A Reevaluation of the Effect of Human Capital Accumulation on Economic Growth: Using Natural Disasters as an Instrument

Transcription

1 A Reevaluaton of the Effect of Human Captal Accumulaton on Economc Growth: Usng Natural Dsasters as an Instrument By Raymond Robertson, Mark Skdmore and Hdek Toya Workng Paper Unversty of Wsconsn Whtewater Department of Economcs 4 th Floor Carlson Hall 800 W. Man Street Whtewater, WI Tel: (262)

2 July 2005 A Reevaluaton of the Effect of Human Captal Accumulaton on Economc Growth: Usng Natural Dsasters as an Instrument Hdek Toya 1, Mark Skdmore 2 and Raymond Robertson 3 JEL: 047 Abstract Theoretc growth models and mcroeconomc evdence suggest that human captal accumulaton s an mportant determnant of per capta ncome growth. However, outlers, measurement errors, and ncorrect specfcatons may have affected early macroeconomc studes that found a weak relatonshp between growth and human captal accumulaton. Whle recent studes addressng these problems are begnnng to show larger postve effects, the potental endogenety of human captal accumulaton has receved relatvely lttle attenton. In ths paper, we demonstrate that endogenety s sgnfcant and fnd that natural dsasters are a good nstrument for changes n schoolng. Our resultng nstrumental varable estmates are larger than our OLS estmates and are generally larger than those n prevous studes. Our analyss also provdes some lmted evdence of human captal externaltes. 1 Faculty of Economcs, Nagoya Cty Unversty, Yamanothata-1, Mzuho-cho, Mzuho-ku, Nagoya, , Japan; toya@econ.nagoya-cu.ac.jp; phone: Department of Economcs, Unversty of Wsconsn-Whtewater, 800 West Man, Whtewater, WI 53190; skdmorm@mal.uww.edu; phone: Department of Economcs, Macalester College, 1600 Grand Avenue, Sant Paul, MN ; robertson@macalester.edu; phone:

3 A Reevaluaton of the Effect of Human Captal Accumulaton on Economc Growth Usng Natural Dsasters as an Instrument JEL: 047 Abstract Theoretc growth models and mcroeconomc evdence suggest that human captal accumulaton s an mportant determnant of per capta ncome growth. However, outlers, measurement errors, and ncorrect specfcatons may have affected early macroeconomc studes that found a weak relatonshp between growth and human captal accumulaton. Whle recent studes addressng these problems are begnnng to show larger postve effects, the potental endogenety of human captal accumulaton has receved relatvely lttle attenton. In ths paper, we demonstrate that endogenety s sgnfcant and fnd that natural dsasters are a good nstrument for changes n schoolng. Our resultng nstrumental varable estmates are larger than our OLS estmates and are generally larger than those n prevous studes. Our analyss also provdes some lmted evdence of human captal externaltes.

4 1. Introducton Theoretc models of economc growth suggest that human captal accumulaton s a sgnfcant determnant of rsng per capta ncome. Mcroeconomc evdence of the postve relatonshp between schoolng and wages supports ths predcton. Estmates usng macroeconomc data demonstrate that the ntal stock of human captal s an mportant determnant of economc growth, 1 but emprcal estmates of the effects of changes n human captal (human captal accumulaton) poorly match theoretc predctons (Barro and Sala--Martn (1995) and Benhabb and Spegel (1994)). Most studes approach ths poor match as a measurement error problem (Temple (1999a), Mankw, Romer, and Wel (1992), Krueger and Lndahl (2001)), ncludng correctng for mperfect measures of qualty (Hanushek and Kmko (2000), Wossmann (2003)). Other studes have focused on the effects of outlers (Temple 1999b) or the use of ncorrect specfcatons (Englander and Gurney (1994) Gemmel (1996), Bassann and Scarpetta (2002), Engelbrecht (2003)). These studes suggest that restrctng the sample to OECD countres can generate a generally postve effect of changes n schoolng or school enrollments on growth that s smlar n magntude to those found n mcroeconomc estmates based on survey data, but tell us lttle about the experence of countres outsde the OECD, whch are often consdered to be the developng countres. Our contrbuton to the lterature s based on the possblty that the poor match between theory and emprcal work results not from how we measure human captal, but from the potentally endogenous relatonshp between changes n human captal and economc growth. Usng data from developed and developng countres, we present 1 1

5 evdence suggestng that human captal s, n fact, endogenously determned and therefore emprcal analyss requres an nstrumental varable approach. Of course, we are not the frst to ntroduce nstrumental varables to ths lterature. Prtchett (2001) and Krueger and Lndahl (2001) apply an nstrumental varables technque to estmate the effect of changes n average years of schoolng on growth, usng Nehru, Swanson, and Dubey (1995) and Kyracou s (1991) schoolng data as nstruments, respectvely. 2 Ther purpose n usng the nstrumental varables method s to overcome the measurement error ssue, and not necessarly to address endogenety per se. Indeed, the Nehru, Swanson, and Dubey and Kyracou schoolng varables are not approprate nstruments f one s tryng to address endogenety. A vald nstrument n ths context s one that determnes changes n schoolng but s not a drect determnant of economc growth; alternatve measures of schoolng are arguably just as mportant a determnant to growth as s the Barro and Lee measure of schoolng. Furthermore, researchers lke Glewwe and Hanan (2004) have shown that demand for educaton s postvely correlated wth ncreases n household ncome and wealth, thus emphaszng the two-way relatonshp between economc growth and human captal accumulaton. It appears that a key reason that researchers have not yet addressed the endogenety ssue s because of the lack of vald nstruments. To our knowledge, no studes exst n whch the endogenety of human captal accumulaton s tested, and f found to be present, the nstrumental varables method s used to estmate the effects of changes n human captal on growth. Skdmore and Toya (2002) demonstrate that 2 Curously, Prtchett (2001) fnds that nstrumental varables does not lead to a postve estmated effect of changes n schoolng on growth, but Krueger and Lndahl (2001) fnd that nstrumental varables yelds a postve effect of changes n schoolng on per capta GDP growth. Dependng on specfcaton and whether the coeffcent on captal s constraned, these coeffcent estmates range from 0 to a range smlar to estmates generated from mcro data. 2

6 clmatc natural dsasters affect growth through human captal accumulaton, ndcatng that a clmatc dsaster varable may be an approprate nstrument. In the aftermath of the 2004 Southeast Asan Tsunam that klled more than 280,000 and affected mllons, t s not unreasonable for economsts to consder how the threat of natural dsasters mght affect human and physcal captal decsons. Skdmore and Toya (2002) suggest that due to relatvely recent advances n forecastng, clmatc dsasters (as opposed to geologc dsasters) are prmarly a threat to mmoble physcal captal but not moble forms of captal such as human captal. The relatve ncrease n exposure to rsk of physcal captal provdes an ncentve for economc agents to nvest relatvely more heavly n human captal. The correlaton between exogenous natural dsasters and endogenous nvestment decsons over tme suggest that dsasters are a vald nstrument for factors that affect growth. In ths paper, we use measures of the propensty for natural dsasters to test for the endogenety of schoolng enrollment and changes n average years of schoolng over the perod. 3 We fnd evdence of endogenety. We therefore employ nstrumental varables technques to estmate the effects of changes n human captal on economc growth. The nstrumental varables estmaton procedure yelds a coeffcent on human captal accumulaton that s larger n magntude than found n our OLS estmates and n most prevous studes that use data from a wde range of countres and s closer to theoretc predctons. Bls and Klenow (2000) attempt to determne the causal relatonshp between schoolng and economc growth. They pont out that a common belef s that reverse causalty or smultanety s lkely to lead to an over-estmate of the effect of human 3 Schoolng enrollment data run through

7 captal accumulaton on growth because antcpated ncreases n future economc growth could cause schoolng to ncrease. In fact, however, the drecton of bas ntroduced by smultanety s ndetermnate. To llustrate, consder Fgure 1. We characterze two-way causalty wth two equatons: One n whch changes n human captal s a functon of changes n output, h = g( y), and vse versa, y = f( h), for two countres A, and B. These two countres can also be thought of as representatve of, say, OECD verses developng countres. The ntersectons between the two equatons for each country depct what we mght observe n the data. In ths example, the lne connectng the two ntersectons ndcates a negatve relatonshp between changes n output and changes n human captal. Of course, ths s just an example; the drecton of bas could be n another drecton. Therefore, to observe the causal relatonshp of changes n human captal on changes n output, we control for other factors that determne economc growth and dentfy the y = f( h) functon wth an approprate nstrument. Our paper mrrors nstrumental varables approaches to estmatng the contrbuton of physcal captal. Barro and Sal--Martn (1995) use the nstrumental varables technque to show that the rate of physcal captal nvestment s not a sgnfcant determnant of long-run growth. A smaller role for captal may be consstent wth the dea that current coeffcent estmates of changes human captal are too small, and an nstrumental varables approach for human captal accumulaton may be valuable. The remander of the paper s organzed as follows. The next secton provdes a revew of the relevant theoretcal consderatons and outlnes our emprcal strategy. In secton 3, we present an overvew of natural dsasters and descrbe the ntuton behnd ther effectveness as nstruments. In secton 4, we carefully evaluate the valdty of 4

8 natural dsasters as an nstrument and present the emprcal analyss. Secton 5 concludes. 2. Theoretcal and Emprcal Underpnnngs Two general theoretc approaches have been used as a bass for determnng the approprate functonal form for emprcal growth research. Frst, Barro (1991) and others buld on endogenous growth models (such as n Romer (1990)) n whch human captal s a prmary nput to research and development. In ths approach, the rate of technologcal progress depends on ntal stocks of human captal. Nelson and Phelps (1966) suggested that countres wth larger stocks of human captal absorb new deas and products that have been developed abroad more easly, whch could generate a feedback effect between growth and human captal. A second approach follows the work of Lucas (1988) who stressed the mportance of externaltes assocated wth connectons to others who are well educated. In ths context, ncreases n human captal per person lead to hgher rates of human and physcal captal nvestment and per capta economc growth. In addton, rsng human captal per person ncreases productvty n the market place, reducng fertlty rates and thus ncreasng output per capta (Becker, Murphy, and Tamura, 1990). These two approaches suggest that human captal could enter nto the growth equaton n ntal levels or n changes. A growth accountng approach s often used to emprcally evaluate the determnants of growth: an aggregate producton functon n whch per capta ncome y for country s dependent upon three nput factors, per capta physcal captal, k, per 5

9 capta human captal, h, and technology, A. Transformng a Cobb-Douglas producton functon, such as y = A k α h 1-α, nto a growth equaton yelds y / y = A / A + α ( k / k ) + (1 α)( h / h ), (1) whch suggests that changes n human captal should be an mportant determnant of growth. Prtchett's (2001) mcroeconomc estmates of the return to schoolng support these theores and mply that even n the absence of any human captal externaltes the contrbuton of changes n human captal to growth should be somewhere on the order of More recent studes also generate estmates n ths range. Evdence of human captal externaltes would requre estmates that exceed ths upper bound, but dsentanglng the feedback effects of ncome, technologcal advances, human captal accumulaton, and physcal captal nvestment s dffcult. The approprate approach would be an nstrumental varables technque such as one used by Barro and Sala-- Martn (1995). The problem has been fndng approprate nstruments. To our knowledge, researchers have not yet dentfed vald nstruments to approprately test for, and (f endogenety s found), use approprate econometrc procedures to estmate the effects of human captal accumulaton on growth. Thus, researchers have been cautous n ther nterpretaton of the coeffcent estmates on changes n average years of schoolng. In the next secton, we examne whether the propensty for natural dsasters s an approprate nstrument, and subsequently use measures of dsasters to estmate a growth equaton usng the nstrumental varables technque. 4 Krueger and Lndahl (2001) summarze the mcroeconomc research on returns to schoolng. Ther concluson regardng the how much educaton should matter n a growth regresson s smlar to that of Prtchett (2001). 6

10 3. Natural Dsasters as an Instrument Exposure to catastrophes vares sgnfcantly from country to country. 5 Although death tolls vary from year to year, major dsasters kll about 140,000 annually worldwde. Whle about 95% of the deaths occur n developng countres, natural catastrophes also have severe mpacts on developed countres. 6 Asa s affected most severely by natural dsasters both n terms of the number of events and deaths. In pre-modern tmes dsasters affected both physcal and human captal decsons. Hstorcally, recovery from extreme dsasters such as regon-wde famne caused by severe drought may have taken as long as 25 years. Physcal captal and sklls dsappeared wth death and out-mgraton of craftsmen. Before the ndustral revoluton, natural dsasters affected the wealthy, who gnorant of engneerng prncples, spent enormous sums of money to over-desgn ther structures to wthstand forces well n excess of the lkely forces (Alexander, 1993), whch may have reduced nvestment n other forms of productve captal. It s mportant to note that dfferent types of dsasters may affect physcal and human captal dfferently. Clmatc dsasters, whch are generally more predctable than geologc dsasters, may ncrease nvestment n human captal relatve to physcal captal because people are easer to evacuate than physcal captal. The hgher relatve rsk assocated wth dsasters provdes an ncentve for economc agents to nvest relatvely more heavly n moble captal lke educaton. As an llustraton of the exposure of 5 For example, Jones (1981) comples data on dsasters and fnds that a person lvng n Asa s about 30 tmes more lkely to de n a sesmc dsaster than one lvng n Europe. Ths calculaton s, of course, based on very mprecse data as talles on deaths and damages was not always compled. Alexander (1993) shows that most hurrcanes occur wthn the tropcs between lattudes 30 N and S, but not wthn ±5 of the equator where atmospherc dsturbances tend to be nsuffcent to cause them. 6 For example, accordng to Alexander (1993), n the Unted States 30 dsasters are declared n an average year, of whch floods account for about 40% of property damage, whle hurrcanes and other tropcal storms yeld 20% of all dsaster related fataltes. See Shah (1983). 7

11 physcal captal relatve to human captal to clmatc dsasters, n 1992 Hurrcane Andrew caused damages n southern Florda and Lousana exceedng $20 bllon but due to effectve forecastng and evacuaton procedures, only 13 deaths occurred. The effects on physcal relatve to human captal of geologc dsasters are less clear. Shaw (1994) estmates the cost of an earthquake equvalent n magntude to the Great Kanto earthquake of 1923 n the Tokyo area, home to about one-ffth of Japan s populaton, to be as much as $1.2 trllon 7 and holds potentally horrfc consequences for human lfe. The recent tsunam event n Southeast Asa s a dre llustraton of the catastrophc human loss that can accompany a dsaster event. In the case of clmatc dsasters or more generally natural events that can be forecasted, dsaster rsk could lower the expected return to physcal captal, reducng physcal captal nvestment. Ths n turn ncreases the relatve return to human captal. We therefore expect a postve relatonshp between clmatc dsasters and human captal, but the net long-run effect of dsaster rsk on physcal captal s theoretcally ambguous. Alternatvely, Dacy and Kunreuther (1969) and Tol and Leek (1999) suggest that the short-run economc effects of natural dsasters are postve. Snce dsaster-prone areas are lkely to use some of the lmted resources for dsaster management (stronger and better engneered structures for example), we mght expect a hgher level of nvestment to meet these needs. Ths dscusson suggests that dsaster rsk may ndeed have an effect on steady state levels of human and physcal captal. We assert, however, that durng the 20 th 7 $1.2 trllon s roughly one-ffth of the Japanese GDP. To provde a frame of reference, the estmated losses from the Kobe earthquake were $114 bllon or about one-tenth of the estmated effect of a quake of smlar magntude n Tokyo. Kobe s populaton s roughly one-ffth of Tokyo s more than 8 mllon people. If economc losses are proportonal to populaton sze, then a quake n Tokyo of smlar magntude would yeld losses of about $570 bllon or about half of Shaw s estmate. But Yokohama (wth a populaton of 3.3 mllon) and the hghly populated area surroundng Tokyo would also be affected. 8

12 century dsaster rsk has also played a role n human and physcal captal accumulaton, and ths asserton s supported by our emprcal analyss. Improvements n forecastng as well as nformaton dssemnaton that occurred over the past 100 years have enabled economc agents to assess rsk, partcularly from clmatc dsasters, and make approprate responses to such events. Technology-enhanced forecastng has effectvely enabled agents to protect human lfe (and thus human captal) from the onslaught of hurrcanes, typhoons, and the lke. Ths change may have altered the relatve expected returns to human and physcal captal accumulaton durng the perod of analyss, and as a result we mght observe changes n the accumulaton of human and perhaps physcal captal. The above dscusson suggests that dsasters can affect growth by affectng human and physcal captal nvestment. In Lucas (1988) and Azarads and Drazen (1990), ndvduals nvest n physcal and human captal, and the aggregate stock of human captal accumulated by prevous generatons has a postve ntergeneratonal externalty on the aggregate level of human captal of succeedng generatons. Ths ntergeneratonal externalty s the drvng force of growth and s mplctly assumed n a number of growth models n whch human captal s the key determnant of growth. 8 Consder the case where an economc agent may nvest n human and physcal captal. Increased rsk of captal destructon lowers the expected return to physcal captal, makng human captal relatvely more attractve. 9 Agents respond by ncreasng human captal nvestment, h / h. In addton, snce human captal s an mportant component n the 8 For example, f, n the Lucas (1988) model, the nfntely-lved representatve agent s nterpreted as a famly consstng of fntely-lved agents, no growth would arse wthout assumng some knd of ntergeneratonal externalty. 9 Of course, natural dsasters are also a rsk to lfe and thus also lower the expected return to human captal nvestment. However, human captal destructon (death) s a far less lkely result than loss of physcal captal. Therefore we expect the rsks to physcal captal to domnate the rsks to lfe. 9

13 adopton of new technologes (Benhabb and Spegel, 1994), the rate of technologcal advancement mght be enhanced, partcularly for developng countres n the process of catch-up. We can formalze ths reasonng wth a smple four equaton- model smlar to the approach used by Frankel and Romer (1999) to evaluate the effects of trade on economc development. Frst, the growth rate n a country s a functon of the rate of technologcal advancement, the rate of human captal accumulaton, and the rate of physcal captal nvestment and other factors: y / y = A / A + β ( k / k ) + λ( h / h ) + ε (2) where y s per capta ncome for country, A represents the level of technology, k s per capta physcal captal stock, h represents human captal stock per capta, and ndcates a change over tme. Fnally, ε represents other factors that determne growth n per capta ncome. In the sprt of Nelson and Phelps (1966), the rate of change n technologcal advancement depends on the ntal stock of human captal, the growth n human captal as well as other factors: A / A = α ( h ) + χ( h / h ) + π (3) The dea here s that n order for a country to adopt and make use of new technology, ts workers must frst have the ablty to learn and put the new technology to use. Substtutng equaton (3) nto equaton (2) yelds: y / y = α ( h ) + β ( k / k ) + ( χ + λ)( h / h ) + π + ε (4) where π represents factors that ndrectly affect growth va technologcal advancement (e.g., government subsdzed research and development) and ε represents factors that affect growth drectly. 10

14 The two other equatons concern the determnants of physcal captal nvestment and human captal accumulaton. The rate of physcal captal nvestment s a functon of two varables that reflect clmatc and geologc dsaster propenstes and other factors: k / k = ϕ + φc + γg + δ (5) n whch C represents the propensty for clmatc dsasters and G represent the propensty for geologc dsasters. The two dsaster types enter nto the equaton separately because each may have ther own effects on nvestment decsons. Lastly, δ represents other factors that determne nvestment n physcal captal. Human captal accumulaton s also modeled as a functon of clmatc and geologc dsasters and other factors: h / h = π + λc + µ G + ν (6) Agan, clmatc and geologc dsasters enter nto the equaton separately. The resdual n equaton (4), π + ε, are lkely to be correlated wth the resduals n equatons (5) and (6), δ, and ν. That s, factors that determne growth are also lkely to determne physcal and human captal accumulaton. The key dentfyng assumpton s that countres dsaster characterstcs are uncorrelated wth the resdual n equaton (2). In other words, the propenstes for clmatc and geologc dsasters are not affected by economc growth or by other factors that affect growth. It s dffcult to thnk of mportant ways that natural dsasters could affect long-run growth other than through ther effects on nvestment decsons. If C and G are uncorrelated wth π + ε, data on y / y h / h, k / k, C and, ntal perod h, G would allow us to estmate equaton (2) by nstrumental 11

15 varables: C and G are correlated wth h / h and k / k by (5) and (6) and are uncorrelated wth π + ε by our dentfyng assumpton. Skdmore and Toya (2002) show that the prevalence of clmatc and geologc dsasters are sgnfcant determnants of human captal accumulaton, suggestng that dsasters may work well as nstruments. To emprcally evaluate the valdty of dsasters as nstruments, we use data from the Center for Research on the Epdemology of Dsasters (CRED) at the Unverste Catholcque de Louvan n Brussels, Belgum (EMDAT, 2000). CRED has compled data on the occurrences and effects of mass dsasters n the world from 1900 to the present. CRED uses specfc crtera for determnng whether an event s classfed as a natural dsaster. 10 The database ncludes nformaton on number of events, damages, numbers affected, and deaths. We are reluctant to use data on damages, number affected, and deaths n ths study for three reasons. Frst, data on these factors are not always avalable. More mportantly, snce total damages ncrease wth ncome, the damages caused by dsasters may be endogenously determned. Smlarly, numbers of people affected fall wth ncome so that low-ncome countres experence more human casualtes and losses. Wealthy countres clearly spend more money on safety n terms of buldng codes, engneerng, and other safety precautons, reducng deaths. On the other hand, wealthy countres also have far more physcal captal at rsk should a natural event occur, ncreasng the possble damages. Fnally, as noted by Albala-Bertrand (1993), the mpacts of dsasters are sometmes exaggerated n developng countres n order to secure 10 The reasons for takng nto account a dsaster are: 1) 10 or more people were klled; 2) 100 or more people were affected/njured/homeless, 3) sgnfcant damages were ncurred; or 4) a declaraton of a state of emergency and/or an appeal for nternatonal assstance was made. 12

16 nternatonal assstance. Therefore, data on damages and loss of lfe are to some degree unrelable. Instead of damages, number affected, and deaths, we use the total number of sgnfcant events occurrng n a country over the perod because we beleve the occurrence of a natural event s the best exogenous measure of dsaster rsk avalable. Whether or not a country experences a natural event does not depend on ts level of development. In the remander of ths paper, we use the total number of natural events normalzed by land area snce larger countres generally experence more natural dsasters. We note, however, that usng the unadjusted total number of natural events yelds qualtatvely smlar results Emprcal Analyss 4.1 Qualty of the Instruments We begn our emprcal analyss by estmatng several regressons of dfferent measures of human captal to assess whether clmatc and geologc dsasters are robust determnants of both human and physcal captal accumulaton. The estmates presented n Table 1 come from a 1960 through 1990 cross-secton of 89 countres (or 87 countres n some specfcatons). We examne the relatonshp between three measures of human captal (secondary schoolng enrollment, changes n average years of secondary schoolng, and changes n average years of total schoolng) 12 and the dsaster varables whle controllng for the log of the ntal level of human captal and several contnent 11 See Skdmore and Toya (2002) for a summary of results usng the total number of natural events. 12 See Appendx Tables A, B, and C for detaled nformaton on specfc defntons, a lst of countres, and summary statstcs for all varables ncluded n the analyss. 13

17 specfc ndcator varables. 13 These and all regressons presented n the paper use Whte s (1980) heteroskedastcty-consstent covarance matrx. The clmatc dsaster varables are sgnfcant and postvely correlated wth each measure of human captal accumulaton, whereas there s a negatve but generally statstcally nsgnfcant coeffcent on the geologc dsaster varable. In column 4 of Table 1 we also present estmates of the determnants of physcal captal accumulaton. Nether geologc nor clmatc dsasters are sgnfcant determnants of growth n physcal captal per worker. 14 Whle these estmates demonstrate that clmatc dsasters are sgnfcantly correlated wth several dfferent measures of human captal accumulaton, they must also be uncorrelated wth the resdual from the growth equaton to be vald nstruments. Table 2 contans the results from tests of the correlaton between the nstruments and the resduals from the growth equatons shown n Table 3 (whch are dscussed below). These results show that the nstruments are uncorrelated wth the resduals from the growth equatons. 4.2 Growth Estmates Gven that the natural dsaster varables appear to be approprate nstruments, we conduct a Hausman test to determne whether an endogenous relatonshp exsts between growth and our measures of human captal. To conduct the Hausman test, we frst calculated the predcted values of our measures of human captal accumulaton (the frststage regresson). Snce physcal captal nvestment s also endogenously determned we 13 In regressons not presented but are avalable upon request, we also examne measures of schoolng qualty or qualty-adjusted human captal stock as n Wossman (2003). However, the prmary objectve n ths paper s to examne changes n schoolng over tme and not stock measures such as schoolng qualty or qualty-adjusted human captal stock. Skdmore and Toya (2002) fnd a postve correlaton between measures of schoolng qualty (Hanushek and Km, 1995) and clmatc dsasters. 14 In our three-stage least squares estmates, we also use the ntal level of physcal captal stock as an nstrument. Barro and Sal--Martn (1995) also use the ntal level of physcal captal stock as nstrument for growth n physcal captal. 14

18 also generate a predcted value from a physcal captal nvestment equaton, whch s presented n column 4 of Table 1. We then nclude the predcted values of human and physcal captal accumulaton varables n the second-stage growth regresson. The coeffcents on the predcted values of human and physcal captal nvestment are tested aganst zero usng an F test. 15 All three measures of changes n schoolng (as well as growth n physcal captal) are shown to be endogenously determned. Results of the Hausman test are presented n Appendx Table D. We now proceed to estmate the relatonshp between the three measures of human captal accumulaton and growth, usng the clmatc and geologc natural dsasters and the ntal level of physcal captal per worker as nstrumental varables, whle controllng for the natural logarthm of the respectve measure of the ntal level of human captal, the growth n physcal captal per worker, and several contnent-specfc ndcator varables. Before we present the results, a bref dscusson of the how changes n schoolng should enter nto the growth regresson s n order. A common approach to estmatng a growth equaton s the log-log specfcaton. As descrbed n Krueger and Lndahl (2001), a log-log specfcaton s approprate f one assumes that schoolng enters an aggregate Cobb-Douglas producton functon lnearly. Topel (1999), however, argues that the Mncer-type specfcaton s more approprate, and that human captal should be specfed as an exponental functon of schoolng n the producton functon. Ths means 15 See Kennedy (1994) for detaled dscusson of ths verson of the Hausman test. 15

19 that the change n lnear years of schoolng would enter the growth functon. 16 We follow Krueger and Lndahl (2001) and others who estmate lnear educaton specfcatons. The frst column n Table 3 contans estmates of growth n GDP per capta regressed on a constant, growth n physcal captal per worker, and secondary schoolng enrollment. Ths regresson yelds a postve and sgnfcant coeffcent on secondary schoolng enrollment. We fnd a smlar coeffcent on secondary schoolng enrollment when we nclude ntal secondary schoolng years and a seres of regonal dummy varables as addtonal covarates. When these varables are ncluded (column 2), the OLS estmates of the contrbuton of human captal accumulaton s nearly dentcal to column 1. Column 3 presents the nstrumental varables estmaton. Here the coeffcent on secondary schoolng enrollment nearly trples. Whle these estmates suggest that the effect of human captal accumulaton s based downward n the OLS estmates, the nature of ths specfcaton prevents us from makng drect comparsons wth the mcroestmates of the effect of human captal accumulaton. We now turn to an examnaton of measures of changes n schoolng, whch provde estmates that are drectly comparable to the mcro-estmates. The fourth column n Table 3 contans estmates of growth n GDP per capta regressed on a constant, growth n physcal captal per worker, and the change n average years of secondary schoolng. Ths regresson yelds a postve and sgnfcant coeffcent on the change n average years of secondary schoolng: a coeffcent estmate of 0.21 s 16 Consder the followng Cobb-Douglas producton functon: y=ak α h 1-α, where y s per capta GDP, A s the level of technology, k s per capta captal stock, and h s per capta human captal. Transformng ths functon nto log form yelds: lny = lna + αlnk + (1-α)lnh. Wth a Mncer-type model, h equals ψe s wth s = average years of schoolng. Takng the log dfference over tme yelds: lny t lny t-1 = (lna t lna t-1 ) + α(lnk t - lnk t-1 ) + (1-α)(lnh t - lnh t-1 ). Substtutng n for h yelds: lny t lny t-1 = lna t lna t-1 + α(lnk t - lnk t-1 ) + (1-α)(lnψ + s t - lnψ - s t-1 ) or lny t lny t-1 = lna t lna t-1 + α(lnk t - lnk t-1 ) + (1-α)(s t - s t-1 ). 16

20 n the lower range suggested by Prtchett (2001). We fnd a smaller coeffcent on changes n secondary schoolng when we nclude ntal years of schoolng and a seres of regonal dummy varables as addtonal covarates. 17 When these varables are ncluded (column 5), the OLS estmates of the contrbuton of human captal accumulaton s about 0.14, a number that falls below Prtchett's (2001) suggested range. Ths result reflects our motvaton for explorng endogenety: OLS estmates are generally smaller than values suggested by theoretc or mcroeconomc studes. In column 6, we present the three-stage least squares estmates of changes n average years of secondary schoolng. Usng nstrumental varables leads to a coeffcent estmate on changes n secondary schoolng of 0.46, whch s two to three tmes hgher than the OLS estmates. Evdence of human captal externaltes would requre estmates to exceed Prtchett s upper range of These fndngs suggest that human captal accumulaton plays a more mportant role n economc growth than many of the exstng emprcal studes that nclude a wde range of countres n the analyses suggest. 18 The estmates presented here also provde some emprcal evdence n support of Lucas human captal externalty theory: an estmate of 0.46 exceeds the upper range value of 0.4 suggested by mcro evdence. We also notce that once we use the nstrumental varable approach, the coeffcent on physcal captal nvestment s reduced and becomes statstcally nsgnfcant, consstent wth Barro and Sala--Martn (1995). 17 The error terms are normally dstrbuted when both changes n schoolng and ntal schoolng are ncluded n the specfcatons. 18 Krueger and Lndahl (2001) present on page 1125 coeffcents on changes n schoolng that range between and On page 1112, they obtan coeffcent estmates on changes n human captal that are as hgh as 0.61, but only f they exclude growth n physcal captal from the regresson. After removng outlers Temple (1999b) present coeffcents on changes n schoolng rangng between and after removng nfluental outlers. Usng data on OECD countres and constranng the coeffcent on growth n physcal captal to 0.35, Englebrecht (2003) generates coeffcents on changes n schoolng that are as hgh as 0.37 and However, he must constran the coeffcent on captal to obtan coeffcent estmates on changes n schoolng that are ths hgh. 17

21 In columns 7-9, we modfy the regressons presented n columns 4-6 by replacng changes n average years of secondary schoolng wth average years of total schoolng. These estmates mrror those found n columns 4-6 except that the coeffcent estmates on change n average years of total schoolng are slghtly smaller. The nstrumental varables coeffcent estmate on the change n average years of schoolng s 0.32, whch s stll n the upper range suggested by mcro evdence. Agan consstent wth Barro and Sala--Martn (1995), the coeffcent on growth n physcal captal becomes nsgnfcant n the nstrumental varables analyss. 4.3 Robustness The estmated coeffcents on human captal accumulaton are robust to the ncluson of other varables that nfluence economc growth. We explored the robustness of human captal effects to the ncluson of a country s dstance from the equator (Lattude), the approxmate proporton of land area subject to a tropcal clmate (Tropcs), the average rato of exports plus mports to GDP for the perod (Trade), and whether a country s landlocked (Landlocked). The estmated fndngs on the varables that characterze human captal accumulaton n these estmates, whch are presented n Appendx Table E-1, are qualtatvely smlar to those presented n Table 3. Countres n Asa have experenced a remarkable rate of economc development over the perod of analyss. Thus, rates of both physcal and human captal accumulaton have been exceptonally hgh. It s also the case the Asan countres experence frequent natural dsasters. It s possble that our fndngs may be drven by a spurous correlaton between dsasters and economc development n these Asan countres. Although we nclude regonal dummes n Table 3 to control for these factors, we also examne 18

22 whether our fndngs are robust to the excluson of these countres. In a seres of addtonal regressons presented n Appendx Table E-2, we fnd that our results are robust to the excluson of these countres. In a seres of regressons that exclude dfferent sets of Asan and rng of fre countres, we show that the coeffcents on the measures of human captal accumulaton are smlar to those presented n ths paper. 19 Temple (1999b) shows that n a broader dataset, such as the one used n the present study, the correlaton between economc growth and ncreases n educatonal attanment can be masked by unrepresentatve data. Usng the same data but omttng a number of outlers, Temple shows that the results of Benhabb and Spegel (1994) are senstve to the excluson of outlers. We therefore use a procedure outlned by Krasker, Kuh, and Welsch (1983) to dentfy outlers. The test results dentfy just fve countres (Botswana, Korea, Lesotho, Sngapore, and Thaland) as potental outlers. We then omtted these countres and then re-estmated each regresson. The results are very smlar to those reported here (see Appendx Table E-2). Thus, the presence of nfluental outlers does not appear to be affectng our results. 4.4 Why Are the Three-Stage Least Squares Estmates Greater Than the OLS Estmates? The fndng that the nstrumental varables estmates generate coeffcents on human captal accumulaton that are larger than the ordnary least squares estmates s consstent wth theory, but, to be thorough, we explore n a mechancal sense why ths s 19 We estmate three sets of regressons. Frst, we exclude fve hgh-growth East Asan countres (Hong Kong, Japan, Korea, Sngapore, and Tawan). We then exclude a larger set of eght hgh-growth Asan countres (Hong Kong, Indonesa, Japan, Korea, Malaysa, Sngapore, Thaland, and Tawan). Fnally, we exclude all 18 countres consdered by the U.S. Geologcal Survey to be n the rng of fre (Canada, Chle, Colomba, Costa Rca, Ecuador, El Salvador, Guatemala, Honduras, Indonesa, Japan, Malaysa, Mexco, New Zealand, Ncaragua, Panama, Papua New Gunea, Phlppnes, and the Unted States). All of these results are qualtatvely smlar to those presented n ths paper. 19

23 so. The ordnary least squares estmate s determned by the partal assocaton between economc growth and human captal accumulaton, whle the nstrumental varables estmate s determned by the partal assocaton between economc growth and the component of human captal accumulaton correlated wth the nstruments. Gven that the ordnary least squares estmates are smaller than the nstrumental varables estmate, the partal assocaton between economc growth and component of human captal accumulaton not assocated wth the nstruments s weaker than ts partal assocaton the component that s assocated wth the nstruments. In Fgures 2, 3, and 4 we present these two partal assocatons for the same two measures of human captal accumulaton used n Table 3. In each of the fgures, Panel A shows the postve partal assocaton between economc growth and the component of human captal accumulaton that s correlated wth the nstruments. Ths s the postve assocaton that underles the postve coeffcent on human captal accumulaton n the nstrumental varables regressons found n Table 3. Panel B shows the partal assocaton between economc growth and the component of human captal accumulaton that s not correlated wth the nstruments. Ths assocaton s consderably smaller than the assocaton shown n Panel A. It s ths smaller relatonshp that causes the ordnary least squares estmate to be less than the nstrumental varables estmates. The fgures agan confrm that the dfference between the ordnary least squares estmate and the nstrumental varables estmates s not due to just a few outlers. IV. Conclusons The gap between the theoretcally-predcted contrbuton of human captal to growth and the contrbuton estmated n most studes s ncreasngly recevng attenton. 20

24 Nearly all studes that address ths problem, however, address the problem as one of measurement or specfcaton error. Very few studes address the possblty that human captal s an endogenous functon of growth. The most lkely reason that most studes do not address ths possblty s that approprate nstruments are dffcult to fnd. In ths paper, we frst show that human captal s, n fact, endogenously determned. We then show that clmatc natural dsasters are a sgnfcant determnant of secondary schoolng enrollment, and changes n secondary and total schoolng, but not of economc growth drectly. Thus, we appear to have dentfed a vald nstrument wth whch we can examne the potental endogenety of human captal accumulaton n estmates of economc growth. We then use an nstrumental varables procedure to estmate the effects of changes n schoolng on long-run economc growth. We demonstrate that our fndngs are robust; they appear not to be drven by outlers and are robust to the ncluson of a wde range of varables consdered mportant determnants of economc growth and factor accumulaton n the prevous lterature. These estmates also provde lmted emprcal evdence n support of the Lucas human captal externalty theory. Our results suggest that prevous estmates may be based downward due to the smultanety between human captal accumulaton and economc growth, and that endogenety should be serously consdered n studes of economc growth. 21

25 References Albala-Bertrand, J. Poltcal Economy of Large Natural Dsasters. Oxford: Clarendon Press, Alexander, D. Natural Dsasters, New York: Chapman and Hall Azarads, C., and A. Drazen. "Threshold Externaltes n Economc Development." Quarterly Journal of Economcs 105 (2), 1990, Barro, R. "Economc Growth n a Cross Secton of Countres." Quarterly Journal of Economcs, 106 (2), 1991, Barro, R., and J. Lee. "Internatonal Measures of Schoolng Years and Schoolng Qualty." Amercan Economc Revew, 86 (2), 1996, Barro, R., and X. Sala--Martn. Economc Growth. Boston: McGraw Hll Bassann, A., and S. Scarpetta. Does Human Captal Matter for Growth n OECD Countres? A Pooled Mean-Group Approach. Economcs Letters, 74 (3), 2002, Becker, G. S., K. M. Murphy, and Tamura, R. Human captal, fertlty, and economc growth. Journal of Poltcal Economy, 98 (5), 1990, S Benhabb, J., and M. Spegel. "The Role of Human Captal n Economc Development: Evdence From Aggregate Cross-Country Data." Journal of Monetary Economcs, 34, 1994 (2), Bls, M., and P. Klenow. "Does Schoolng Cause Growth?" Amercan Economc Revew, 90 (5), 2000, Dacy, D. C., and H. C. Kunreuther. The Economcs of Natural Dsasters. New York: Free Press, Easterly, W., and H. Yu. Global Development Network Growth Database. Taken from the World Bank Research Department's web page, Engelbrecht, H. Human Captal and Economc Growth: Cross-secton Evdence for OECD Countres. Economc Record, 79 (2), 2003, S40-S51. Englander, A., and A. Gurney. Medum-term Determnants of OECD Productvty. OECD Economc Studes, 22 (2), 1994, EMDAT, The OFDA/CRED Internatonal Dsaster Database, Unverste Catholcque de Louvan, Brussels, Belgum,

26 Frankel, J., and D. Romer. Does Trade Cause Growth? Amercan Economc Revew, 89 (3), 1999, Gemmel, N. Evaluatng the Impacts of Human Captal Stocks and Accumulaton on Economc Growth. Oxford Bulletn of Economcs and Statstcs, 58 (1), 1996, Glewwe, P., and J. Hanan. Economc Growth and the Demand for Educaton: Is There a Wealth Effect? Journal of Development Economcs, 74 (1), 2004, Hanushek, E., and D. Km. Schoolng, Labor Force Qualty, and Economc Growth. NBER Workng Paper No. 5399, Hanushek, E., and D. Kmko. Schoolng, Labor-Force Qualty, and the Growth of Natons. Amercan Economc Revew, 90 (5), 2000, Hall, R.E., and C.I. Jones. Why Do Some Countres Produce So Much More Output per Worker than Others?", Quarterly Journal of Economcs, 114 (1), 1999, Jones, E. L. The European Mracle: Envronments, Economes and Geopoltcs n the Hstory of Europe and Asa. Cambrdge: Cambrdge Unversty Press, Kennedy, P. A Gude to Econometrcs. Cambrdge: The MIT Press, Krasker, W., E. Kuh, and R. Welsch. Estmaton of Drty Data and Flawed Models. Handbook of Econometrcs, Volume I. Grlches and Intrllgator eds. North- Holland Publshng Company, New York, 1983, Krueger, A., and M. Lndahl. Educaton for Growth: Why and for Whom? Journal of Economc Lterature, 39 (4), 2001, Kyracou, G. Level and Growth Effects of Human Captal, workng paper, C. V. Star Center, NYU, Lucas, R., "On the Mechancs of Economc Development." Journal of Monetary Economcs, 22 (1), 1988, Mankw, G., D. Romer, and D. Wel. "A Contrbuton to the Emprcs of Economc Growth." Quarterly Journal of Economcs, 106 (2), 1992, Nelson. R., and E. Phelps. Investment n Humans, Technologcal Dffuson, and Economc Growth. Amercan Economc Revew, 56 (1/2), 1966, Nehru, V., E. Swanson, and A. Dubey. New Database on Human Captal Stock n Developng and Industral Countres: Sources, Methodology, and Results. Journal of Development Economcs, 46 (2), 1995,

27 Prtchett, L. "Where Has All the Educaton Gone?" World Bank Economc Revew, 15 (3), 2001, Romer, P. Endogenous Techncal Change. Journal of Poltcal Economy, 98 (5), 1990, Sachs, J. D. and Warner, A. M. Fundamental sources of long-run growth. Amercan Economc Revew Papers and Proceedng, 84 (2) 1997, Shah, B. V. Is the Envronment Becomng More Hazardous? A Global Survey 1947 to Dsasters, 7, 1983, Shaw, H., As quoted n the New York Tmes, September 20, p. C9, Skdmore, M., and H. Toya. "Do Natural Dsasters Promote Long-run Growth?" Economc Inqury, 40 (3), 2002, Summers, R., and A. Heston. "The Penn World Table (Mark 5.6)." Taken from the NBER Web page, Temple, J. The New Growth Evdence. Journal of Economc Lterature, 37 (1), 1999a, Temple, J. A Postve Effect of Human Captal on Growth. Economc Letters, 65, 1999b (1), Temple, J. Growth Effects of Educaton and Socal Captal n the OECD Countres. OECD Economc Studes, 33 (2), 2001, Tol, R., and F. Leek. Economc Analyss of Natural Dsasters, n Clmate, Change and Rsk. T. E. Downng, A. J. Olsthoorn and R. S. J. Tol, eds. Routledge, 1999, Topel, R. Labor Markets and Economc Growth, n Handbook of Labor Economcs. Orley Ashenfelter and Davd Card, eds. Amsterdam: North Holland, Whte, H. A Heteroskedastcty-consstent Covarance Matrx and a Drect Test for Heteroskastcty. Econometrca, 48 (4), 1980, Wossman, L. Specfyng Human Captal. Journal of Economc Surveys, 17 (3), 2003,

28 Dependent varables Table 1 Dsasters and Captal Accumulaton Secondary School Enrollment Change n Secondary Schoolng Years Change n Total Schoolng Years Growth n Physcal Captal Per Worker Constant (8.304) (4.352) (9.658) (5.550) Per Land Clmatc Dsasters (3.223) (3.143) (1.671) (0.878) Per Land Geologc Dsasters (-2.758) (-1.214) (-0.146) (-1.020) Log (Intal Secondary Schoolng Years) (2.708) (-1.356) Log (Intal Total Schoolng Years) (-0.951) Log (Intal Physcal Captal Per Worker) (-4.434) Sub-Saharan Afrca (-4.377) (-3.112) (-3.718) (-3.409) Latn Amerca (-0.821) (-0.849) (-0.021) (-1.224) NIES and ASEAN (0.416) (1.292) (1.121) (4.105) OECD (4.569) (2.548) (1.707) (3.169) Number of Observatons Adjusted R Numbers n parentheses are t-values based on the Whte (1980) heteroscedastcty-consstent covarance matrx. 25

29 Dependent Varables Table 2 Resduals and Natural Dsasters Varables Resduals from OLS Estmate Usng Secondary School Enrollment Resduals from OLS Estmate Usng Change n Secondary Schoolng Years Resduals from OLS Estmate Usng Change n Total Schoolng Years Per Land Clmatc Dsasters (1.056) (0.971) (0.955) Number of Observatons Adjusted R Dependent Varables Resduals from OLS Estmate Usng Secondary School Enrollment Resduals from OLS Estmate Usng Change n Secondary Schoolng Years Resduals from OLS Estmate Usng Change n Total Schoolng Years Per Land Geologc Dsasters (0.493) (0.211) (0.135) Number of Observatons Adjusted R Resduals, whch are used as dependent varables here, come from equatons 2, 5, and 8 of Table 3, respectvely. Numbers n parentheses are t-values based on the Whte (1980) heteroscedastctyconsstent covarance matrx. 26

30 Table 3 Human Captal Accumulaton and Growth Dependent Varable: Per Capta GDP Growth ( Average) Estmaton OLS OLS IV OLS OLS IV OLS OLS IV Constant (-0.985) (0.680) (-0.696) (0.237) (1.987) (0.491) (0.319) (0.333) (0.807) Growth n Physcal Captal Per Worker (9.336) (6.805) (0.960) (9.213) (6.918) (0.723) (9.397) (6.665) (0.965) Secondary School Enrollment (5.914) (2.664) (3.710) Change n Secondary Schoolng Years (4.193) (3.029) (3.362) Change n Total Schoolng Years (2.278) (2.308) (1.866) Log (Intal Secondary Schoolng Years) (0.708) (-1.900) (2.171) (1.760) Log (Intal Total Schoolng Years) (2.821) (3.626) Sub-Saharan Afrca (-0.224) (-0.025) (-0.304) (0.078) (-0.475) (0.628) Latn Amerca (-1.653) (-1.819) (-1.607) (-1.621) (-1.968) (-0.831) NIES and ASEAN (3.029) (3.769) (2.760) (2.083) (2.675) (1.201) OECD (-0.371) (-1.760) (0.390) (-0.327) (0.432) (-1.177) Number of Observatons Adjusted R Numbers n parentheses are t-values based on the Whte (1980) heteroscedastcty-consstent covarance matrx. 27