (23) N J N 1 σ Jg (24) σ 1 σ s N 1 σ Js (25) (21) follows by dividing (24) and (25) by each other. Duernecker and Herrendorf 53

55 Multiplying (24) (25) with the respective labor and adding up gives that: w = (1 θ)p J ( KJ N J ) θ ( ) 1 θ AJ L J (26) N J Dividing (26) by (23), we find: w r = 1 θ K J (27) θ N J Hence, which was (18). K J N J = K C N = K C (28) Duernecker and Herrendorf 54

56 Equalized capital labor ratios imply (19) and (20): Y G /N G Y S /N S = ( ) 1 θ AG L G /N G = P S A S L S /N S P G It remains to show (22). Using (25) for J = G, S, we obtain: P G KG θ A1 θ G L θ 1 G L σ G (1 α G) 1 σa σ 1 σ s N 1 σ Gs = P S KS θ A1 θ S L θ 1 S L σ S (1 α S ) 1 σa σ 1 σ s N 1 σ S s Using (20) and (28), this can be simplified to (22): N S s N Gs = 1 α S 1 α G ( LS L G ) 1 σ ( NS N G ) σ QED Duernecker and Herrendorf 55

57 Proof of Proposition 1 Need to show that there is a unique GBGP. (17) implies that r t = r = A x. (14) implies that C t+1 P t+1 C t P t = γ β(1 + A X δ) w t = w t N t = (1 θ)c t P t implies that w t grows at the same factor as C t P t, i.e., γ. r t K Ct = A X K Ct = θc t P t implies that K Ct grows at the same factor as C t P t, i.e., γ. Duernecker and Herrendorf 56

58 The consumer budget constraint can be rewritten to: θc t P t K t + K t+1 K t = 1 + A x δ Hence, if K t grows at a constant factor, then that factor must be γ. K t = K Xt + K Ct implies that K Xt grows at factor γ too. QED Duernecker and Herrendorf 57

59 Proof of Proposition 2 Strategy of the Proof We first prove that given (i) (v) hold, we have SF 1. Then we prove SF s 3 and 4. Then we prove SF 2. Lastly we prove SF s 5 7. Again, we drop the time indexes when this does not cause confusion. Duernecker and Herrendorf 58

60 Derivation of SF 1 Need to show that N S /N G increases. (21) implies: N J = N Jg + N Js = [ ] NJg + 1 N Js = N Js α J 1 α J ( Ag A s ) σ N Js Hence, the ratio of sectoral labor satisfies: N S N G = 1 + [ α S /(1 α S ) ]( ) σ 1 A g /A s 1 + [ α G /(1 α G ) ]( ) σ 1 A g /A s N S s N Gs (29) Duernecker and Herrendorf 59

61 Combining (16) and (20) and rearranging gives: P S P G = Substituting this into (22), we obtain N S s N Gs = 1 α S 1 α G ( 1 αu α U ( α U 1 α U N S N G ) 1 1 ε ) 1 σ ( ) 1 σ (1 ε)(1 θ) N ( 1 S (1 ε)(1 θ) A G N G A S ) 1 σ Substituting this into (29) gives: N S N G = ( 1 αs 1 α G ) (ε 1)(1 θ) σ 1 1 α U α U 1 + [ α S /(1 α S ) ] ( ) σ 1 A g /A s 1 + [ α G /(1 α G ) ] ( ) σ 1 A g /A s (ε 1)(1 θ) σ 1 ( ) (1 ε)(1 θ) AG A S (30) Duernecker and Herrendorf 60

62 Define where α J α J /(1 α J ). f (x) [ 1 + αs x σ α G x σ 1 ] 1 σ 1 It is straightforward to show that given Assumption (i) we have f (x) < 0. Fact 1 now follows from (30), f (x) < 0, and Assumptions (iii) (v). QED Duernecker and Herrendorf 61

63 Derivation of SF 3 N Js /N J g increases. This follows directly from (21) and Assumptions (ii) and (iv). QED Derivation of SF 4 N Ss > N Sg and (N Gg > N Gs. (i) and (21) imply the claim. QED Duernecker and Herrendorf 62

64 Derivation of SF 2 N s increases and N g decreases. To see this, note that: Hence, N s = N Gs + N S s = N G N Gs N G + N S N S s N S N s = N G N Gs N G + N G N Gs N G + N S N S s N S + N S N S s N S Duernecker and Herrendorf 63

65 Using that N S = 1 N G, this becomes: N s = N G N Gs N G + N S N S s N S + N S ( NS s N S N ) Gs N G SF 1 implies N S > 0; SF 3 implies N Js /N J > 0; SF 4 implies N S s /N S > N Gs /N G. Hence, the right hand side is positive and N s grows. Since N g = 1 N s, this implies that N g falls. QED Duernecker and Herrendorf 64

66 Derivation of SF 5 We need to show that (P S Y S )/(P G Y G ) grows. To see this, note that (20) implies that Y S P S Y G P G = N S N G Fact 5 therefore follows from Fact 1. QED Duernecker and Herrendorf 65

67 Derivation of SF s 6 and 7 We need to show that P S /P G increases and (Y S /N S )/(Y G /N G ) decreases. (20) implies that either one of these statements is true iff the other one is true. We therefore only show that (Y S /N S )/(Y G /N G ) decreases. (19) implies that this is equivalent to showing that (A S L S /N S )/(A G L G /N G ) decreases. Duernecker and Herrendorf 66

68 To see that (L S /N S )/(L G /N G ) decreases, rewrite (3) while using (21): L S L G = = 1 + [ α S /(1 α S ) ] 1 [ σ (A g N S g )/(A s N S s ) ]σ 1 σ 1 + [ α G /(1 α G ) ] 1 [ σ (A g N Gg )/(A s N Gs ) ]σ 1 σ ( 1 αs 1 α G ) 1 σ [ α S /(1 α S ) ] ( ) σ 1 A g /A s 1 + [ α G /(1 α G ) ] ( ) σ 1 A g /A s σ σ 1 ( 1 αs σ 1 α G ) 1 σ 1 N S s N Gs σ 1 NS s N Gs (31) Duernecker and Herrendorf 67

69 Multiplying both sides by A S /A G and dividing the result by (29) gives: A S L S /N S A G L G /N G = ( 1 αs 1 α G ) 1 σ [ α S /(1 α S ) ] ( ) σ 1 A g /A s 1 + [ α G /(1 α G ) ] ( ) σ 1 A g /A s 1 σ 1 AS A G (32) Using that f (x) < 0 and Assumptions (iv) (v), it follows that (A S L S /N S )/(A G L G /N G ) decreases. QED Duernecker and Herrendorf 68

70 Proof that (i) (iv) are necessary To get the SF 1 7 conditions (i) (iv) must hold. (21) implies that we need (i) to get SF 4. (16) implies that given SF 6, we need (iii) to get SF 5. To get SF 1 given (iii) holds, we need (iv). (21) implies that given (iv), we need (ii) to get SF 3. QED Duernecker and Herrendorf 69

71 Detailed Intuition for Proposition 2 Recall Y Jt = (K Jt ) θ [(α J ) 1 σ(a gt N Jgt ) σ 1 σ + (1 α J ) σ(a 1 st N Jst ) σ 1 ] σ σ σ 1 1 θ C t = [(α U ) 1 ε(c Gt ) ε 1 ε + (1 α U ) 1 ε(c S t ) ε 1 ] ε ε 1 ε SF 3: Shares of service occupation in sector employment increase: A gt /A st increases and σ < 1. SF 4: Service occupation has larger employment share in service sector: α S < α G. SF 6: Price of services relative to goods increases: A gt /A st and A Gt /A S t increases and SF 4. SF 7: Labor productivity of goods relative to that of services increases: (Y Gt /N Gt )/(Y S t /N S t ) = P S t /P Gt and SF 6. Duernecker and Herrendorf 70

72 Recall Y Jt = (K Jt ) θ [(α J ) 1 σ(a gt N Jgt ) σ 1 σ + (1 α J ) σ(a 1 st N Jst ) σ 1 ] σ σ σ 1 1 θ C t = [(α U ) 1 ε(c Gt ) ε 1 ε + (1 α U ) 1 ε(c S t ) ε 1 ] ε ε 1 ε SF 5: Expenditure share of services increases and of goods decreases: ε < 1 and SF 6 (relative price of services increases). SF 1: Labor is reallocated from goods to service sector: and SF 5. P Gt P S t = Y S t/n S t Y Gt /N Gt = N S t N Gt = P S tc S t P Gt C Gt SF 2: Labor is reallocated from goods to service occupation: SF 1, 4 imply N S t /N Gt increases while N S st /N S t > N Gst /N G1 ; SF 3 implies N Jst /N Jgt increases for both J {G, S }. Duernecker and Herrendorf 71