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Faculty Working Papers
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University of Illinois at Urbana-Champaign
FACULTY WORKING PAPERS
College of Commerce and Business Administration
March 3, 1972
Capital Coefficients, Propensities to
Save, Calculated and Actual Growth Rates
in Bight Countries 1954-1969
Hans Brems
University of Illinois
#42
24
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ee batik
spk Sele
core Gera at Le |
March 1, 1972
CAPITAL COEFFICIENTS, PROPENSITIES TO SAVE, CALCULATED
AND ACTUAL GROWTH RATES IN EIGHT COUNTRIES 1954-1969
Hans Brems
1. Introduction
On the eve of its changeover to a new system of national
accounts, the OECD has brought together in one volume [10]
comparable and consistent national accounts for its member countries
1953-1969 based upon its current standardized system. As a farewell,
let us use it to see what has happened lately to capital
coefficients and propensities to save in eight advanced? countries.
Let our theoretical framework be the Harrod-Domar model“, crude
enough to fit such crude data.
2. Capital Coefficients
What the capital coefficient b is used for in the Harrod-Domar
model is the derivation from its Fqs. (2) and (3) of the investment
galntauoo | agitiven eti-ret_eynuonan ‘fsnotten: ‘tnageteno lb
howe & 8, smeteye ‘beskbubnate Sean atk Alogi boand ee
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; ~ eburro tobe, sanoGrbpraalt eit od epitanie® Enobsoncedt
namod~Sorrsit ody, a aoe been at d. bokakt? von apsoncaia ont staat |
romteovnt edt Lo shld bars 8), apa art nowt alan teat nat oo
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(fot) ty Lov ene al nadtogoy, tdguord ead aoH0. oe
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. dstiqas ot, sores, ponsaget aan tone. roe ot $i pany
aaa abun dove 242 om
function
It follows from Eq. (2) that Harrod-Domar investment I is
net investment and from Eq. (5) that Harrod-Domar output X is net
output. Consequently use Part Three, Table 2, lines 3, 8, and
17 of the OECD accounts [10] to define
I = net domestic fixed asset formation = gross domestic fixed
asset formation at 1963 prices (line 3) minus depreciation
and other operating provisions at 1963 prices (line 17).
X = net national product = gross national product at 1963 market
prices (line 8) minus depreciation and other operating
provisions at 1963 prices (line 17).
AX = annual increments of X.
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7 et aa “snd ken, ot beds ata a0 coil
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. ; fet BoReOE AUAES ” te antt)) eankag: fees. +5 sotsae: eon
as: enkt) sent. eae, 25, pansies btu wodto b
= Z fi * ena ca x 8 ta Nn * or tae oe at at 7 E ;
g.- measem eaes te soubor. Apnoiten. ebony 2 taubor “iencktea ton Be
gntpenego neito. brs agtystosaqeb ui (8 anit) :
a CCL, emit) faninl gabe te anoie :
on ele Yee aa Ai IF a oS
| ak 30 Pediekee #
Net domestic fixed asset formation
Net domestic fixed asset formation
T ali
100
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69
10
50 c
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=
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w
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BamEtons: Oc 3
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uw
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Sa SS aL | a
e 30 6 Trilli
5 rillions
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f 7,
O a eee eee
fay tae) i
0 5
67 & Annual increments of NNP
oO a I
(6) fe)
60 oa | ©
50 = eee 68 © 66
F 56 By ee
© 54 €555
7 2 oO © «¢ 63 56D
© 57 @ 62
@55 im ee)
n
5 58
vu
x
GERMAN FEDERAL REPUBLIC a UNITED STATES
Billions of 1963 DM a Billions of
as 1963 dollars
ida)
a)
i Nioe Meier leeway 2 oe shu cereal at AX
a Aaa —7 Cai Se eae ——e ay
=10. 0 50 t=O, 10 50
Annual increments of NNP a Annual increments of NNP
FIGURE 1,—CAPITAL COEFFICIENTS IN FRANCE, JAPAN, GERMANY AND THE UNITED STATES
: y hg or ' ‘
5
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i
te ‘
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In Figures 1 and 2 we have plotted corresponding values of I
and AX thus defined for each of the sixteen years 1954-1969 for
each of the eight countries. If for any country from any of the
sixteen points a straight line were drawn to the origin, the slope
of that line would represent the value of the capital coefficient
for that year in that country. To avoid cluttering the diagrams,
such lines have not been drawn explicitly.
For each country one straight line through the origin has
been drawn, however. For each country, sum net investment over the
sixteen years and call the result ZI. Sum incremental net national
product over the same sixteen years and call the result ZIAX. The
slope of the straight line through the origin shows the ratio
LI/XAX = b
representing the overall capital coefficient for the entire period
1954-1969. The eight values of b appear as labels on the straight
i ay t ne eoutav gndbnoqaerio> bettosq. suse ow iy bas Fa £ sarin Fe
a ‘20% ener wget koh aoorala att Qe fo a patted at hy
eu Sey
ia
ae agote, oe \atgero ole ot cunt oroN ake seaiwa es , stniog 1
BS: Snotokttses. Lesiqse sat to ovisv ont ‘tnoessqoa - biuee onth tai
. ee “comeregab ont anbuod uta biove, ba “werhawos: hel ak inet +8
, ; ( ch Racer Gt rt aoe 2 ettel ine push nod ‘ton ‘event dents
} | asd kigine ois fers enki tdgierte. af0, yxiauee 259 pee ;
wets 120 poms eovnd “fom aug Pr watawos oso coe ssaveuort i
| Lencitsa tea Istnoworont mye 4 tweet, ote iiss bre “aro 6
‘ ae pat KA2 dives auld iss one acne, astute 3 attoe od ert! ee
et ott: odd. wots Ais ris eaves sarees site 40,
a
es eh ves
ae Ea
TABLE 1.—-CAPITAL COLFFICIENTS, PROPENSITIES TO SAVE, CALCULATED
AND ACTUAL GROWTH RATES IN EIGHT COUNTRIES 1953-1969
Calculated Actual By where
log,
b Li= ie By = e i
Ge = e075 X(1969)/X(1953)
Denmark 3.24 OAH 0.040 0.940
Finland 4.02 Oni 0.044 0.046
France 2.66 0.138 OS 052 0.053
Germany* 3.06 Ong 7 0.055 0.059
Japan 2.41 Oa 223 0.093 0.091
Netherlands 3.66 (o) Fake 0.047 0.048
Norway 4. 84 0.192 0.040 0.039
United States 2.26 0.081 0.035 0.034
*Federal Republic.
i
1
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GSTAIUOIAD eAVAZ OT earetausaons ay sooienottb i
n Ore ae akstenedtst effssose “ue ‘sadond 128s CET s
ay
=
Net domestic fixed
asset formation
Net domestic fixed Net domestic fixed
asset formation
asset formation
Net domestic fixed
asset formation
il
100 69
FRANCE ae 550 oo
Billions of 1963 francs ea oe 00 oS"
57 59) myo GE. 68
55 Pepe ©6664
9.138 a Qe? = 60 62
1 cir. 58
el 5 = EOE AT AR ET
0 L- bene Sa a aac A ee Gs SS: y PONISI ONLI S = = | x
0 100 200 300 400 500 600
NNP
I 68 ©69 =
10
JAPAN afar OSes
Trillions of 1963 yen je Fi
Cay ""67
56 57 6 op O—~
see Oo 62 63
Ca 59
0 10 20 30 40 50
NNP
I
100 GERMAN FEDERAL REPUBLIC ROSS
Billions of 1963 DM ieee OD Or fF
0 x
NNP
I
100
UNITED STATES 69
Billions of 1963 dollars 56 65 66 10)
OB ern
ek cme ae ee eo
lee oo sae ee i ic ame Vv |e amare
Q 100 200 300 400 500 600 700
NNP
FIGURE 3,—-PROPENSITIES TO SAVE IN FRANCE, JAPAN, GERMANY AND THE UNITED STATES
RT MO Ns ate ii seed
.% , : . /epaiet ber G amazitts
ee
aa anion
Her ee
de.
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ie it
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asset formation asset formation
N@t GOMeEeStIC LLlxnea
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omest1 Lxeda
asset formation
e
8 Mh =
65
10 « DENMARK 55 oO © oO Ones
Badeinvoms) Or wiaibst ikroner on a _ olen 68
0 SF ian F ~ Tia ee a ais a Tae aca Ic — |
0 10 20 30 40 50 60 70
NNP
ag
: FINLAND 66
Sore Bion Gd =
Billions of 1963 markka 60 61 62 5
8 oo “o
6
0 Xx
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Ai
1 58 ad
. NORWAY eget ba 9 ea
Billions of 1963 kroner Mw 869-0056 as ©,
eb 2
60
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a asec: x
0 10 20 30 40 50
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68
ii ; aE Oo oO
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NETHERLANDS 57 60 02 cee
. . . 5506 a O19) 65
Baicions "Om S63) euaiiders COs Os, 63
DSS
58
0 a t — Se) tee SiS "t TMCS oe ts Lae a Se SRE aaa |
0 10 20 30 40 50 60 70
FIGURE 4,—PROPENSITIES TO SAVE IN DENMARK, FINLAND, NORWAY AND THE NETHERLANDS
x
N ry i
be a) 0 Lely Siti) Ae oa) vy
Ba-'s> Mon
ow | ei Powe |
ae OS , ees vee OF haa
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mae: LP etn) os ponaltayra: baa
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Piet
[6], 27, Lindberger [7], 45-52, and Lundberg [9], 110-111, we know
that capital coefficients differ markedly among industries. Hence
national capital coefficients must reflect national industry mix.
And the smaller a country is, the more one-sided its industry mix is
likely to be. Thus the traditionally high Norwegian capital
coefficient must reflect the high capital coefficients of electric
power generation [4], [71], and transoceanic transportation [4]. The
high Finnish capital coefficient must reflect the high capital
coefficient of wood pulp [1], [9].
3. Propensities to Save
What the propensity to save 1 - c may be used for in the
Harrod-Domar model is the derivation from its Eqs. (4) and (5)
of the investment-savings equation
Aen at xis econ: ath bobiscerra eran’ ad? gah erranon, ahi r
pS oistooli to sinietotiteos levis ute ote soles, feu a
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: ve | eu, nokreupe eomtbvae~tnoadas if
ih pall
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ney re
12 -
Part Three, Table 10, lines 6 through 9 of the OECD accounts
[10] use the terminology that gross addition to national wealth
equals gross fixed asset formation plus change in stocks minus
Bestdual error plus®nct Lending to the rest of the world. A
Harrod--Domar economy is a closed one, so there is no lending to
or borrowing from the rest of the world, and Eq. (5) of the
Harrod-Domar model rules out change in stocks. Ignoring the
residual error, then, Harrod-Donar gross saving equals gross
addition to national wealth equals gross fixed asset formation.
Harrod-Domar net saving at 1963 prices equals I as defined in
Section 2 above. Harrod-Domar net national product at 1963 prices
equals X as defined there.
In Figures 3 and 4 we have plotted corresponding values of I
and X thus defined for each of the sixteen years 1954-1969 for
each of the eight countries. If for any country for any of the
sixteen points a straight line were drawn to the origin, the slope
of that line would represent the value of the propensity to save
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. | "ot gated on at otteild oe vena boeats, 8 et ‘yonote sesnoll-bo
7 aT. ent to cay pa bats know ods Ro vane ont dno? Bain
ont gakrorg? sstvote nk ‘wamarta tuo. oot Eubodt ‘qoinoU-be
220o7y eisape’ paves’ paory enivodbowtit steele tors sub
Hosni teres bexit secs ‘wLeups tt tnbw Lenotssre of nobe
at beniteb se I sLoups oping caek ite pnives fort rst bot
meee cael ts souborg, teaokten ten aemod-bowisit sevods $
| | | = “anody beniteb 25 ea
int t0 seulnv pabbisqaecace betota ovad ih mi bn’ e ‘eonuyd ak
74s
mot eael~ soot: etsay motte | eet to dose 0% bontteb HS :
od to yas tot vata yas a0? ar seobatnuon: aegte’ sity
oqole, ott Abubxe edt of none ot onks igients & ataiog :
ovse ‘ot eo henoqotg odt ae oulsy edt snbabager bivow onbE toss
jh i—» @
Oe 5:0
0.40
Fe)
wo
rep)
Geeeto).<310
A so
Zi a cok
p a
4 Oo ae
ey ©
fe) Ore
iS Solas
AS 2
ox
CUE Ae eee eae W
0.05 = SS De a a
Das ik 2 3 vee
Gross national product per capita,
Ubi thousands: of Ws tS. dollars
FIGURE 5.-—PROPENSITY TO SAVE AS A FUNCTION OF GROSS
NATIONAL PRODUCT PER CAPITA, INTERNATIONAL CROSS SECTION
«4
=
Ss
a oo
ie —
=
, a 7
ca
ys
ua
yy > eae
AOL
tad -
Ct) Cree
v un" Caen e
a _ oy ; rh mF i he
ms fn
| sity See
7 uP a) ¥
a *
\
“ ¥ 1
i. { '
*) 7
Vy . Bs /
ie f
t
tem a
bad i’ & ;
taf
OF RAT Tae
Losioizan, 80nd
ahnaaventy ~ldel
/
’ oy tiniewasi
4 5) . 2 ‘U +o
Toe ia ye ) 1. oo
a ra _ are a? a
Leet YO HOTPOMON BA DRE GT WTLAAIIONI—.< RAVOLT®
Noe LORD TAMOTRARMATAL jANTEAO 127, TOMCORT sTAMOLEAM
i * i ; - ri - ; > 4 q _
; ay iy
~ my
a -
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ite he
ea tes
for that year in that country. The sixteen lines would cluster
very heavily. To avoid the congestion, they have not been drawn
explicitly.
For each country one straight line through the origin has
been drawn. For each country, sum net investment over the sixteen
years as before and call the result ZI. Sum net national product
over the same sixteen years and call the result EX. The slope of
the straight line through the origin shows the ratio
LI/=x = 1+ ¢
representing the overall propensity to save for the entire period
1954-1969. The eight values of 1 - ¢ appear as labels on the straight
lines through the origins in Figures 3 and 4 as well as in the
second column of Table 1.
Figures 3 and 4 raise the same two questions as did Figures 1
and 2. In each country could the sixteen implicit, undrawn, lines
through the origin be said to cluster around the drawn one? The
answer is that the cluster is far better than it was in Figures 1
= a hers
and 2. Furthermore, no noticeable difference between the marginal
and the average propensity to save exists in Finland, Germany,
Norway, or the United States. But in Denmark, France, Japan, and
the Netherlands the marginal propensity to save is visibly higher
than the average one. This is another way of saying that the Danish,
French, Japanese, and Dutch average propensity to save must have
been rising from 1954 to 1969.
The second question raised by Figures 3 and 4 is whether or not
the eight countries differ in their propensities to save. They do
indeed: The highest value 0.223 (Japan) is about 2°/, times the
lowest value 0.981 (United Pee can such differences be
explained? Much of them will be explained by per capita gross
national product. Use Part One, lower table p. 10 to define
y = gross national product at market prices per capita in U. S.
dollars for 1961
In Figure 5 we have plotted corresponding values of 1 - c and
y for each of the eight countries. On the double-logarithmic scale
‘ie 0 oe ee Ny ir an ; id ‘a ay 7 , wilt | A vay,
Fan Pe te? ony Ah rf ‘ ey LCcl Ser 4 4 tia if } y i, 5 Uy
ees al Gees . et ay hale a ae ee eee) OR) Se eee ey mi H iat bee en
ry ~y Lent , ‘ ti t ve re Pee a f tO Pre ma) ae 7
ia AT, am f F STA BEE cr oh. Tn a wae ete oh ?
- pd ; De ; Ne RT eae Ue emer) Ob Cn aa a ny
\ ‘ena ‘ H Wk y ee : i f ‘is } oi Pn 7 as Ps > , ren
ee Po is oe OS
Teh Oe on ian , LS) aK oh a oF ea ee i ‘ fo PADS Pee ir F io
i } oY i aed ay, i Lai ut
i)
Renal a tetadio biuow eents, meet ia | oft ‘ seranues deste ak feces
ake nwereh aved ton ivan vents saobaaognes: edt Bhods, er ee |
Del a }
t Wah ¥ . ‘ See
j , i Lan ae
; : oe va, é “f ; .
a wv
1
es rm, aor nisi acts cued omik, [ tiotense: one iav9e tore *
Bs | aootute ont ‘teve snumtpovad ren me certains foes aol | :
S i doubonq Lenoksan tan mie Pee. ‘thueer edd ‘Eize ban oxoted ep
i a, to, eqote oat ite siuaots ont! ‘tine bas annoy aostute ance
: | : ip ie ba iran verte x alain odd dower ake ec
¥ zeal Li
\ whi oh
nik vi ios “yayrz i Be alse
i
bebe oritne ott ok ovES ca teregone Luireve elt anit
i eis: srt no grates, en areas a £ to poulev ‘ttyte oT 48
eet * oft nb a5 tow 2B. 4 ‘bas § aru nk angio oat dguond
ee oon | Wry . | i) 4g eidat Yo. ee
Ret)
f siligi bib ¢ as. “aaoktepup ows ome oft aioe # brs e ans
a ponil emvectbras etkoEaink noodute ort bEY09 ‘yatauco fore a
| ed? fort mn sit. bavots netauts ot bina od népicno 2 Be
.
i fe. of sary k ot ann ial at aotiod mek ak woteuta ei aadt oh a
: . We has le nA ;
Wi ns pat iv Py at
: i ‘ E.4 } ‘aioe aN
a ; Fike ~ Pers
ik i f fh
en ot bose
i ) war Lee, \ ’ Me , iu
ie Le te Die
vo ‘ ye
See aL ea so
Ta ty
a’ Ass oe !
hy wa ie aw
Ue a - A "
; ay
‘ u ; i
icon \ nae
See
and 2. Furthermore, no noticeable difference between the marginal
and the average propensity to save exists in Finland, Germany,
Norway, or the United States. But in Denmark, France, Japan, and
the Netherlands the marginal propensity to save is visibly higher
than the average one. This is another way of saying that the Danish,
French, Japanese, and Dutch average propensity to save must have
been rising from 1954 to 1969.
The second qucstion raised by Figures 3 and 4 is whether or not
the eight countries differ in their propensities to save. They do
indeed: The highest value 0.223 (Japan) is about 2°/, times the
lowest value 0.981 (United Se Ae can such differences be
explained? Much of them will be explained by per capita gross
national product. Use Part One, lower table p. 10 to define
y = gross national product at market prices per capita in U. S.
dollars for 1961
In Figure 5 we have plotted corresponding values of 1 - c and
y for each of the eight countries. On the double-logarithmic scale
gee wnat «bane at abekxd. over ot + Leaotont, en 6
bes ,feqsbl . sais rsanec ag ud " yeogeve oe ott a
aodgid widkaty st vee ot viieagoye Lontgrtpe ot abaniise
yn
‘\ileined od? tedt sakysa 6 uate nodzons ak ein i ‘200! egenevs:
.
ts
ty Tes at
en ee sie wits | or 820k wot gad
: ton 0 ronsodw sk u bas 5 A sont ya beaten noktesup noose’
Se
ob yetiT-..evse of + aeisieneqoxg ukoils as ae ‘ebistau0s
a . avert Faum oVB@ oF sprbaniiqnrg egpiovs: coded ‘oni _esensget Ab
oat aonkt «\ s tuods ei (neqaby eee.0 outey: taorgtd edt
od saonexo%t: 6 fove aso voit *absaee | bostasy 180.0, oul
_ Be01g ntiqso 12g vd: benkalgne od” cote, ma te oul ,
oniteb oy OL ag plist sow! 900 tand-o6U” -touborg &
Fey
“ a 4 7 }
a ; ; i Sy aK * Fal g y a
‘ tay i ; es; j Te yg ¢ q
is2 .U ab atigso weq aooing ease 3s Soubouq Lanotzem Be
ee oe tint tanpol-elduveb ons, Las sdetadhues Aagte ort —
S| Ses
used, the relationship is well approximated by a negatively sloped
straight line.
Why negatively sloped? Remember that we have measured saving by
measuring investment. OECD accounts know only investment in physical
capital. If, as they advance, economies invest more in human capital
(education) and less in physical capital, the propensity to save as
measured will drop as observed.
4. Calculated Versus Actual Growth Rates
The solution (6) of the Harrod-Domar model finds the proportion-
ate rate of growth of output to equal the ratio between the propensity
to save and the capital coefficient. That ratio is shown in the third
column of Table 1 and may be confronted with the actual rate of growth
shown in the fourth column. Should we congratulate ourselves on the
ood correspondence between calculated and actual growth rate?
Much of the correspondence must be inherent: Let growth be
steady-state growth and let v and t be any two points of time. That
Pecimcvat inh ar oie ee
- beqote vievitesan f ve betamixorqer “Low eb qivenottesen 2
gow | iv os, ee ay aah a vomit
ea qatves ‘betirente ved ow. Sade xodmonne A ‘Sbogete sbwsenond
Leotevrta ae tnecdeoved xine’ worst adnuooor 30 | tSaemacoved -
frtigns minwuaset fe oon teovnd eoimonose (ysnovbs: yous ee a ’
86 ove ot eitieanare ony einsiqas tadteude ab\eeek brn. (ae
| ‘ | sbuvaoede ‘ee Gort utws
- rm al ip { o4 y
eu oe a ae) 4
phe ei Satan eS ee
‘goknd’ diswox9 sudo evans bites
ono! Foaoeg ont’ ebait Lebor asaol-borsait ‘ona %o. 4a) noitute
vikeriegorg: ont noswtod olgat ont Erups: oF tugs to de wory, to 94
” iy: edt ab awoda: ‘ab obtaa ind “taoboitioen teviges » vit nee
dtworxg te tee isusos efit tie Borncvtnon | of wen bas i efdc? &
on no: gavieeTvo. statute A009 ‘OW, stworte E08 diet shoal ‘
Sater dovorn Lsuton brs bute ntuotes asowted ages
sd Atwors, tod sonevadad cot saa ‘consbroqeantoo ortt Jo fol
foiT .amtt to atniog: ows i sd +t ‘bas, v sli: Sas dovorg otates
ee
- y a e |
2B os
a variable X is growing at the steady-state rate B,, may then be
defined
7) XCE) Se X(v)
Now we estimated the overall propensity to save 1 - c as YI/IX
and the overall capital coefficient b as ZI/ZAX, hence
(i = e)/b ZAX/=EX = CX(1969) - X€1953)]/£X(1954 + ... + X(1969)]
With v = 1953 and t
LUSH «25 5) 2969 Use ~C7) upon thas:
16¢,, By 16g,
(8) Gis -evainteecer ee ee oe we es )
In the denominator, find the sum of the terms of the
geometrical progression and write
Gi elf(p =. i = 'e
yn Mr ihy Mane
APN (aie : oy it
“ mal 1 } ae a ce
‘ le ae igs ye
. yt ie ; 4 = ; A ‘
f a ai nt i ee year: A 7
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7 ‘
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ame, eontod t eXAS\IE en d sustottive Lstiqeo Lisiove ef
7 ; . : ; - . a 4 b. Te)
" ie ae a mal is ed Me a . Si an ieee aut ‘ i z
feeaerx +... + seen caer - copes 2 REAR 5)
fi - } j a ; ane i S 3 anes nua i pronase
ees gt vB ROLY . fuel
a y ig eT ae ‘* - a ONCE hae a if @) at hiss mis eb at '
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; ; eat pe enh -othaw ban nokesongong 6 ‘tal
a 4
ea rs ? Sih an
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; Re ea ds to
i : ‘ fy i ~ f i
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a
/
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j i, hie i .
Bs ae oi
1 : - i ' fi rh iti
a an vA } 7 ! r da
ae ' | ' - mn it i}
: 4 i AN :
ne - ' ’ y iy y
x 7 7 i
a) Je a ; va nis
Ws he ar i
= ie
So far in this section, all equalities have been definitional
ones. But
a Seis tf OT FIP St es.
Replacing x by “Sy we have
(9) io @ =
where the symbol = is used to denote approximate equality. In
addition to this approximation, the steady-state growth assumed in (7)
was an approximation to actual growth, hence the sum of the terms of
the geometrical progression in the denominator of (8) was also an
approximation. Approximations (7) as well as (9) being good,
we expect the third column of Table 1 to be a good approximation to the
fourth column.
oy
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FOO) N 0. T ES
loapital coefficients require net national product data, and
those in turn require depreciation data. Belgium and Switzerland
offer depreciation data only from 1956; Sweden offers none at all.
2Denoting our variables
c
consumption
g., = proportionate rate of growth of output
I = investment
S = Capital ‘stock
Mee TOWED UE
and using two parameters, i.
propensity to consume c, the
Harrod-Domar model [2], [3],
(1)
(2)
(3)
(4)
(5)
(6)
x
C
X
Taking (1) through (5)
oO
oO
ox
e., the capital coefficient b and the
following six equations constitute the
[5], and [8]:
Vv
a
dt
|r
as
dt
= bX
= eX
ese ey ee
together we solve for Byt
=—(12=e)i/b
NE
’
m™.
oft Bas d gaetaiveens Intiqso ony eitlek ‘erotomonnd ow? yak
edt stutitenoo enoktsups ¥ie sniwol lot ont 9° ‘emwemtoo oF habs:
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i ( i TV ey, Les i i
ie rae oe ; iw ae 4 H
pie 2aTouT ode, Se
ban ‘gate povhen ‘Esnottnn tor oakupes oe Leth
bar feustive bis suelo a pe) mokteiovaqub orskupat aut nk &
fis tn ono atetio mobowe.. Rsk ot mort Rage gab nobtriownqab +
‘madden WO snbtedei
is | soraieeeae 2-3 ee he
tuqtue te primer to oem otsniolisoqoxy 2 e 4
Sh uc Eon ein Ree ne taomteovits. 1 a!
Sore ve dos Deshsaeend =
ae Vie car’
£8) bas «£23 «CEI .[83 fobom one “0
oe ' Xd = 2 |
q ‘Sp 29 : \ way
iy 108 evioe ow mone enee «@ fquonds w waited
j me ) | aq
4 ' y rt iti i
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2 ee
3
The German cluster is much bctter than it looks: Adding in
1960 the Saar and West Berlin to the territory covered means, in
effect, treating the 1960 Saar and West Berlin product as an
increment to the German product without treating existing Saar and
West Berlin capital stock as German investment. Since that existing
capital stock is not known, we made no attempt to remedy the anomaly.
As a result, the slope of a straight line connecting the 1960 point
with the origin must be too low.
“The United States capital coefficient and propensity to save
are both understated, because United States government expenditure
on machinery and equipment is treated as government current expend-
iture rather than as gross domestic fixed asset formation. How much
understated?
Government gross fixed asset formation, defined as excluding
machinery and equipment, is known, [10], Part Three, Table 7, Line
19. Deduct it from gross domestic fixed asset formation minus
machinery and equipment, [10], Part Three, Table 1, Lines 3 minus 3c,
and find nongovernment gross fixed asset formation other than
machinery and equipment. Domestic is around */3 of nongovernment
sross fixed asset formation other than machinery and equipment.
Suppose the fraction */3 applicd to machinery and equipment as well.
Then gross domestic fixed asset formation with government expenditure
on machinery and cquipment included would be around '/., higher than
as recorded without. If the same were truc of net domestic fixed
asset formation, then our understated capital coefficient and
propensity to save should both be raised by '/.5 to 2.66 and 0.095,
respectively. Even so, still no other country would have lower
values than the United States.
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