This prediction can be tested by use of times series analysis: should be negative. Where i=region1, region2, region3, region4,, region25.

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1 Lecture: EMPIRICAL EVIDENCE ON ECONOMIC GROWTH One predcton of the model s that f ncome per capta ncreases the subsequent growth rate of per capta ncome decreases. For example f an econom s below ts stead state and ncome per capta ncreases, ths means that the subsequent growth rate of per capta ncome decreases. Ths predcton can be tested b use of tmes seres analss: / e t 1 t t 1 t t Where t = 1970, 71, 72, 73, Accordng to ths predcton 1 should be negatve. If we assume that regons n a countr have the same savng rate, same populaton growth rate and technolog; that s, share the same stead state, then ths predcton can be tested on cross-sectonal data: e / Where =regon1, regon2, regon3, regon4,, regon25.

2 Evdence from the 24 Swedsh Regons, Regons that were relatvel poor n terms of real ncome per capta n 1911, on average had a hgher growth rate of real ncome per capta. Hgher growth rates n poor regons caused relatve dfferences n real per capta ncome to dmnsh across the Swedsh Regons between 1911 and The dsperson s lower for real per capta ncome when t s adjusted for regonal dfferences n cost of lvng as countes wth hgh unadjusted real per capta ncomes tend to have cost of lvng.

3 Per capta Income adjusted and unadjusted for cost of lvng The emprcal evdence on convergence n real per capta ncome across the Swedsh regons s consstent wth the predcatons of the textbook model: Low real per capta ncome Read b ourselves: Värmland moves to top categor of per capta ncome when regonal dfferences n cost of lvng are accounted for n 1993 Per capta ncome (p.c.) s n 1980 prces Lttle captal (phscal + human) per worker, low wages, hgh rates of return to captal captal per worker producton per worker ncome per capta Also factor moblt tends to contrbute to convergence: Low wages and hgh returns to captal out-mgraton, and foregn nvestment captal per worker producton per worker

4 Growth rate of GDP p.c. Evdence from regons and countres: Real per capta ncome tends over tme to converge across economes, whch are smlar wth respect to nsttutons. An econom wth an ntall relatvel low real ncome per capta has on average a hgher growth rate of real ncome per capta than an econom wth an ntall relatvel hgh real ncome per capta f nsttutons are smlar. Ex.: EU-countres and regons wthn countres. Ths means that the model predcton s consstent wth data Evdence from the OECD-countres (the currentl rch countres) Average annual growth rate of GDP p.c., , and GDP p.c. n Sere Real GDP per capta 1960 Sample ncludes: Australa, Austra, Belgum, Canada, Denmark, Fnland, France, Greece, Iceland, Ireland, Ital, Japan, Netherlands, New Zealand, Norwa Portugal, Span, Sweden, Swtzerland, Unted Kngdom and USA. Intall poor countres grow faster n terms of real GDP per capta durng the perod than ntall rch countres. The correlaton between the average annual growth rate of real GDP per capta between 1960 and 2000 and real GDP per capta n 1960 =

5 Growth rate of GDP per capta Evdence from the countres of the world Average annual growth rate growth rate of GDP p.c., , and GDP p.c. n Real GDP per capta n 1960 S Sample ncludes 80 countres. No convergence n real GDP per capta across the countres of the world. The correlaton between the average annual growth rate of real GDP per capta between 1960 and 2000 and real GDP per capta n 1960 = Is lack of convergence n GDP per capta for the countres of the world, evdence aganst the model? NO! The model sas that f countres have the same equlbrum, the poorer countr should grow faster n terms of per capta ncome (and captal per worker) than the countr that s rcher n terms of per capta ncome and captal per worker.

6 A more complete regresson model controls/takes account of the other varables that mpact growth (A, savng rate, populaton growth). For example, a hgher savng rate ncrease the growth rate of per capta ncome untl the new stead state has been reached. The complete regresson equaton on tmes seres data: / ( S / Y) n etc t1 t t 1 t 2 t 3 t, t1. Accordng to model 1, 3 should be negatve. And 2 should be postve. Number of observatons= number of tme perods. The complete regresson equaton on cross-sectonal data: / ( S / Y ) n etc where = swe, Norwa, fnland, usa, etc. Accordng to model 1, 3 should be negatve. And 2 should be postve. Number of observatons= number of countres. Combnng cross-sectonal and tmes seres data (panel or pooled data): / ( S / Y) n etc t1 t t t t t, t Number of observatons = number of countres * number of tme perods When varables that hold constant/control for the stead state (A, savng rate, populaton growth rate) are ncluded as explanator varables n the regresson equaton for samples of countres of the world, estmates of 1 turn from zero to negatve and statstcall sgnfcant whch s consstent wth the model. See Barro artcle.

7 Other varables than the standard varables n the SOLOW model n growth regressons In emprcal analss often more varables than ntal ncome per capta (or ntal ncome per emploed), the nvestment rate, the populaton growth rate are ncluded. For example, educatonal level, varables measurng tax rates, corrupton, openness to trade, populaton age structure, populaton denst. To make the emprcal analss full consstent wth the Solow model, t s tpcall assumed that these varables mpact the level of technolog (A) and thereb the stead state level of producton per worker. Thus, A s assumed to depend on a host of varables. If the model s tested n terms of per capta, often age structure varables; the share of the populaton below 15 and above 65 ears, are ncluded as explanator varables n the regressons to account for the fact that people of these age groups tpcall do not work See Barro artcle. The dependent varable n growth regresson s tpcall the average annual growth rate of GDP per capta: (1 g) (1 g) /40 1 g 1960 Alternatvel an approxmate formula, (t s approxmate because n the real world data s dscrete). g 40 (2000) (1960) e ln (2000) ln (1960) g 40 ln (2000) ln (1960) / 40 g Note: gr for small r and g=ln(1+r)>r. 5-ear or 10-ear perods nstead of annual data Moreover, nstead of annual data man researcher use 5-ear or 10-ear perods when studng growth: t5 t 1/5 1) t Read also INEQUALITY ARTICLE b Barro.