450 Class Note for ECON 570 at PSU
450 Class Note for ECON 570 at PSU
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Date Created: 02/06/15
Lecture Note on the Growth and Development Econ 570 Spring 2004 1 Some Empirics A key point about economic growth is how recent it is at least in the modern sense To see this note the vivid description of Jones Conservative estimates suggest that humans were already distinguish able from other primates 1 million years ago 1magine placing a time line corresponding to this million year period along the length of a football eld On this time line humans were hunters and gatherers until the agricultural revolution perhaps 10000 years ago that is for the rst 99 yards of the eld The height of the Roman empire occurs only 7 inches from the right most goal line and the 1ndustrial Revo lution begins less than one inch from the eld s end Large sustained increases in standards of living have occurred during a relatively short time equivalent to the width of a golf ball resting at the end of a football eld We thus need to distinguish modem economic growth Kuznets from the pe riod of Malthusian stagnation 1n the latter growth was slow as per capita income growth led to population increase That is why the growth rate of per capita in come is so low prior to 1800 in gure 13 1n the post Malthusian period we see rapid economic growth due to technological change and positive feedback Something clearly changed That is why we think of modern economic growth Should one theory explain both Now some would argue that it is all determined by nature e e g Deemnna whe axguzs thet gengxaphc aetennente e cxuculr the etuheng d exemes hetween the lungrtexm hetnee nt penples ntthe d exem enntenente heye heen due tn d exemes m the enyhnnneent 405 39 He hnhe mndexn pnepety tn the ennnhtenne tn the emexgence ntegeu1tue m Nenhthee tnee e Seehe ehee the skung genguphxul pneetenn emphasnmg eheeeee envlmnr nente tunepnt enete He empheenee the ehnng nle nt eneethnee But theee thenee dn net exphen the dumahc changes m the tntunee nt xegmns neeent pexmds Cnnsxdex the tnunweng tehle guu 1 1 mm Meaaenn wheeh enmpeue twn gmups nt enuntee and hnhe t peneepet GDP eye yey lung henne The twn gmups e Weeten Emnpe Weeten Eumpun nesehente 1he the Us Canada Auethe and Japan Gmup B e eyeynne else Leten Amenee Eeten Emnpe and 1751 he excluding Jepen and Afnu me e kmHmmuannanuwmndlnnnmwaa Figure 11 Nnteee thet peneepet mcnmz 1eye1e ett tn dwexge enmewhee hetween 1mm and 1500 hut thet the hey pennd e thet Lust Thet e when the d exences becnmz yeqeegne eent Fxgme 1 2 e yey netuetye m the xegaxd The hey pnent hee e thet the nee 1 the Weet e yeyeeent One 1weye wente tn hnew why Chum het te enventegev We went tn hnew why Japan hee gxnwn en teet eenee Meuxxestnuhnn The e whee the Dumnndrtype uguneente eel 1t eennnt exphen hnw Mlhm the tempete nnee eennenne petnnenee e en yenea Tn enhee the 1eeenne 11 2 we een hnh t peneepet nutput m Weeten Eumpe h the 1eet 2mm yeene gure 1 a The euggeete hnw eeent the tehenes 1T aet neaemeenmm e BPpud te the Emmchchxmtlrnt chme we m eheea er wten Eurep n 18m Th In nee er Lhu aehet whet wtn Eurep we nehe Llrnn et ee when eexenuetnn nenea 1t n thet t we EEE Figure 12 China and Western Europe 400 to 1998 really is The sharp impression from gure 13 is that of a sharp break There is a fundamental non convexity here that occurs somewhere in the 19th century It is the most dramatic qualitative change in human history since at least the start of the bronze age Another way to think about this is cross country at a point in time In 1960 for example for 113 countries for which gdp per capita was available at PPP the riches country Switzerland 14980 was 39 times higher than the poorest Tanzania 381 The mean was 3390 1996 dollars The richest coun try was 39 times the poorest By 2000 we have date for 150 countries and the dispersion has grown as has the mean 8490 The richest Luxembourg is 91 times that of Tanzania 482 The US is second 33350 and this is 69 times Tanzania So dispersion has grown std deviation of the log of gdp increased from 089 to 112 This about this If Tanzania were to grow at the long term US growth rate of 18 1870 to 2000 it would take 235 years to reach the 2000 level of US gdp At the Japanese growth rate of 275 it would take 154 years 2Actually the Democratic Republic of Congo is poorer but there is no data 18000 16000 14000 12000 10000 8000 6000 4000 2000 0 0 250 500 750 1000 1250 1500 1750 2000 F1 gmc Ha Output Pcr1uu m u cslcrn Europe m the your 1L 2mm Dal wurcc Mmhhwn 2001 Figure 13 PeriCapita Output in Western Europe Comparing 1960 with 2000 we can see that 16 countries had negative growth rates of real pericapita gdp DRC Central African Republic Niger Angola Nicaragua Mozambique Madagascar Nigeria Zambia Chad Comors Venezuela Senegal Rwanda Togo Burundi Mali All but Nicaragua and Venezuela were in subisaharan Africa Of course if not for missing data there would be more data are more likely to missing from those that do worst a one thing to note about this list is that none of these countries with negative growth rates is rich they are all relatively low income a the oil shock increased the variation in growth rates as it reduced average levels I another thing is that if we had split the sample 1960772 and 19732000 only one country had a large 73 negative growth rate in the rst period Burundi several in the second Nicaragua over 74 and four over 73 a total of 32 countries had negative growth rates for this subisample Several countries also had growth rates over 5 during this period and re ally moved up in the rankings Taiwan Singapore South Korea Hong Kong Botswana Cyprus Thailand China has done real well for half the period So the differences in performance over 40 years are huge The problem is to explain why Let us start with some of the new stylized facts of growth SF 1 Factor accumulation does not account for the bulk of crossicountry di eri ences in the leuel or growth rate of GDP per capita Rather it is TFP whateuer that means TFP growth is the great free lunch With the same inputs we get more output In the Solow model it is really manna from heaven Now we want to endogenize it But rst we need to document its importance 1 1 Lucas Paradox The key question of growth and development economics is how to combine the notion of increasing returns 7 which is critical to raising per capita incomes 7 with diminishing returns which is the key to explaining allocation The Solow model explains this with exogenous technical change But this is unsatisfying for economists precisely because it is exogenous The Lucas paradox is a good way to start thinking about this Consider the standard production function in intensive form y AM 11 TFP is represented by A Countries differ not only in their capital labor ratios but in their levels of productivity as well Suppose this were not the case lndia s per capita income is about that of the US If Ajndl39a AUS it follows that Now a good estimate of 6 capital s share of national income would be 04 a rough average of the two countries This would imply that the capital labor ratio in the US is 152395 m 871 This is obviously way too high It would imply that we save at a rate 800 times that of India Since our savings rate may be 17 we know this cannot be true Moreover if the capital labor ratio were really 5 this much higher in the US than in 1ndia the return to capital in 1ndia would be about 58 times higher Why To see this note that if we ignore A the marginal product of capital per worker is 7 k l From expression 11 it follows that k yl Now using this in the expression for 7 we obtain 7 634 Since yUS 15 yjndm we have Tjndl39a 71515 Now 151395 is about 58 so the rate of return would have to be 58 times higher in 1ndia than the US3 But this should mean that capital should ow from the US to 1ndia Some does but not that much4 Why One reason could be TFP differences Ajndm lt AUS would alter the rate of return calculation5 Explaining these differences is one of the most important issues in development economics But we will ignore them here for the most part Notice that because it is measured as a residual it is really many things that include real technological advances real cost reduction Harberger improve ments in institutions and policies This is an exercise in growth accounting Some results across regions are given in table 14 Note the importance of TFP growth in the advanced countries and the lesser role in the Tigers The results of Alwyn Young called this into question for Asian Tigers His well known claim is that factor accumulation played a much larger role in these cases This immediately raises the question of why they did not succumb to the extensive growth trap that the Soviet Union could not escape from One explanation might be that capital owed primarily into exporting sectors of the economy Since these were small open sectors they did not encounter diminishing returns A second point could be that nancial institutions prevented really bad investments this was easier to say before the Asian crisis But the interpretation of his results may be wrong 0 First interest is in per capita growth not output growth 3To see this note that if we ignore A the marginal product of capital per worker is 7 k l From expression 11 it follows that k 311 Now using this in the expression for 7 we obtain 7 y g l Since yUS 15 96 dem we have 71mm TUS15 Now 151 5 is about 58 so the rate of return would have to be 58 times higher in India than the US 4This is sometimes referred to as the Lucas Paradox Robert Lucas rst pointed out that capital ows to developing countries were too small compared with predictions of standard economic models 5You can see this by taking the opposite assumption TUS 71mm and letting differences in A explain the higher US output nun 5mm 01mm muman mm mama Cuumnrs nzcn mm 7mm GumHY m Jun um mm um Ms W pm GumHY m leln umm mman um Sm mm M an mm mu m Mama by Asia wear m Hana my 5mm 5mm Km 1mm nicmwmsmm mamquot mm nndJnWervsnn mmmwmmm m m m an m m 2 n 22 2 u an m W hen n55 n37 man an m m mmn Mm sew 5m um am New am 320 mm m 24 am 354M 540 am am 5m 1 um um Mow mquotmmmmmzmmnm m Ay msm mm mm mm 1 4 Growth Accoummg 5m eumm n mm mm 1 m m 55 m M 55 3w 2 m m 2m 42 m m m m m m 55 m m m 75 m m s w 57 u 294 m 4 52V m an m 4m 2s m w m m m 2s m m m m w m 9 m 2m 309 m 52 75 AM m m m m m 0 Second and much more important some capital accumulation is induced by productivity growth Suppose y Aka then if there is a productivity shock 7 ie a shock to A then the marginal product of capital increases and this raises capital accumulation But this should be attributed to produc tivity growth not factor accumulation But if growth in capital is taken as exogenous then this is ignored To see the problem more clearly suppose that output and capital are growing at rate so Using growth accounting we attribute act of the steady state output growth to capital and 1 7 158 to TFP Now in the standard Solow model with exogenous technical change in the absence of TFP output and capital do not grow at all So in a elem sense we are under valuing the role of TFP in generating this growth It only occurred due to TFP The problem is that the growth of capital is endogenous but growth accounting treats it as erogenous Now if TFP itself is truly exogenous then one could say that differences in TFP show up one for one in differences in output growth This could help explain the difference with the Soviet case In that case factor accumulation was high in the face of negative productivity shocks 7 the economy was becoming less ef cient In the Asian Tigers case there were positive pro ductivity shocks that allowed capital accumulation to proceed at very fast rates without reducing returns Growth accounting exercises thus suggest that TFP plays the major role in explaining per capita output growth This is evident in gure 15 from Easterly and Levine Notice that TFP is more important in the fastest growing countries How to interpret the group of countries with positive growth in capital per worker but negative TFP growth and hence negative output growth Clearly it is not technical regress More likely it is very bad policies which cause inputs to be used much less ef ciently than before Increases in transaction costs would be one example What happens when human capital accumulation is added to the investigation Very little 1 1 1 Variance Decomposition Easterly and Levine perform a variance decomposition to see how much of the variation in the growth of per capita output y is explained by factor accumu lation versus TFP growth Start with y AW and let 04 04 Taking logs mwum Atrmmmlz nclt mumquot rum l c u RLs nlnni mqu Run mum sum r mm mum tutu mum mum mule Flgure 1 5 Growth Accouhtrhg by Country Groups and deferentJatmg w1th respect to tlme we have the farmhar growth accountmg expresslon y A k 0 4 y A 10 so the Vanance of output growth can he wrltten as cor va r 2 614 var 20 4 00v 3 12 One can a1so conslder hurhah capltal by lookmg at factor accurhulatroh per worker w f de ned as g where h 15 educatlonal attamrheht per worker Expresr 310D 1 2 lsnow y am i i ii mg ltAgt07 Q How WM The results are glven 1n tah1e 1 o for both estlmatlons Notlce that TFP growth accounts for almost 60 of the Varlatlon 1h growth rates and that factor accumulatlon a1ohe 15 hot that rrhportaht at 1east m the 198071992 perlod male 2 Vananeu Dncnmnusman I Wlhcul human eapllal Cunmbulmn a 5n non all cmmm Umpk gm CMHWDK qlku Val lssmssz n as n M n m b lsswssz n 55 n 21 an n mm human eanllal Cumnbulmn a Dmpkm alkm enllglupm alkml m 19604992 my w as 7045 b 19En4587 50 n as a 2n n12 Flgule l o Vallanee Decomposlclon 2 Development Accounting Developmenc aeeounllng ls the analog f0 levels co glowlh aeeounllng The latte shows how lnpuc glowlh and MI glowlh detezmme dlffezences ln glowlh laces The folme clles co explaer dlffezences ln levels of lncome Suppose we lelale lncome co factozs and emeleney Yl FIEl If factozs explaln dlffezences chen che ploblem f0 developmenc ls co explaln low aeeumulaclon e chls ls che elassleal developmenc apploaeh If dlffezences ln e r clency ale elllleal then we have no guze that ouc The analylleal ploblem ls how no speclfy che funeclonal Tom and how no caxefully measule lnpuls Thlnk of che Solow leslolual When Solow lsc esllmaceol hls glowlh equallon mosc onhe effect was due no Lechnologlcal change As we measule lnpuls bellel che lmpaec of Lechnlcal change ls ledueeol F0 example aeeounclng f0 lmplovemenls ln che quallly of labol and olhel lnpuls slmllal effect may be elllleal f0 developmenc Thls apploaeh was ploneeleol by Hall and Jones Hall and Jones 7 show that clossrcountzy ploduellvlly dlffezences measuleol ln levels ale lalge and eannol be explalned by dlffezences ln lnpuc use both physleal and human Lec oulpuc be plodueeol accozdmg co Coberouglas plodueclon functlon x MAM 2 1 10 where Hi is the amount of human capital augmented labor used in production and Ai is a labor augmenting measure of productivity The former is given by Hi e E Li where the function re ects the ef ciency of a unit of labor with E years of schooling relative to one with no schooling O6 The derivative gt E is the return to schooling estimated in a Mincerian wage regression an additional year of schooling raises a worker s ef ciency proportionally by Z We can re write 1 in terms of output per worker a K E i 1 hiAi 22 y where h E The nice thing about 22 is that we can use it to decompose differences in output per worker into differences in capital output ratios levels of human capital and levels of productivity7 Hall and Jones use data from 1988 to measure productivity differences using Penn World Tables They correct for natural resource endowments by subtracting value added from mining from GDP This prevents Saudi Arabia from being the 1 world leader in productivity8 They use a value of 04 5 and assume that Z is 6The rationale for this functional form is as follows Given our production function7 perfect competition in factor and good markets implies that the wage of a worker with s years of ede ucation is proportional to his human capital Since the wageeschooling relationship is widely thought to be logelinear7 this calls for a logelinear relation between h and s as well7 or some thing like h E with ab a constant However7 international data on educationewage pro les Psacharopulos7 1994 suggests that in Sub7Saharan Africa which has the lowest levels of ede ucation the return to one extra year of education is about 134 percent7 the World average is 101 percent7 and the OECD average is 68 percent Hall and Jones s measure tries to reconcile the logelinearity at the country level with the convexity across countries 7Notice the use of capital output ratio rather than capitalelabor ratio This follows the lead of David 19777 Mankiw et al 1992 and Klenow and RodriguezeClare 1997 in writing the decomposition in terms of the capitaleoutput ratio rather than the capitalelabor ratio7 for two reasons First7 along a balanced growth path7 the capitaleoutput ratio is proportional to the investment rate7 so that this form of the decomposition also has a natural interpretation Second7 consider a country that experiences an exogenous increase in productivity7 holding its investment rate constant Over time7 the country s capitalelabor ratio will rise as a result of the increase in productivity Therefore some of the increase in output that is fundamentally due to the increase in productivity would be attributed to capital accumulation in a framework based on the capitalelabor ratio 8Is this procedure really correct This rationale is inherently dubious then why not sube stracting the value added of agriculture and forestry7 that also use natural resources abune dantly 11 piecewise linear9 This analysis shows that productivity levels and output per worker are highly correlated Figure 21 plots these in logs mum l I mlumviu m Hmpm 1m mm n m l V in no m M W m 5mg m A R2 m man mm mm gran mum xznon vaulpchmkr mxx m mm 3 Baum Figure 21 Productivity and Output Per Worker From table 22 we can see the role of productivity differences in explaining output differences Notice that the values are ratios to US levels To see what goes on in this table look at the row for the Soviet Union In the Soviet Union investment was extremely high as was the capitalioutput ratio In addition human capital intensity was also high But it also had a rather low productivity level For the developing countries in the table differences in productivity are the most important factor in explaining differences in output per worker For example Chinese output per worker is about 6 percent of that in the United States and the bulk of this difference is due to lower productivity without the difference in gWith respect to human capital Psacharopoulos 1994 surveys evidence from many countries on returnitoischooling estimates Based on his summary of Mincerian wage regressions we assume that is piecewise linear Specifcally for the rst 4 years of education we assume a rate of return of 134 percent corresponding to the average Psacharopoulos reports for sub Saharan Africa For the next 4 years we assume a value of 101 percent the average for the world as a whole Finally for education beyond the 8th year we use the value Psacharopoulos reports for the OECD 68 percent 12 Tnhh 1 PIVHIYKHHM 1211111111111 R11HHgt 111 K15 V7111le Conmbuuon 11 0111 C mmuv 17L 7 quot 1 HL 11111124 sum 1 DUB 1 mu 1 11m 1 mu 11111111 n 9111 1002 n gas 1014 0231 1 1163 u 550 1207 mm 1118 uxuz 11912 Puma 11311 1091 11660 1125 11111154 Kingdom 11 727 0891 n m 1 D11 Hung Run 1 503 n 7111 n 735 1 1 15 Singnpme n 506 1 021 u 515 1 D78 1111111 u 587 1119 m 638 1111121 11 m u 868 u 925 Argentum u 115 n 953 0648 USSR 0417 1231 6468 1111111 00115 0709 0151 n 2117 111111 01150 n 1191 mu 0 1m 1mm o 1156 n 7117 01157 n 111 21112 o 013 0199 u 103 a 15m Average 127 11111111195 n was mass 0 51s smmm Devmtmn u 263 0125 1111211111111 11 39 L may 1 111111 mm C unelatmn n 1 legs 0 say 1 11110 Nute 1111 9111119111 DE 11111 mhle are L11 e111p111m1 1111119111111 111 11111 mmponunt of 111111011 111 111 memmed 11 1111111 10 ha 11 s 17117 Hes T1111 11 IE 11111 column 111 11111 11 the pmduct cf the M1191 Hues 1111111115 Figure 22 Productivity Calculations 13 productivity Chinese output per worker would be more than 50 percent of US output per worker The bottom half of Table 1 reports the average and standard deviation of the contribution of inputs and productivity to differences in output per worker According to either statistic differences in productivity across countries are sub stantial A simple calculation emphasizes this point Output per worker in the very countries in 1988 with the highest levels of output per worker was 317 times higher than output per worker in the very lowest countries based on a geomet ric average Relatively little of this difference was due to physical and human capital differences in capital intensity and human capital per worker contributed factors of 18 and 22 respectively to the difference in output per worker Produc tivity however contributed a factor of 83 to this difference with no differences in productivity output per worker in the very richest countries would have been only about four times larger than in the very poorest countries 1n this sense differences in physical capital and educational attainment explain only a modest amount of the difference in output per worker across countries The reason for the lesser importance of capital accumulation is that most of the variation in capital output ratios arises from variation in investment rates Aver age investment rates in the very richest countries are only 29 times larger than average investment rates in the very poorest countries Moreover this difference gets raised to the power which for a neoclassical production function with 04 13 is only 12 so it is the square root of the difference in investment rates that matters for output per worker Similarly average educational attainment in the very richest countries is about 81 years greater than average educational attainment in the very poorest countries and this difference also gets reduced when converted into an effect on output each year of schooling contributes only something like 10 percent the Mincerian return to schooling to differences in output per worker Given the relatively small variation in inputs across countries and the small elasticities implied by neoclassical assumptions it is hard to es cape the conclusion that differences in productivity the residual play a key role in generating the wide variation in output per worker across countries 21 Caselli Decomposition Caselli alters the decomposition Rather than use 22 he uses 34139 Aikahlia E Aiykh 23 14 The reason is that the impact of differences in A are cleaner 7 the Hall and Jones measure is not invariant to differences in tfp since A affects 3410 This measure allows one to ask quite strictly what would the world income distribution look like if all countries had the same level of A Using 23 we can decompose the variance in log y as va log y var logykh varlogA 20011 logA logykh 24 If all countries have the same level of A then the varlog A 0 thus one measure of success would be var logykh successl va log y Caselli uses PWT60 to estimate this counterfactual and nds var logykh 05 and the observed va log y 125 so successl 04 The only problem with this measure is that it is sensitive to outliers so it may be useful to look at inter percentile differences He de nes 90 10 successg ygg 913 y y where ya is the cum percentile of the distribution of y In the data the value of the 31223115 7 and the value of 31903110 20 so the value of SUCCESSZ 035 Notice that with either measure the variance of log y is much greater than the variance of log ykh which is why there is so much interest in TFP differences But it is interesting that there is also some signi cant variation in gym as well We will return to this when we talk about the relative price of investment for example 2 1 1 Subsamples It is interesting to look at subsamples Consider table 23 We observe that the variance in per capita income is lower in richer countries 7 this is obvious In Africa 7 the poorest regions 7 the variance is highest More important it is clear that the simple model explains richer countries better than poorer countries compare the above and below median success variable for example The one apparent puzzle is Europe 7 but that is entirely due to the inclusion of Romania which has high human capital but low per capita income It has the typical transition legacy If you drop Romania Europe looks like the Americas 10Obviously m h kahl aA o 15 sumample Obs ar ogy var ogltyKH 1 mam Above the median 47 o 174 n 112 o 64 Below the mechan 46 n ass 0 257 o 4238 OECD 24 0 077 n 047 o 6 06 NonrOECD 59 1 001 n 373 o 375 Afnca 26 o 843 n 271 o 322 Americas 25 0 341 n 175 o 513 Am and Oceama 25 o 652 o 292 o 448 Europe 17 11 128 n 033 o 255 All 93 1 246 n 501 o 400 gure 2 a Success In Subsamples 1s One conclusion from this exercise is that the factors only model works worst where we need it most 7 in the poorest regions 22 Chipping Away Can we chip away at the differences That is can we improve the t of the factor only model to reduce the impact of A Notice rst that one important variable is 04 Since countries differe more in terms of k than in terms of h if you have a higher capital share you can explain more of the cross country differences lf capital received 60 of income you could do pretty well But this is just too high 221 Human Capital Adjustments There are various issues here First what are we really measuringThere are two views of human capital 1 typical view resource cost incurred in learning the world s stock of knowl edge ie as a factor of production 2 alternative view human capital allows one to absorb new techniques at lower cost Nelson and Phelp 1968 On this view schooling is learning how to learn not that much of what is learnt is useful Hard to say which view is correct Econometric evidence indicates that human capital has negligible effects on productivity but is positively associated with improvements in productivity11 On the second view low human capital impedes the ability to follow But perhaps causation runs the opposite way when the conditions exist for entrepre neurship and innovations there is a large demand for human capital to implement these innovations Klenow conducted an interesting test of these two hypotheses using US data on manufacturing industries He noted that if the rival human capital story is correct then those industries where labor intensity is high should have higher productivity growth Higher labor intensity would signal more human capital accumulation If the Romer idea is correct on the other hand then industries with 11In Communist economies human capital was high and productivity was low but so was the growth rate of productivity 17 low labor intensity and high capital intensity would have the higher productivity growth Klenow tested this using growth rates 1959 1991 for 449 4 digit US manu facturing industries He found that TFP growth is faster in the industries that are more intensive in capital and intermediate goods and less intensive in labor 7 favoring the idea models12 A second big issue is measurement First results are sensitive to how M R W used secondary school enrollment This varies more across countries than other measures so it explains more Klenow and Rodriguez Clare added primary school enrollment for example and this re duced the explanatory power of human capital They also constructed an index that used returns to schooling with years of schooling This also reduced the explanatory power of human capital Aside from this we have practical issues First not all human capital is iden tical Education Most adjustments to education do not account for the differences For example hours worked varies across countries is inversely related to per capita income So accounting for this would actually raise labor input in the poor countries and leave more to explain Unemployment rates could differ but there seems to be no pattern Of course underemployment may differ but again this is probably higher in the poorer countries so again it does not help 23 Quality The quality of human and physical capital may differ Perhaps this can explain some of the difference It could be that h is lower in poor countries but this is hard to measure and it does not seem to explain much The most important element could be health and nutrition This could indicate that labor input is less in poorer countries Weil 2001 uses as a proxy for health the Adult Mortality Rate AMR which measures the fraction of current 15 year old people who will die before age 60 under the assumption that agespeci c 12Klenow uses an interesting analogy This paper could have been typed on a 1970 typewriter Correcting spelling errors would have been tedious using the human capital accumulated to type Even using the human capital accumulated in the PhD program But the word processing program made it trivially easy No change in typing human capital but ideas embedded in the pc and in the software dramatically improved productivity 18 death rates in the future will stay constant at current levels In practice this is a measure of the probability of dying young and is therefore a plausible inverse proxy for overall health status Suppose then that h Ahe E as before but that A e amrAMR 25 where bum lt 0 since a higher adult mortality ratio means a less energetic work force Using Weil s preferred value for foamAcclOO is 168 This allows for a big improvement in explanatory power of the factors only model 7 by at least one third Weil s estimate puts a high value on health 7 equal to a year s human capital and thus a year s human capital worth of wages13 ls this too high Hard to tell 24 Social versus Private Returns Note that the estimates of Z that are used measure private returns to schooling but what is important for growth are social returns What if there are externalities from a more educated workforce The question is which way do they go 0 what if rent seeking is higher in the poorer countries Governments may employ graduates in poor countries to a greater extent than in rich countries Then the social return might be lower in poor countries This could mean that h is higher in rich countries and could explain income variation 3 Quality of Physical Capital It could be that physical capital varies in quality across countries Since most countries import capital goods from a small nulnber of countries it is possible to use imports of capital as a proxy for investment Furthermore the RampD content of investment goods differs as well so this may proxy for the quality of capital goods 13Weil uses published micrdlevel estimates from three developing countries to infer the elasi ticity of human capital to height He then uses time series data from Korea and Sweden to estimate a relationship between height and the AMR He then combines these two pieces of information to infer the elasticity of human capital to the AMR In essence he is using the AMR to predict height and then applies to the predicted height the microeconomic estimate of the effect of height on wages 19 Suppose that YB 2xp7 l ylt1 31 101 where x are intermediate goods and B is a TFP term Suppose further that intermediate goods are produced by 17 A prpyi pr 0 lt 0 lt1 32 where hpr is human capital augmented labor in sector p and AP is TFP in that sector The key assumption is that capital is heterogeneous there are P distinct types of capital and each type is product speci c in the sense that intermediate p can only be produced with capital of type p The assumption that I lt 1 implies that 7 in producing aggregate output 7 all these activities are imperfect substitutes Notice also that AP is product speci c 7 this implies that the embodied technol ogy content of good p may be greater because the industry producing equipment of type p is more RampD intensive Within a country the law of one price should be enough to insure that we are measuring physical differences But in a cross country setting we would also have to worry about the relative price of investment which is differs across countries Now suppose that we can let hp h for all sectors 7 labor is mobile Then it is possible to write 31 as YKahL1 aB iampm p l 33 101 where 1 is the share of the capital stock in sector p The important point about this equation is evident if we compare this with the expression we have been using to explain output differences something like Y AKO hL1quotquot It is evident that 33 provides an expression for A in terms of the composition of the capital stock This suggests perhaps that variation in equipment shares could imply variation in the quality of capital and this could over and above variation in the quantity of K explain income variations The only problem is that if you look at expression 33 you can see that it is extremely sensitive to variation in 7 And it is hard to know what the proper value is 7 recall this measures how di icult it is to substitute different types of capital 20 Hence it is hard to know if capital differences account for income variation It could be the case but with current data it is still too hard to tell But it is a promising idea 31 Public vs Private Capital Another important point is that capital may differ in its productivity if it is the result of private or public investment PWT does not distinguish Government investment may not be as productive 7 rent seeking Or it could be more produc tive if there are large externalities 7 ala Aschauer The important point however is that in poorer countries governments play a larger role in investment decisions It poorer governments have more corruption or less effective cadres then we might expect capital to be less e icient in poorer countries If the data existed one could recalculate the capital stock in the manner of Kt Iprivaiei VIpublici 7 6Kt71 but it is hard to nd such series Moreover you would have to de ate them appro priately for purchasing power We will discuss some evidence on the productivity of state investment a bit later 0 Notice that what this exercise would be doing is to peer into the institutional differences that account for differences in A since one reason we expect corruption to matter is the e iciency of investment 32 Sectoral Differences Caselli also looks at sectoral and industry differences For example TFP could differ across industries and countries differ in the mix Similarly TFP could differ across sectors and poor countries have larger agricultural sectors But still one would want to know why the sectors or industries have different TFP s It is worth noting the interesting nding of Gregory Clark with respect to cotton mills He examined the productivity of cotton mills around the world in the early years of the twentieth century He shows that assuming constant capital labor ratios the textile industries of Britain and New England would have had a huge cost disadvantage relative to India Japan and many other countries Yet British cotton textiles dominated export markets Clark shows that the various countries industries used identical equipment and that the expertise to organize and run the mills could not have differed too much Rather the source 21 of the productivity differences boils down to the fact that each English worker was willing to tend to a much larger number of machines In low productivity countries workers were idle most of the time Why this was so remains a bit of a mystery and one shouold be cautious in assuming that this nding would still hold up one century later Nevertheless Clark s ndings reinforce the case that labor practices may be an important source of observed differences in productivity This is clearly somehow an institutional difference but we need models to understand how exactly 33 I ntative Conclusion With the evidence to date development accounting still shows that TFP accounts for most of the differences in income variation across countries It could be that low substitution of capital types or of capital for human capital explains a lot but not at the current level of knowledge 4 Growth and Externalities here are several key stylized facts of cross country growth that indicate the im portance of spillovers o The growth slowdown that began in the mid 1970s was a world wide phe nomenon It hit both rich countries and poor countries and economies on every continent o Richer OECD countries grew much more slowly from 1950 to around 1980 despite the fact that richer OECD economies invested at higher rates in physical and human capital 0 Differences in country investment rates are far more persistent than differ ences in country growth rates 0 Countries with high investment rates tend to have high levels of income more than they tend to have high growth rates 22
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