Lecture 2 Factor Bias in Cross-country Technology Differences. Barcelona, June 17

Transcription

1 Lecture 2 Factor Bias in Cross-country Technology Differences Barcelona, June 17 1 / 52

2 Yesterday Aggregate Production Function Y c = A c [Kc σ + CL σ c ] 1/σ Human Capital z 1 L c = h( H c, T c ) e β j L j,c j=1 j=z Physical Capital K c = [(N c ) η + D (M c ) η ] 1/η ρ ρ J + B e β j L j,c 1/ρ 2 / 52

3 Today Aggregate Production Function Y c = A c [Kc σ + C c L σ c ] 1/σ Human Capital z 1 L c = h( H c, T c ) e β j L j,c j=1 j=z Physical Capital K c = [(N c ) η + D c (M c ) η ] 1/η ρ ρ J + B c e β j L j,c 1/ρ 3 / 52

4 Reasons to Expect Non-Neutrality Appropriate technology - Theory: Atkinson and Stiglitz (1969), Diwan and Rodrik (1991), Basu and Weil (1998), Acemoglu and Zilibotti (2001), Caselli and Coleman (2006) - Evidence: Caselli and Coleman (2001), Caselli and Wilson (2004) Induced innovation/directed change - Hicks (1932), Kennedy (1964), Samuleson (1965, 1966), Acemoglu (1998, 2002), Jones (2005) 4 / 52

5 The Questions Are there systematic non-neutralities in technology differences across countries? If so, can they be seen as evidence of appropriate-technology choice, i.e. can they be rationalized by factor endowments? How does this fit with the "standard" view whereby poor countries suffer from "barriers" to technology adoption? 5 / 52

6 Alternative representation We have written aggregation functions of the form Alternative representation is With mapping X c = Ω 1c [ (X 1c ) ζ + Ω 2c (X 2c ) ζ] 1/ζ X c = [(Z 1c X 1c ) ζ + (Z 2c X 2c ) ζ] 1/ζ Ω 1c = Z 1c Ω 2c = ( ) ζ Z2c Z 1c Can retrieve the Zs from the Ωs and viceversa Will be switching between two representations according to convenience 6 / 52

7 Some terminology Consider again Time series: X c = [(Z 1c X 1c ) ζ + (Z 2c X 2c ) ζ] 1/ζ Technical change factor-i augmenting if Z i increases over time Technical change factor-i biased if (Z i /Z j ) ζ increases over time Rationale ( ) ζ ( ) ζ 1 MP i Zi Xi MP j Cross-section: Z j Technology differences factor-i augmenting if Z i higher in high-x i countries Technology differences factor-i biased if (Z i /Z j ) ζ higher in high X i /X j countries X j 7 / 52

8 Quick aside You might be more comfortable with X c = [ ) ζ ) ] ζ 1/ζ ω ( Z 1c X 1c + (1 ω) ( Z 2c X 2c Think of the ωs as being there - I am just omitting them to keep equations uncluttered (Will just remember they are there when let ζ 0) The mapping is Z 1c = ω 1/ζ Z 1c, Z 2c = (1 ω) 1/ζ Z 2c ( ) ζ Ω 1c = ω 1/ζ Z 1c, Ω 2c = 1 ω Z 2c. ω Z 1c 8 / 52

9 Plan of the lecture Is there a bias towards workers with more schooling (relative to workers with less schooling)? Is there a bias towards reproducible capital (relative to natural capital)? Is there a bias towards labour (relative to capital)? 9 / 52

10 Education Bias Production Function Y c = F c (K c, C c L c ) Labour input z 1 L c = h( H c, T c ) e β j L j,c j=1 j=z ρ ρ J + B c e β j L j,c Want to know if/how B c varies across countries 1/ρ 10 / 52

11 Backing out B c Yesterday we wrote W z,c W 1,c = B c ( J j=z eβ j L j,c ) ρ 1 ( z 1 j=1 eβ j L j,c ) ρ 1 We assumed B c = B, retrieved it from skill premium and relative supplies in USA, and 1/(1 ρ) = 1.5 For country-varying B, need estimates of country-specific skill premia Problem: cross-country data sets don t report skill premia 11 / 52

12 Mincerian Returns v. Skill Premia Cross-country datasets report b c from log W i,c = α c + b c s ic + ε ic estimated on country-specific microdata Tempting to say W z,c W 1,c = e bcn Where n is year-of-schooling difference between benchmark skilled type and benchmark unskilled type Tempting, but wrong 12 / 52

13 Another slide from yesterday (almost) Consider special case β j = βs j Implies z 1 e βs j L j,c j=1 j=z ρ ρ J + B c e βs j L j,c 1/ρ log(w j, j < z) = α + βs j log(w j, j z) = α + βs j 13 / 52

14 Mincerian Returns under imperfect substitution Log Wage profile 2.4 log wage years of schooling 14 / 52

15 Mincerian Returns under imperfect substitution Estimated Mincerian return 2.4 log wage years of schooling 15 / 52

16 Using Mincerian returns to back out skill premia Recall W j (j < z) = W 1 e β j W j (j z) = W z e β j OLS Formula b = P j L j (S j µ s)(log(wj) µ log(w ) ) Pj L j (S j µ s) 2, µ s = X j L j S j µ log(w ) = X j L j log(w j ) Plug from above and do some algebra b = (log Wz log W 1) P j z L j (S j µ s) + P j L j (S j µ s)β j P j L j (S j µ s) 2 Solve for skill premium (log W z log W 1 ) = b P j L j (S j µ s) 2 P j L j (S j µ s)β j P j z L j (S j µ s) 16 / 52

17 Data on Mincerian returns A collection of collections plus a new collection 70 countries in the 1990s 31 countries in the 2000s 17 / 52

18 Data on Mincerian returns (1990s).3 JAM mincerian coeff log relative supply of skills ZAF GHA IDN PER SGP BGR SLV RUS POL NOR DNK BRA SVK USA DEU FRA HUN ARG SVN SWE AUT IRL EGY MEX NLD CHL URY TUR THA ISR CYP PRT GRC HRV CZE CHE GBR BEL EST AUS CAN JPN FIN IND CHN PAK VEN CMR ZWE ZMB PAN JAM UGA NIC CRI PRY SDN TZA NPL KEN ECU BOL HND DOR VNM mincerian coeff TZA KEN IND SDN UGA PAK BRA PAN SGP JPN NIC CHN CHL ZMB PRY THA ECU ZAF BOL ARG NPL SVN IRL HND GBR VEN DOR URY PRTUR CRI HUN CAN FIN SLV GHA IDN RUS MEX GRC DEU AUS POL FRAUT CHE CMR SVK BEL ISR NLD ZWE PER EGY BGR DNK NORCZE HRV CYPEST VNM SWE USA log relative supply of skills 0 1 b = (.004) [without Jamaica b = (.003)] 18 / 52

19 Data on Mincerian returns (2000s) mincerian coeff log relative supply of skills.15 THA BRA ZAF IDN BGR RUS POL BRA SVK HUN ARG SVN AUT IRL MEX CHL TUR THA PRT GRC HRV CZE BEL PAK BOL CHN BGD VEN mincerian coeff..1 ZAF CHN CHL IDN MEX ARG POL VENBGD TUR BOL HUN PAK RUS SVN PRT HRV AUT BGR SVK IRL BEL GRC CZE log relative supply of skills 0 1 b = -.02 (.007) 19 / 52

20 Backed-Out Skill Premia (1995) log skill premium log relative supply of skills ZAF GHA IDN PER SLV NOR DNK SVK USA DEU FRA HUN ARG SVN SWE AUT IRL EGY MEX NLD CHL URY TUR THA ISR CYP PRT GRC CZE CHE GBR BEL EST AUS CAN JPN FIN IND CHN CMR ZWE ZMB PAN UGA NIC CRI PRY SDN TZA NPL KEN ECU VNM TZA log skill premium 4 KEN UGA SDN IND ZMB PRY THA NIC PAN ECU ZAF CHN SVN CHL NPL GHA ARG JPN GBR PRT URY IDN SLVTURMEX HUN DEU CMR SVKFRA AUT IRL GRC CHE ZWE CRI FIN CAN CZE DNK NOR PER BEL ISR NLD AUS VNM EGY CYPEST SWE USA log relative supply of skills 0 1 b = -.5 (.09) [without Tanzania b = -.27 (.06)] 20 / 52

21 Backed-Out Skill Premia (2005) log skill premium log relative supply of skills ZAF IDN BGR RUS POL BRA SVK HUN ARG SVN AUT IRL MEX CHL TUR THA PRT GRC HRV CZE BEL PAK BOL CHN BGD VEN 2 THA BRA ZAF 1.5 IDN MEX CHL BGD CHN VEN ARG BOL PAK TUR SVN HUN POL PRT RUS HRV SVK AUT BGR GRC IRL BEL CZE 0 log skill premium log relative supply of skills 0 1 b = -.32 (0.09) 21 / 52

22 Reminder z 1 L c = h( H c, T c ) e β j L j,c j=1 j=z ρ ρ J + B c e β j L j,c 1/ρ W z,c W 1,c = B c ( J j=z eβ j L j,c ) ρ 1 ( z 1 j=1 eβ j L j,c ) ρ 1 22 / 52

23 Education bias (1995) 4 TZA ZAF GHA IDN PER SLV NOR DNK SVK USA DEU FRA HUN ARG SVN SWE AUT IRL EGY MEX NLD CHL URY TUR THA ISR CYP PRT GRC CZE CHE GBR BEL EST AUS CAN JPN FIN IND CHN CMR ZWE ZMB PAN UGA NIC CRI PRY SDN TZA NPL KEN ECU VNM log of Bc log relative supply of skills log of Bc KEN SDN IND JPN PAN CHL CHE AUS ZAF HUN DEU AUT IRLCAN ECU CHN CZE SWE NLD NIC ARG FRA GRCNOR PER BEL ISR EST ZMB SVN FIN URY SVK CYP PRY THA MEXCRI DNK PRTUR GBR GHA SLV ZWE NPL IDN EGY CMR USA VNM UGA log relative supply of skills 0 1 b =.16 (.09) 23 / 52

24 Education bias (1995) without Tanzania 12 2log of Bc log relative supply of skills ZAF GHA IDN PER SLV NOR DNK SVK USA DEU FRA HUN ARG SVN SWE AUT IRL EGY MEX NLD CHL URY TUR THA ISR CYP PRT GRC CZE CHE GBR BEL EST AUS CAN JPN FIN IND CHN CMR ZWE ZMB PAN UGA NIC CRI PRY SDN NPL KEN ECU VNM USA 1 log of Bc 0 KEN SDN IND JPN PAN CHL AUS CHE DEUCAN ECU CHN HUNIRL SWE ZAF AUT CZE NLD NIC ARG FRA GRC NOR PER BEL ISR EST FIN ZMB SVN CYP URY SVK PRY THA CRI MEX DNK PRTUR GBR GHA SLV ZWE NPL IDN EGY CMR VNM UGA log relative supply of skills 0 1 b =.4 (.06) [without Uganda b=.35 (.05)] 24 / 52

25 Education bias (2005) 1.5 CZE of Bc log relative supply of skills ZAF IDN BGR RUS POL BRA SVK HUN ARG SVN AUT IRL MEX CHL TUR THA PRT GRC HRV CZE BEL PAK BOL CHN BGD VEN CHL BOL 1 THA BRA CHN HUN log of Bc.5 0 ZAF AUT MEX ARG IRL BEL SVK BGD IDN PAKSVN TURHRV BGR GRC VEN RUS POL PRT log relative supply of skills 0 1 b =.34 (.09) 25 / 52

26 Notation J L Hc = e βs j L j,c j=z z 1 L Lc = e βs j L j,c j=1 26 / 52

27 Understanding the result Log(W z /W 1 ) Data Model Model Where: «LHc Model = log(b c) + (ρ 1) log L Lc Log(L H /L L ) 27 / 52

28 Interpreting the result Use version L c = [(B Lc L Lc ) ρ + (B Hc L Hc ) ρ ] 1/ρ want to explain why B H BL increases with L H LL Firms choose among blueprints Each blueprint implies a certain combination of B L and B H Firms choose the appropriate blueprint given factor prices Skill-abundant countries adopt skill-biased technologies, and vice versa 28 / 52

29 Modelling strategy: technology frontiers Efficiency of Skilled Labor A b A B b B A a B a Efficiency of Unskilled Labor A (B) is the technology frontier of country A (B). A a and B a (A b and B b ) are appropriate choices of technology for unskilled-labor (skilled labor) rich countries. 29 / 52

30 The model Competitive firms maximize profits subject to [ ] Y = F K, [(B L L L ) ρ + (B H L H ) ρ ] 1 ρ (B H ) ω + γ (B L ) ω B Choice variables: K,L L,L H, and B L W L, W H, and R determined in competitive factors markets K,L L,L H inelastically supplied 30 / 52

31 Equilibrium If ω > ρ/(1 ρ) equilibrium is symmetric (all in the middle) If ω < ρ/(1 ρ) equilibrium is asymmetric (all at the corners) 31 / 52

32 Properties of equilibrium Firms choices L H L L = B H B L = ( ) ω ρ Wz ωρ (ω ρ) ρ γ (ω ρ) ωρ W 1 ( ) ρ Wz ωρ (ω ρ) 1 ρ γ (ω ρ) ωρ W 1 Hence: L H LL decreasing in Wz W 1 if ρ > 0, B H BL if ρ < 0, B H BL decreasing in Wz W 1 increasing in Wz W 1 32 / 52

33 Properties of equilibrium (cont.) General equilibrium ( BH ) ω ρ = γ ( ) ρ LH B L L L Hence: if ρ > 0, B H BL if ρ < 0, B H BL increasing in L H LL, or skill bias decreasing in L H LL 33 / 52

34 Properties of equilibrium (cont.) General equilibrium (cont.) B H = B L = ( B 1 + γ ρ/(ρ ω) (L H /L L ) ωρ/(ρ ω) ( B/γ 1 + γ ρ/(ω ρ) (L H /L L ) ωρ/(ω ρ) ) 1/ω ) 1/ω With ρ > 0, B H increasing in both B and L H /L L B L increasing in B but decreasing in L H /L L 34 / 52

35 Using the empirical results to parametrize the frontier We said ( BH ) ω ρ = γ ( ) ρ LH B L L L Or log ( BH B L ) = log γ ω ρ + ρ ω ρ log ( LH L L ) This is the OLS regeression we run before! for both years we found ρ ω ρ = 0.35, so ω / 52

36 (not so small) aside: Bias and Income (1995) log Bc of income per worker ZAF GHA IDN PER SLV NOR DNK SVK USA DEU FRA HUN ARG SVN SWE AUT IRL EGY MEX NLD CHL URY TUR THA ISR CYP PRT GRC CZE CHE GBR BEL EST AUS CAN JPN FIN IND CHN CMR ZWE ZMB PAN UGA NIC CRI PRY SDN NPL KEN ECU VNM USA 1 KEN CHN NIC ZMB IND GHA SDN NPL CMR JPN PAN CHL AUS CHE CAN ECU DEU HUN CZE SWE IRL ZAF NLD AUT EST PER ARG GRCISR FRA BEL NOR SVK URY SVNCYP FIN PRY THA CRI MEX DNK TUR PRT GBR ZWESLV IDN EGY VNM UGA -2 2 log of Bc log of income per worker 12 b = 0.33 (0.07) 36 / 52

37 Bias and income (2005) 1.5 CZE Bc log of income per worker ZAF IDN BGR RUS POL BRA SVK HUN ARG SVN AUT IRL MEX CHL TUR THA PRT GRC HRV CZE BEL PAK BOL CHN BGD VEN 1 BOL CHN BRA THA CHL HUN log of Bc.5 0 BGD ZAF AUT MEX ARG IRL BEL SVK PAK IDN SVN BGR TUR HRV GRC VEN RUS POL PRT log of income per worker 12 b = -.03 (0.11)) 37 / 52

38 How can it be? Answer: small correlation between relative skill supply and income in 2005 sample All Data My Sample (N=142) 0.82 (N=58) (N=142) 0.42 (N=31) 38 / 52

39 Natural v. Reproducible Capital Y c = F c ( [(N c ) η + D c (M c ) η ] 1/η, L c ) Impose no arbitrage (ignore capital gains) MPMc P Mc = MPNc P Nc Hence D c = P M c P Nc ( ) Mc 1 η Nc 39 / 52

40 Implications Recall D c = P M c P Nc ( ) Mc 1 η Nc Significant variation across countries in M/N M/N higher in rich countries Assume variation in quantities dominates variation in prices Hence Rich countries should have higher D c Consistent with theoretical model if η > 0 40 / 52

41 Capital v Labor Work with alternative notation Marginal product pricing So Y c = [(A Kc K c) σ + (A Lc L c) σ ] 1/σ «1 σ W c = (A Lc ) σ Yc L c «1 σ R c = (A Kc ) σ Yc L c A Lc = A Kc = «WcL 1/σ c Y c Y c L c «RcK 1/σ c Y c Y c K c and As can be retrieved if we know shares in income (and σ). 41 / 52

42 Stylized fact on income shares Gollin: no systematic variation with income Note: does not imply it s the same for everyone! 42 / 52

43 Implication of Gollin fact A Lc = A Kc = ( ) Wc L 1/σ c Y c Y c L c ( ) Rc K 1/σ c Y c Y c K c will inherit properties of Yc L c and Yc K c 43 / 52

44 Labor productivity using L c = e β H H c [L ρ Lc + B cl ρ Hc ]1/ρ, log labor productivity (schooling only) of income per worker ZAF GHA IDN PER SLV NOR DNK SVK USA DEU FRA HUN ARG SVN SWE AUT IRL EGY MEX NLD CHL URY TUR THA ISR CYP PRT GRC CZE CHE GBR BEL EST AUS CAN JPN FIN IND CHN CMR ZWE ZMB PAN UGA NIC CRI PRY SDN NPL KEN ECU VNM log labor productivity (schooling only) CMR VNM SDN NPL UGA IND GHA KEN NIC ZMB CHN GBR PRT DNK NOR EGY FRA BEL IDN ZWESLV MEX SVN TUR CYP FIN ISR AUT CRI NLD URY GRC THA ARG SVK IRL DEU PRY ZAF SWE CAN CHE HUN CZE AUS EST PER ECU CHL JPN PAN USA log of income per worker 12 b = 0.35 (0.10) [Tanzania excluded] 44 / 52

45 Labor productivity using L c = e β H H c [L ρ Lc + B cl ρ Hc ]1/ρ, log labor productivity (schooling and health) of income per worker ZAF IDN BGR RUS POL BRA SVK HUN ARG SVN AUT IRL MEX CHL TUR THA PRT GRC HRV CZE BEL PAK BOL CHN BGD VEN log labor productivity (schooling and health) PRT GRC POL SVN RUS BEL IRL VEN HRV TUR AUT SVK BGR ZAF ARG IDN PAK MEX HUN THA BRA BGD CHL CHN CZE BOL 8 10 log of income per worker 12 b = 0.89 (0.22) 45 / 52

46 Labor productivity using L c = e β H H c +β T T [L ρ Lc + B cl ρ Hc ]1/ρ log labor productivity (schooling, health, and tests) PRT POL SVN GRC RUS IRL BEL HRV TUR SVK AUT BGR ZAF IDN ARG MEX HUN THA BRA CHL CZE 8 10 log of income per worker log labor productivity (schooling, health, and tests) of income per worker ZAF IDN BGR RUS POL BRA SVK HUN ARG SVN AUT IRL MEX CHL TUR THA PRT GRC HRV CZE BEL b = 0.7 (0.29), year / 52

47 Capital productivity using reproducible capital TTO TTO TTO ZAF ZAF ZAF MAR MAR MAR KWT KWT KWT IRN IRN IRN QAT QAT QAT ROM ROM ROM GHA GHA GHA KGZ KGZ KGZ IDN IDN IDN PER PER PER SGP SGP SGP ROU ROU ROU BGR BGR BGR BWA BWA BWA SLV SLV SLV ALB ALB ALB SAU SAU SAU LUX LUX LUX RUS RUS RUS LTU LTU LTU POL POL POL NOR NOR NOR DNK DNK DNK ISL ISL ISL BRA BRA BRA SVK SVK SVK USA USA USA DEU DEU DEU TUN TUN TUN FRA FRA FRA HUN HUN HUN ARG ARG ARG SVN SVN SVN SWE SWE SWE DZA DZA DZA AUT AUT AUT IRL IRL IRL NZL NZL NZL EGY EGY EGY MEX MEX MEX NLD NLD NLD JOR JOR JOR CHL CHL CHL HKG HKG HKG SYR SYR SYR URY URY URY BHR BHR BHR TUR TUR TUR THA THA THA ISR ISR ISR CYP CYP CYP PRT PRT PRT GRC GRC GRC MLT MLT MLT UKR UKR UKR HRV HRV HRV ARM ARM ARM LVA LVA LVA MYS MYS MYS CZE CZE CZE CHE CHE CHE MAC MAC MAC GBR GBR GBR BEL BEL BEL EST EST EST AUS AUS AUS CAN CAN CAN JPN JPN JPN FIN FIN FIN KOR KOR KOR UGA UGA UGA ECU ECU ECU SLE SLE SLE BRN BRN BRN JAM JAM JAM GMB GMB GMB KAZ KAZ KAZ BDI BDI BDI VNM VNM VNM LKA LKA LKA CRI CRI CRI LSO LSO LSO RWA RWA RWA ZMB ZMB ZMB ARE ARE ARE MNG MNG MNG IRQ IRQ IRQ GUY GUY GUY MRT MRT MRT COG COG COG CMR CMR CMR LBY LBY LBY TZA TZA TZA PAK PAK PAK PNG PNG PNG TWN TWN TWN COD COD COD NER NER NER MWI MWI MWI YEM YEM YEM CIV CIV CIV SEN SEN SEN DOR DOR DOR SDN SDN SDN ZWE ZWE ZWE MDV MDV MDV BOL BOL BOL MUS MUS MUS NAM NAM NAM BRB BRB BRB PRY PRY PRY HTI HTI HTI NPL NPL NPL BEN BEN BEN PAN PAN PAN IND IND IND LBR LBR LBR FJI FJI FJI GAB GAB GAB HND HND HND AFG AFG AFG KHM KHM KHM TGO TGO TGO SWZ SWZ SWZ MLI MLI MLI MOZ MOZ MOZ KEN KEN KEN NIC NIC NIC LAO LAO LAO BLZ BLZ BLZ CHN CHN CHN TON TON TON CUB CUB CUB CAF CAF CAF BGD BGD BGD VEN VEN VEN log productivity of reproducible capital log productivity of reproducible capital log productivity of reproducible capital log of income per worker log of income per worker log of income per worker b = -.26 (0.04), year / 52

48 Capital productivity using total capital log productivity of total capital.5 log productivity of total capital BDI LKA PAK SWZ MUS BRB GMBMOZ CHN BGD SLV IND MAR NPL FJI HTI BGR TUN ZAF MWI KEN SEN IDN ALB DOR HUN GHA EGY JOR CHL THA NAM BWA GRC ZMB ZWE MYS BEN PER ROU JAMLVA KOR IRL EST TUR LSO CRI NIC CIV HND BRAURY PRT BOL ROM BLZ PRY IRN SGP MRT ARG GBR SWE NLD BEL TGO PAN FRA RWA MLI TTO ISR USA DEU AUS AUT MEX FIN NER CMR ECU CAN RUS DNK CHE NZL DZA NOR COG VEN SYR JPN GUY GAB log of income per worker TTO ZAF MAR IRN ROM GHA IDN PER SGP ROU BGR BWA SLV ALB RUS NOR DNK BRA USA DEU TUN FRA HUN ARG SWE DZA AUT IRL NZL EGY MEX NLD JOR CHL SYR URY TUR THA ISR PRT GRC LVA MYS CHE GBR BEL EST AUS CAN JPN FIN KOR ECU JAM GMB BDI LKA CRI LSO RWA ZMB GUY MRT COG CMR PAK NER MWI CIV SEN DOR ZWE BOL MUS NAM BRB PRY HTI NPL BEN PAN IND FJI GAB HND TGO SWZ MLI MOZ KEN NIC BLZ CHN BGD VEN log of income per worker 12 b = -.10 (0.05), year / 52

49 Labor productivity vs K/L 9log labor productivity and ratio tot. cap./labor (schooling and health) ZAF IDN BGR RUS BRA HUN ARG AUT IRL MEX CHL TUR THA PRT GRC BEL PAK BOL CHN BGD VEN log labor productivity (schooling and health) CHN BGD PAK HUN THABRA CHL BGR ZAF IDN PRT GRC BEL IRL RUS VEN TUR AUT ARG MEX 5 BOL ratio tot. cap./labor (schooling and health) 10 b =.79 (0.05), year / 52

50 Capital productivity vs K/L PAK CHN BGD log productivity of total capital BOL CHL HUN THA BRA ZAFBGR IDN GRC IRL TUR PRT BEL ARG AUT MEX RUS VEN log productivity of total capital ratio tot. cap./labor (schooling and health) ZAF IDN BGR RUS BRA HUN ARG AUT IRL MEX CHL TUR THA PRT GRC BEL PAK BOL CHN BGD VEN ratio tot. cap./labor (schooling and health) 10 b = -.21 (0.05), year / 52

51 Summing up on A K and A L Seems likely A L higher in rich countries Seems possible A K higher in poor countries Consistent with theoretical model? Previous results also implies A L /A K increasing in K/L Consistent with model if and only if σ < 0 51 / 52

52 Summary of lecture 2 Intimations of non-neutrality all over the place Highly-educated labor relatively more efficient than less educated labor in countries with larger relative endowments of highly- educated labor Reproducible capital relatively more efficient than natural capital in countries with larger relative endowments of reproducible capital Aggregate labor relatively more efficient than aggregate capital in countries with smaller relative endowments of labor These findings are consistent with a simple model of appropriate-technology choice if: Highly educated and less educated are good substitutes (ρ > 0) Reproducible and natural capital are good substitutes (η > 0) Capital and labor are poor substitutes (σ < 0) 52 / 52