Solow and the States: A Panel Data Approach *

Transcription

1 Solow and he Saes: A Panel Daa Approach * (JEL Caegory: O47, C32, R11) (Keywords: Growh Empirics, Panel Daa, Regional Growh) Ocober, 2000 Seven Yamarik Deparmen of Economics, The Universiy of Akron, Olin Hall, Akron, OH phone: (330) fax: (330) yamarik@uakron.edu Absrac This sudy adops a panel daa approach o explain he pos-war growh process across U.S. saes. Using sae-level daa for five decades, we esimae he growh empirics model of Mankiw, Romer and Weil (1992). This paper finds ha pos-war growh raes across U.S. saes have been converging following he process prediced by he Solow growh model. However, by conrolling for sae-level echnology differences, he esimaed impac of human capial is significanly reduced, while he rae of convergence increases from 2.7 o 5.0 percen and varies across geographic regions. As a consequence, his sudy suggess ha regional variaions in convergence found in he ime series ess can be explained by he neoclassical growh process of Solow. * This paper was presened a he 2000 Wesern Economic Associaion Inernaional Conference in Vancouver.

2 1 I. INTRODUCTION The process of regional growh has reemerged as an area of ineres for economiss and geographers. Much of he renewed ineres can be aribued o he rise of endogenous growh heory and he challenges i poses o radiional, neoclassical growh heory. In an endogenous growh model, differences in invesmen raes, educaion and public policy can lead o persisen differences in per capia growh raes across economies. However, he neoclassical growh model predics ha growh raes should converge over ime condiioned upon invesmen raes, populaion growh raes and educaion. Thus, in he neoclassical model, public policy ha seeks o raise privae and public invesmen will only have a ransiional effec on he growh rae. The framework adoped for invesigaing regional growh is he growh empirics mehod of Mankiw, Romer and Weil (1992). Using daa on income, invesmen, populaion and schooling, Mankiw, Romer and Weil develop esable implicaions of he neoclassical or Solow growh model. Holz-Eakin (1993), Holz-Eakin and Schwarz (1995), Vohra (1996) and Garofalo and Yamarik (1999) apply he Mankiw, Romer and Weil framework o he U.S. saes for he period. These auhors find srong evidence ha he Solow growh model augmened wih human capial explains sae-level growh in real oupu. However, hese sudies do no adequaely conrol for echnological and oher unobserved differences across saes. For example, he cross-secional sudies by Vohra (1996) and Garofalo and Yamarik (1999) conrol for regional differences, bu canno conrol for sae-wide differences. By creaing year-o-year variaion in each variable, Holz-Eakin and Schwarz (1995) are able o include sae dummy variables. However, he shor lengh of heir panel inerval does no seem appropriae for he sudy of long-run growh. Moreover,

3 2 he shor lengh exacerbaes measuremen error in annual observaions, emphasizes shor-erm flucuaions and reduces he ime series variaion across panels. This sudy adops a panel daa approach o explain he pos-war growh process across U.S. saes. Using sae-level daa for five decades, we esimae he growh empirics model of Mankiw, Romer and Weil. Our approach exends he regional growh lieraure in four imporan ways. Firs, he overall ime period under observaion is increased from he ypical, 20-year period o a 50-year span. This exended ime period is no only more appropriae in capuring long-run growh phenomena bu i also brings in he pre- and pos-produciviy slowdown periods. Second, by increasing he number of observaions, a panel daa approach improves he efficiency of he esimaes. Third, he use of panel daa can conrol for he possibiliy of unobserved, echnological differences. In he inernaional growh lieraure, sudies by Knigh, Loayza and Villanueva (1993), Islam (1995) and Caselli, Esquivel and Lefor (1996) indicae ha hese cross-secional differences may be imporan. Moreover, Karras and Evans (1996) and Evans (1997) find ha he esimaed rae of convergence is biased downward if cross-sae heerogeneiy is no properly conrolled for. Fourh, he choice of a 10-year panel lengh no only reduces measuremen error bu i also allows for a direc comparison wih he convergence ess of Barro and Sala-í-Marin (1991, 1992). This paper finds ha pos-war growh raes across U.S. saes have been converging following he process prediced by he Solow growh model. As in he cross-secional sudies, he regressions resuls here show srong evidence of condiional convergence. 1 1 There are wo ypes of convergence -- absolue and condiional. Absolue convergence is a siuaion where saes wih lower levels of income per worker grow faser. Condiional convergence, on he oher hand, is where saes wih lower levels of income per worker grow faser condiioned upon differences in invesmen raes, populaion growh raes and educaion. See Barro and Sala-í-Marin (1995, chaper 10), for a more complee discussion of hese conceps.

4 3 Specifically, he coefficien on he iniial level of income per worker is negaive, while hose on physical and human capial are posiive. Moreover, he implied capial share of oupu falls is close o he naional income share paid on capial. These coefficien values are obained no only when fixed sae effecs are included, bu also are also robus o he exclusion of ransfer paymens, inclusion of a measure of indusrial srucure and he division of he saes ino geographic regions. In using a panel daa approach, however, several differen resuls emerge relaive o hose found in he cross-secional sudies. Firs, by conrolling for unobserved, sae-level differences, he esimaed rae of convergence increases from 2.7 o 5.0 percen. Second, he esimaed impac of human capial, measured as he percenage of he populaion holding a four-year college degree, is significanly reduced wih he inclusion of fixed sae effecs and indusrial srucure. Third, when U.S. saes are separaed ino geographic regions, he Solow growh model explains he pos-war growh process wihin each region. Furhermore, he speed of convergence ranges from a 2.2 percen divergence rae o a 19.4 percen convergence rae. As a consequence, his sudy suggess ha regional variaions in convergence found in he ime series ess of Carlino and Mills (1993) and Loewy and Papell (1996) can be explained by he neoclassical growh process of Solow. The remainder of he paper proceeds as follows. Secion II derives he Solow growh model along he lines of Mankiw, Romer and Weil. Secion III describes he empirical design and he daa. Secion IV provides he esimaion resuls. Concluding remarks are presened in secion V.

5 4 II. THE SOLOW GROWTH MODEL The Solow growh model sars wih a consan reurns o scale producion funcion. There are wo inpus, capial and labor, which are paid heir marginal producs. Assuming a Cobb- Douglas producion funcion, oupu a ime is: y = α 1 α ( A l ) k 0 < α < 1 (1) where y is oupu, A is he level of echnology, k is he sock of capial and l is he quaniy of labor a ime. The coefficiens α and (1-α ) represen he elasiciies of oupu wih respec o capial and labor, respecively. Because each facor is paid is marginal produc, equaion (1) predics ha α and (1-α ) equal he income share paid o capial and labor, respecively. Technology and labor are assumed o grow a consan raes g and n, respecively: A = l = g A 0 e (2) n l 0 e. (3) Lasly, he sock of capial is governed by he capial accumulaion equaion k! = sk y k δ 0 < δ < 1 (4) where s k represens he percenage of income saved for gross invesmen in physical capial and δ represens he rae of depreciaion. Le k ~ K / AL and ~ y Y / AL represen he sock of capial and oupu in unis of effecive labor. Log-differeniaing k ~ wih respec o ime and subsiuing in (2) - (4), one ges he fundamenal differenial equaion of he Solow growh model ~ ~. (5) k!~ α = sk k ( n + g + δ ) k

6 5 Wih (5) and (1), he model can be solved for he seady-sae Equaion (5) implies ha k ~ and y~ converge o seady-sae values ~ y * in erms of α, g, n, sk and δ. ~ * k and ~ y * defined as ~ * k = ( s k n + g + δ ) 1/(1 α ) (6) α /(1 α ) ~ y * = s k ( δ ). (7) n + g + Taking he logarihm of (7) and rearranging erms, we ge y α α ln = ln[ A 0 ] + g + ln[ sk ] ln[ n + g + δ ]. (8) l 1 α 1 α Equaion (8) describes he seady-sae value of oupu per worker. I predics ha he log of oupu per worker should be posiively relaed o he log difference beween he gross invesmen rae s k and he erm [ n + g + δ ]. Lasly, he Solow growh model makes predicions abou he ransiion o seady-sae. Approximaing y~ around he seady-sae ~ y *, he ransiion is given by ln[ ~ y ] λ. (9) = ( ln[ ] ln[ ~ ]) ~* y y where λ = ( n + g + δ )(1 α). The parameer λ is he speed or rae of convergence. Solving he differenial equaion (9) and hen subsiuing ino (7) for esable implicaion ~ y *, we ge he following y ln l y ln l 0 0 λ α λ α = ( 1 e ) ln[ sk ] (1 e ) ln[ n + g + δ ] 1 α 1 α λ λ ( 1 e ) ln[ y0 / l0 ] + (1 e )ln[ A0 ] + g. (10)

7 6 Equaion (10) predics ha U.S. saes wih low iniial oupu per worker possess faser ransiional growh raes han saes wih higher iniial oupu per worker, condiioned upon he values {s k, n, g, δ}. Mankiw, Romer and Weil find ha augmening he Solow model wih measures of human capial improve is predicive power of explaining cross-counry growh raes. This paper follows previous regional growh sudies and incorporaes human capial as a sock variable h. As a resul, he producion funcion becomes y = α β 1 α β k h ( A l ) 0 < α, β < 1 (11) where β represens he oupu elasiciy on he sock of human capial. Therefore, he seadysae equaion (8) can be rewrien as y ln = l ln[ A 0 ] α 1 α α 1 α β ~ 1 α * + g + ln[ sk ] ln[ n + g + ] + h (12) δ where ~ * h represens he seady-sae level of human capial per uni of effecive labor. Lasly, wih human capial, he ransiion equaion (10) becomes y ln l y ln l 0 0 λ α λ α = ( 1 e ) ln[ sk ] (1 e ) ln[ n + g + δ ] + 1 α 1 α λ β ~ * λ λ ( 1 e ) h (1 e )ln[ y0 / l0 ] + (1 e )ln[ A0 ] 1 α + g (13) where λ = ( n + g + δ )(1 α β ).

8 7 III. EMPIRICAL DESIGN Economeric Design The seady-sae and ransiional growh equaions can be represened by he following dynamic panel models: j ln y i, = β j xi, + η + µ i + ν i j j ln yi, ln yi, T = yi, T + j ln xi, + + i i j ln (14) γ ln β η µ + ν (15) where i indexes he sae, indexes ime and T is he lengh of he ime inerval. y i, is he level of real income per worker a he end of he panel, while yi T, is he level of real income per worker a he beginning of he panel. The x, 's are measures of invesmen, labor force j i growh and he sock of human capial. µ i is he saespecific erm. ν i is he ransiory error erm. η is he ime-specific erm, while The ime- and sae-specific erms are assumed o be fixed. The η erm capures oal facor produciviy shocks ha are common o all saes for each decade. Since echnology improves over ime, η is fixed and no randomly deermined from a saionary process. The µ i erm, on he oher hand, conrols for land area, weaher, raw maerials and oher facors ha can cause oal facor produciviy differences across saes. Since he enire populaion of coniguous saes is included in he sample, µ is also assumed o be fixed. i Daa A panel daa approach requires ha he enire ime period be divided ino muliple panels. Using he Summers-Heson inernaional daa se, Knigh, Loayza and Villanueva (1993) and

9 8 Islam (1995) choose five-year inervals in order o creae five panels for he period. However, he lengh of he panel is imporan. As Barro (1997) poins ou, shor-erm periods are no appropriae for he sudy of long-run growh. The daa will more likely be influenced by measuremen error and shor-erm disurbances. Given he duraion of he U.S. business cycle, hese issues seem imporan in a sudy of sae-level growh. In his paper, we selec he period. This choice provides wo benefis. Firs, i allows us o selec five panels of daa covering one decade each. This en-year panel lengh no only reduces shor-erm flucuaions, bu i also allows for comparison wih he convergence resuls of Barro and Sala-í-Marin. Second, i brings in he decades before and afer he produciviy slowdown. The inclusion of his episode seems essenial in a sudy of long-run growh in he U.S. economy. The one drawback, however, is ha personal income mus be used as a measure of oupu. Given he increase in he scope of he sudy, we believe ha his decision is jusified. The sample is annual daa on income, labor and capial for he fory-eigh coniguous U.S. saes. The daa on real income and labor are obained from he Bureau of Economic Analysis (2000) and he Bureau of Labor Saisics (2000), respecively. Real income is measured as nominal income divided by he consumer price index. Labor is measured as oal nonagriculural employmen. Esimaes on invesmen in physical capial are aken from Garofalo and Yamarik (1999). Lasly, he sock of human capial is measured as he percenage of individuals, age 25 or older, who have compleed four or more years of college. The daa are obained from he 1950, 60, 70, 80 and 90 Census of Populaion. Lasly, growh raes are esimaed as follows y ) = a + bi rend + u i, for = 0,,T (16) ln( i,

10 9 where rend is a ime rend. This regression is run for each sae i where he parameer value of b i is used as he esimae of he annual growh rae. As deailed by Chaerji (1998), he advanage of esimaing growh raes using his process raher han aking log differences is ha more han wo daa poined are used. As a resul, volailiy in a sae's growh rae in he inervening years can be accouned for and measuremen errors in an observaion(s) are minimized. IV. ESTIMATION RESULTS Resuls for Seady-Sae In Table 1, he seady-sae equaions (8) and (12) are esimaed. The resuls for he unresriced model are shown on he op half, while hose of he resriced model (where he coefficiens on ln(s) and ln(n + g + δ) are forced o be equal in magniude and opposie in sign) are on he boom half. The labor force growh rae n is esimaed using equaion (16), while he rae of depreciaion is from Garofalo and Yamarik (1999). The produciviy growh rae is assumed o be 0.02 in all panels. In columns 1 and 2, he basic seady-sae equaion (8) is esimaed wih fixed ime and region effecs and wih fixed ime and sae effecs, respecively. 2 The coefficiens for boh he unresriced and resriced models have heir anicipaed signs. However, he coefficiens are significan only under he fixed sae effecs represenaion. Moreover, in he resriced model, he poin esimaes imply a low value for he oupu elasiciy α. 2 We use he regional classificaion of he Bureau of Economic Analysis o allow comparison wih he ime series resuls of Carlino and Mills (1993) and Loewy and Papell (1996). The eigh regions are New England, Mideas, Grea Lakes, Plains, Souheas, Souhwes, Rocky Mounain and Far Wes.

11 10 The seady-sae equaion wih human capial (12) is esimaed in columns 3 and 4. The coefficiens on ln(s) and ln(n + g + δ) remain largely unaffeced. The coefficien on he sock of human capial, however, is posiive and highly significan under boh specificaions. Noneheless, he imprecision of he coefficien esimaes and he low values of he oupu elasiciies α and β cas doub on he validiy seady-sae equaion. Therefore, he resuls in Table 1 sugges ha U.S. saes have no been in a seady-sae equilibrium during he poswar period. Resuls for Transiional Growh In Table 2, he ransiional growh equaions (10) and (13) are esimaed. As before, he model is esimaed wih fixed ime and region effecs or wih fixed ime and sae effecs. The coefficien on he iniial level of income per worker is negaive and srongly significan under boh specificaions. This confirms ha growh raes of U.S. saes are converging condiioned upon differences in invesmen, labor force growh and educaional aainmen. In columns 1 and 3, he implied rae of convergence is 2.7 and 3.2 percen, which is close o he values found by Barro and Sala-í-Marin. However, when fixed sae effecs are included in columns 2 and 4, he speed of convergence rises o 4.9 percen. The rae of convergence esimaed here is close in value o hose found by Knigh, Loayza and Villanueva (1993) and Islam (1995) in a panel of counries. The coefficiens on invesmen, labor force growh and human capial ener in wih heir prediced signs. In all columns, he coefficiens on ln(s) and ln(n + g + δ) are significan a he 1% level. Moreover, he implied oupu elasiciy α is close o he income share paid on capial. In column 3, he coefficien on human capial is posiive and highly significan. When fixed sae effecs are included in column 4, however, he coefficien on human capial

12 11 falls quie sharply and is no longer significan a he 5% level. The reducion in he esimaed impac of human capial suggess ha some of he explanaory power of educaion may be coming from unmeasured sae-level differences. The implied elasiciies in columns 3 and 4 are consisen wih he esimaed rae of convergence. The rae of convergence λ in equaion (13) equals (n + g + δ)(1 - α - β). Subsiuing an average value of 0.08 for (n + g + δ) and he esimaes of α and β, he rae of convergence prediced by he augmened Solow model is idenical o hose found in Table 2. Therefore, he resuls find ha pos-war growh raes across U.S. saes have been converging following he process prediced by he Solow growh model. Sensiiviy Analysis for Transiional Growh There are wo issues ha need o be addressed. Firs, he personal income measure includes ransfer paymens which are paymens made on neiher labor nor capial. As a resul, he inclusion of hese paymens could bias he esimaes on he oupu elasiciies. Moreover, Barro and Sala-í-Marin (1991) documen ha ransfer paymens reduced he dispersion of income across saes in he pos-war period. Therefore, i could be he ransfer of income and no capial accumulaion ha is driving he convergence resul. Second, previous sae-level sudies find ha measures of indusrial srucure help explain he level and growh in real income per worker. We follow Barro and Sala-í-Marin (1991) and measure indusrial srucure as 8 STR i, = j= 1 w i g, j, T j, (16)

13 12 where w, is he percenage of personal income earned in secor j in sae i a ime -T and i j, T g, is he naional growh rae of labor produciviy in secor j beween ime -T and. 3 j If he indusrial composiion of a sae is in higher-produciviy indusries, hen STR would be above he naional average. If, on he oher hand, he indusrial composiion were in lowerproduciviy indusries, hen STR would be below he naional average. Therefore, STR picks up produciviy effecs driven solely by he indusrial composiion of a sae. Table 3 presens he resuls of he wo sensiiviy ess. In columns 1 and 2, he ransiional growh equaions (10) and (13) are esimaed using personal income minus ransfer paymens. In excluding ransfer paymens, he coefficien esimaes on ln(n + g + δ) and human capial fall in significance. However, hose on he iniial level of income per worker and invesmen remain srongly significan wih an implied rae of convergence and oupu elasiciy equal o 5.0 percen and 0.26, respecively. In columns 3 and 4, indusrial srucure STR is included in he ransiional growh equaions. As expeced, he STR variable eners in posiive and is significan. The poin esimae implies ha a 1.0 percen increase in labor produciviy driven by a sae s indusrial composiion raises he growh rae of income per worker by 0.89 o 0.98 percen. The coefficiens on he oher variables, however, remain he same as hose in Table 2 excep human capial. In column 4, he coefficien on human capial falls in value suggesing ha educaional aainmen may be picking up cross-sae differences in indusrial srucure. 3 The eigh secors used are mining, consrucion, manufacuring, rade, finance and real esae, ransporaion, services and governmen. Agriculure could no be used due o he unavailabiliy of a pos-war employmen series.

14 13 Resuls for Transiional Growh across Regions Time series ess of convergence find regional and sae variaions in convergence across he U.S. Using Augmened Dickey-Fuller ess, Carlino and Mills (1993) and Loewy and Papell (1996) find srong evidence of sochasic convergence in he Grea Lakes, Plains and Far Wes regions and o a lesser degree in he New England and Souheas regions. 4 Carlino and Mills (1996b) and Evans (1997) esimae a convergence rae for each sae and find a wide range of values. Carlino and Mills find an average speed of convergence below 1.0 percen in he pos-war daa. However, in conrolling for cross-sae heerogeneiy, Evans esimaes a median rae of convergence of 15.5 percen. In Table 4, we esimae he basic ransiional equaion (10) of he Solow growh model for each region of he U.S. The resriced model wih fixed ime and sae effecs is used. The resuls find ha he basic Solow growh model explains he pos-war growh process in seven of he eigh regions. Firs, in each region excep he Mideas, he coefficien on he iniial level of income per worker is negaive and significan. Second, he coefficien on ln(s) - ln(n + g + δ) eners in wih is prediced sign and is significan for each region. The implied oupu elasiciy α averages 0.26 across he eigh regions. Moreover, he resuls in Table 4 show ha he Solow model can explain he regional variaions in raes of convergence. In he Mideas region, growh raes are diverging a a rae of 2.2 percen. In he oher seven regions, growh raes are converging a an average rae of 8.0 percen. Therefore, as in Evans, he conrolling of cross-sae heerogeneiy raises he rae of convergence well beyond 2.0 percen. Moreover, in hose regions where sochasic 4 See Table 1 in Carlino and Mills (1996a).

15 14 convergence is srong, cross-secional or condiional convergence is occurring as prediced by he Solow model. V. CONCLUSION In his paper, we used a panel daa approach o explain he pos-war growh process across U.S. saes. We esimaed he growh empirics model of Mankiw, Romer and Weil using sae-level daa for five decades. As in he cross-secional sudies, we found ha poswar growh raes have been converging following he process prediced by he Solow growh model. This finding was no only robus o he inclusion of fixed sae effecs, bu also o he exclusion of ransfer paymens, inclusion of a measure of indusrial srucure and he division of he saes ino geographic regions. However, in conrolling for sae-level echnology differences, he esimaed speed of convergence rose from 2.7 o 5.0 percen. Moreover, he convergence rae exhibied variaions across geographic regions consisen wih he ime series ess. We also found evidence ha he esimaed impac of educaion may be picking up sae-level differences in echnology, ransfer paymens and indusrial srucure. Therefore, his paper suggess ha he convergence resuls found in he cross-secional and ime-series sudies are in no way unique, bu raher are being driven by he neoclassical growh process of Solow.

16 15 REFERENCES Barro, Rober J., (1997) Deerminans of Economic Growh: A Cross-Counry Examinaion, Cambridge, MA: The M.I.T. Press. Barro, Rober J., and Xavier Sala-í-Marin, (1991) Convergence across U.S. Saes and Regions, Brookings Papers on Economic Aciviy I, Barro, Rober J., and Xavier Sala-í-Marin, (1992) Convergence, Journal of Poliical Economy 100, Barro, Rober J., and Xavier Sala-í-Marin, (1995) Economic Growh, New York, NY: McGraw Hill. Bureau of Economic Analysis, (2000) Regional Accouns Daa websie: hp:// Bureau of Labor Saisics, (2000) Selecive Access websie: hp://sas.bls.gov/sahome.hml. Carlino, Gerald A., and Leonard O. Mills, (1993) Are U.S. Regional Incomes Converging? A Time Series Analysis, Journal of Moneary Economics 32, Carlino, Gerald A., and Leonard O. Mills, (1996a) Are U.S. Regional Incomes Converging? Reply, Journal of Moneary Economics 38, Carlino, Gerald A., and Leonard O. Mills, (1996b) Convergence and he U.S. Saes: A Time Series Analysis, Journal of Regional Science 36, Caselli, Francesco, Esquivel, Gerardo and Fernando Lefor, (1996) Reopening he Convergence Debae: A New Look a Cross-Counry Growh Empirics, Journal of Economic Growh 1, Chaerji, Monoji, (1998) Teriary Educaion and Economic Growh, Regional Sudies 32, Garofalo, Gasper, and Seven Yamarik, (1999) Regional Growh, unpublished mimeo. Evans, Paul and Georgios Karras, (1996) Do Economies Converge? Evidence from a Panel of U.S. Saes, The Review of Economics and Saisics 78, Evans, Paul, (1997) How Fas do Economies Converge? The Review of Economics and Saisics 79, Holz-Eakin, Douglas, (1993) Solow and he Saes: Capial Accumulaion, Produciviy, and Economic Growh, Naional Tax Journal XLVI, Holz-Eakin, Douglas and Amy E. Schwarz, (1995) Infrasrucure in a Srucural Model of Economic Growh, Regional Science and Urban Economics 25,

17 16 Islam, Nazrul, (1995) Growh Empirics: A Panel Daa Approach, Quarerly Journal of Economics 110, Knigh, Malcom, Norman Loayza, and Delano Villanueva, (1993) Tesing he Neoclassical Theory of Economic Growh: A Panel Daa Approach, IMF Saff Papers 40, Loewy, Michael B., and David H. Papell, (1996) Are U.S. Regional Incomes Converging? Some Furher Evidence, Journal of Moneary Economics 38, Mankiw, N. Gregory, David Romer, and David N. Weil, (1992) A Conribuion o he Empirics of Economic Growh, Quarerly Journal of Economics 107, Vohra, Rubina, (1996) How Fas Do We Grow? Growh and Change 27, Whie, Halber, (1980) A Heeroscedasiciy Consisen Covariance Marix and a Direc Tes for Heeroscedasiciy, Economerica 48,

18 17 Table 1 Resuls for Seady-Sae, (Dependen variable = level of real income per worker) Variable (1) (2) (3) (4) UNRESTRICTED: Fixed Time and Region Effecs Fixed Time and Sae Effecs Fixed Time and Region Effecs Fixed Time and Sae Effecs Inercep ( ) ( ) ( ) ( ) ln(s i, ) ( ) ( ) ( ) ( ) ln(n i, + g + δ) ( ) ( ) ( ) ( ) ln(h i, ) ( ) ( ) Adjused R-squared RESTRICTED: Inercep ( ) ( ) ( ) ( ) ln(s i, ) - ln(n i, + g + δ) ( ) ( ) ( ) ( ) ln(h i, ) ( ) ( ) Implied α Implied β Adjused R-squared p-value for resricion Number of observaions Noes: Esimaion is by ordinary leas squares. The esimaed coefficiens for ime, region and sae dummy variables are no repored. Sandard errors are shown in parenheses and have been correced for heeroscedasiciy using he mehod of Whie (1980). ln(n i, + g + δ) is he log of he sum of labor force growh rae, produciviy growh rae and depreciaion rae. ln(h i, ) is he percenage of individuals, age 25 or older, who have compleed four or more years of college.

19 18 Table 2 Resuls for Transiional Growh, (Dependen variable = average growh rae of real income per worker) Variable (1) (2) (3) (4) UNRESTRICTED: Fixed Time and Region Effecs Fixed Time and Sae Effecs Fixed Time and Region Effecs Fixed Time and Sae Effecs Inercep ( ) ( ) ( ) ( ) ln(y i, ) ( ) ( ) ( ) ( ) ln(s i, ) ( ) ( ) ( ) ( ) ln(n i, + g + δ) ( ) ( ) ( ) ( ) ln(h i, ) ( ) ( ) Implied λ Adjused R-squared RESTRICTED: Inercep ( ) ( ) ( ) ( ) ln(y i, ) ( ) ( ) ( ) ( ) ln(s i, ) - ln(n i, + g + δ) ( ) ( ) ( ) ( ) ln(h i, ) ( ) ( ) Implied λ Implied α Implied β Adjused R-squared p-value for resricion Number of observaions Noes: Esimaion is by ordinary leas squares. The esimaed coefficiens for ime, region and sae dummy variables are no repored. Sandard errors are shown in parenheses and have been correced for heeroscedasiciy using he mehod of Whie (1980).

20 19 Table 3 Sensiiviy Analysis of Transiional Growh, (Dependen variable = average growh rae of real income minus ransfer paymens per worker) Variable (1) (2) (3) (4) UNRESTRICTED: Inercep ( ) ( ) ( ) ( ) ln(y i, ) ( ) ( ) ( ) ( ) ln(s i, ) ( ) ( ) ( ) ( ) ln(n i, + g + δ) ( ) ( ) ( ) ( ) ln(h i, ) ( ) STR i, ( ) ( ) ( ) Implied λ Adjused R-squared RESTRICTED: Inercep ( ) ( ) ( ) ( ) ln(y i, ) ( ) ( ) ( ) ( ) ln(s i, ) - ln(n i, + g + δ) ( ) ( ) ( ) ( ) ln(h i, ) ( ) STR i, ( ) ( ) ( ) Implied λ Implied α Implied β Adjused R-squared p-value for resricion Number of observaions Noes: Esimaion is by ordinary leas squares wih fixed ime and sae effecs. The esimaed coefficiens for ime and sae dummy variables are no repored. Sandard errors are shown in parenheses and have been correced for heeroscedasiciy using he mehod of Whie (1980). STR i, is a measure of he indusrial composiion relaive o he naional average.

21 20 Table 4 Resuls for Transiional Growh across Regions, (Dependen variable = average growh rae of real income per worker) Variable New England Mideas Grea Lakes Plains RESTRICTED: Inercep ( ) ( ) ( ) ( ) ln(y i, ) ( ) ( ) ( ) ( ) ln(s i, ) - ln(n i, + g + δ) ( ) ( ) ( ) ( ) Implied λ Implied α Adjused R-squared p-value for resricion Number of observaions Variable Souheas Souhwes Rocky Mounain Far Wes RESTRICTED: Inercep ( ) ( ) ( ) ( ) ln(y i, ) ( ) ( ) ( ) ( ) ln(s i, ) - ln(n i, + g + δ) ( ) ( ) ( ) ( ) Implied λ Implied α Adjused R-squared p-value for resricion Number of observaions Noes: Esimaion is by ordinary leas squares wih fixed ime and sae effecs. The esimaed coefficiens for ime and sae dummy variables are no repored. Sandard errors are shown in parenheses and have been correced for heeroscedasiciy using he mehod of Whie (1980). ln(y i, ) is he iniial log level of real income per worker. ln(s i, ) is he log of he raio of real gross invesmen o income. ln(n i, + g + δ) is he log of he sum of labor force growh rae, produciviy growh rae and depreciaion rae.