growth facts. solow-swan model - uniwersytet warszawski
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Growth facts. Solow-Swan modelApplied Macroeconomics: Lecture 6
Marcin BieleckiSpring 2018
University of Warsaw
1
In case you need a review of basic concepts
https://www.mruniversity.com/courses/principles-economics-macroeconomics
Chapters 1-3
2
GDP per capita and welfare: consumption
500 1000 2000 5000 10000 20000 50000 100000
GDP per capita (2011 USD)
500
1000
2000
5000
10000
20000
50000
100000
Con
sum
pti
onp
erca
pit
a(2
011
US
D)
GDP vs consumption per capita in 2014
3
GDP per capita and welfare: life duration
500 1000 2000 5000 10000 20000 50000 100000
GDP per capita (2011 USD)
45
50
55
60
65
70
75
80
85
90
Lif
eex
pec
tan
cyat
bir
thin
2014
(yrs
)GDP per capita vs life expectancy in 2014
4
GDP per capita and welfare: life satisfaction
Stevenson and Wolfers (2013)Economic Growth and Subjective Well-Being: Reassessing the Easterlin Paradox
5
Growth in total income vs income of bottom 40%
Dollar, Kleineberg and Kraay (2016)Growth still is good for the poor
6
Growth fact 1
There is enormous variation in GDP per capita across economies.
0 20 40 60 80 100
GDP per capita relative to USA
0
20
40
60
80
100
Cu
mu
lati
vew
orld
pop
ula
tion
(%)
World population by GDP per capita in 2014
7
Growth fact 1
There is enormous variation in GDP per capita across economies.
500 1000 2000 5000 10000 20000 50000 100000
GDP per capita (2011 USD)
0.00
0.01
0.02
0.03
0.04
Pop
ula
tion
den
sity
GDP per capita population-weighed density
1960
1985
2014
8
Growth fact 1
There is enormous variation in GDP per capita across economies.The poorest countries have per capita incomes that are less than5 percent of per capita incomes in the richest countries.
• Income per capita (or GDP per capita) is not the sole measureof well-being, but it’s a useful summary statistic.
• Income per capita ignores distribution of incomewithin a country.
• Comparing income per capita across countries is not trivial:• You have to convert between currencies.• Countries have different relative prices for goods.• Large uncertainty in comparing income across countriesand over time: Johnson et al. (2013) Is newer better?Penn World Table Revisions and their impact on growth estimates.
9
Growth fact 2
Rates of economic growth vary substantially across countries.
−4 −2 0 2 4 6 8
Annual GDP per capita growth rate, 1970-2014 (%)
0
5
10
15
20
25
30
Nu
mb
erof
cou
ntr
ies
Histogram of GDP per capita growth rates
Developed countries
Lagging behind
Catching up
10
Growth fact 2
Rates of economic growth vary substantially across countries.
• We will try to distinguish whether these are long-termdifferences or just transitional differences.
• If they are long-term, then eventually some countrieswill be infinitely rich compared to others.
• We think most differences are transitional.
Small differences in rates of growthtranslate to big differences in incomes over time:
Rate Initial Income after ... yearsof growth income 25 50 70 1001.0% 100 128 164 201 2701.5% 100 145 211 284 4432.0% 100 164 269 400 7242.5% 100 185 344 563 11813.0% 100 209 438 792 1922 11
Rule of 70
A way to estimate the number of years it takesfor a certain variable to double.
Find T for which xT = 2x0, assuming constant (annual) growth rate g
xT = x0 · (1+ g)T
2x0 = x0 · (1+ g)T
2 = (1+ g)T | lnln 2 = T · ln (1+ g)0.7 ≈ T · g
T ≈ 0.7g =
70100 · g
If g is expressed in percent, the number of years for a variableto double is approximately equal to 70 divided by g(expressed in percentage points).
12
There are both “growth miracles” and “growth disasters”GDP per capita GDP per worker Emp. rate GDP per capita Avg. growth Years to
Country 2014 2014 2014 1970 1970-2014 double
United States 52 292 112 517 0.46 23 608 1.8 38
United Kingdom 40 242 83 612 0.48 15 176 2.2 31
France 39 374 95 498 0.41 16 436 2.0 35
Japan 35 358 68 989 0.51 12 956 2.3 30
Singapore 72 583 117 472 0.62 5 814 5.9 12
Hong Kong 51 808 100 467 0.52 7 613 4.5 16
Taiwan 44 328 92 979 0.48 4 738 5.2 13
South Korea 35 104 67 247 0.52 2 100 6.6 10
Botswana 16 175 37 637 0.43 798 7.1 10
China 12 473 21 394 0.58 1 285 5.3 13
Indonesia 9 707 21 853 0.44 995 5.3 13
India 5 224 13 261 0.39 1 282 3.2 21
Zimbabwe 1 869 4 384 0.43 2 429 -0.6 -117
Madagascar 1 237 2 833 0.44 1 479 -0.4 -171
Dem. Rep. of Congo 1 217 3 757 0.32 2 536 -1.7 -42
Niger 852 2 397 0.36 1 395 -1.1 -6213
Growth fact 3
World growth rates have increased sharply in the twentieth century.
1500 1600 1700 1800 1900 2000
Year
500
1000
2000
5000
10000
GD
Pp
erca
pit
a(1
990
US
D)
0.04
0.20
1.11
2.24
Evolution of world GDP per capita
14
Growth fact 3
For individual countries, growth rates also change over time.
1880 1900 1920 1940 1960 1980 2000
Year
1000
2000
5000
10000
20000
50000
GD
Pp
erca
pit
a(2
011
US
D)
GDP per capita in Japan
15
Growth fact 3
For individual countries, growth rates also change over time.
1950 1960 1970 1980 1990 2000 2010
Year
500
1000
2000
5000
10000
GD
Pp
erca
pit
a(2
011
US
D)
GDP per capita in India
16
Growth fact 3
Growth rates are not generally constant over time.For the world as a whole, growth rates were close to zero over mostof history but have increased sharply in the twentieth century.For individual countries, growth rates also change over time.
• The big changes in growth rates over history are frompre-Industrial Revolution (close to 0% growth) to modern times(roughly 1.85% growth per year for developed countries).
• The big changes in growth rates within countries tend to be asthey transition from poor to rich (e.g. Japan), after which growthslows down.
17
Growth fact 4
Countries can go from being “poor” to being “rich”.
1950 1960 1970 1980 1990 2000 2010
Year
500
1000
2000
5000
10000
20000
50000
100000
GD
Pp
erca
pit
a(2
011
US
D)
Evolution of GDP per capita: “growth miracles”
USA
UK
Japan
South Korea
Botswana
China
India
Indonesia
10:90 percentile range
18
Growth fact 4
Countries can go from being “rich” to being “poor”.
1950 1960 1970 1980 1990 2000 2010
Year
200
500
1000
2000
5000
10000
20000
50000
100000
GD
Pp
erca
pit
a(2
011
US
D)
Evolution of GDP per capita: “growth disasters”
USA
UK
Niger
Nigeria
Djibouti
Zimbabwe
Madagascar
Dem. Rep. of Congo
10:90 percentile range
19
Growth fact 4
A country’s relative position in the world distribution of per capitaincomes is not immutable. Countries can go from being “poor”to being “rich”, and vice versa.
• The “growth miracles” in 1960 were very poor.Now they are catching up to the rich countries.
• The “growth disasters” were in 1960 richer than East Asia.Now they are well behind.
20
Kaldor's stylized facts
In the USA (and other developed countries):
1. Per capita output grows over time,and its growth rate does not tend to diminish.
2. Physical capital per worker grows over time.3. The rate of return to capital is not trending.4. The ratio of physical capital to output is nearly constant.5. The shares of labor and physical capital in national incomeare nearly constant.
6. Real wage grows over time.
21
Kaldor's stylized fact 1
Per capita output grows over time,and its growth rate does not tend to diminish.
1880 1900 1920 1940 1960 1980 2000
Year
2000
5000
10000
20000
50000
100000
GD
Pp
erca
pit
a(2
011
US
D)
GDP per capita in USA
22
Kaldor's stylized fact 2
Physical capital per worker grows over time.
1950 1960 1970 1980 1990 2000 2010
Year
105
2× 105
3× 105
4× 105
Cap
ital
per
wor
ker
(201
1U
SD
)
Capital per worker in USA
23
Kaldor's stylized fact 3
The rate of return to capital is not trending.
1880 1900 1920 1940 1960 1980 2000
Year
−20
−10
0
10
20
Exp
-pos
tre
alin
tere
stra
te(%
)
Real interest rate in USA and UK
United States
United Kingdom
24
Kaldor's stylized fact 3
The rate of return to capital is not trending.
DeLong (2015)blogpost
25
Kaldor's stylized fact 3
The rate of return to capital is not trending.
Gomme, Ravikumar and Rupert (2015)Secular Stagnation and Returns on Capital
26
Kaldor's stylized fact 4
The ratio of physical capital to output is nearly constant.
1950 1960 1970 1980 1990 2000 2010
Year
2.0
2.5
3.0
3.5
4.0
4.5
Rat
io
Capital to GDP ratio in USA
27
Kaldor's stylized fact 5
The shares of labor and physical capital in national incomeare nearly constant.
1950 1960 1970 1980 1990 2000 2010
Year
50
55
60
65
70
75
Sh
are
inin
com
e(%
)
Labor share in income in USA
28
Kaldor's stylized fact 6
Real wage grows over time.
1950 1960 1970 1980 1990 2000 2010
Year
101
2× 101
3× 101
4× 101
Mea
nh
ourl
yco
mp
ensa
tion
(200
9U
SD
) Real mean hourly compensation in USA
29
Explaining growth
We want to explain:
• Why some countries are poor and other rich?• Why some countries that were previously poor become rich?• Why not all poor countries catch up to rich countries?• Why do rich countries still grow?
30
Solow-Swan model
Developed by Robert Solow (1956) and Trevor Swan (1956).
Growth in income per capita comes from two sources:
• Capital accumulation (endogenous).• Improvements in technology (exogenous).
But capital accumulation alone cannot sustain growthin the absence of technology improvements.
Does not explain “deep” sources of economic growth.
Departure point for growth theory.
31
Simplifications and assumptions
• Closed economy.• No government.• Single, homogenous final good with its price normalized to 1in each period (all variables are expressed in real terms).
• Two types of representative agents:• Firms.• Households.
32
Production
Real GDP is produced according to a neoclassical prod. function:
Yt = F (Kt,AtLt)
where Y is real GDP, F is a neoclassical prod. function, K is capitalstock, A is the technology level and L is the number of workers.
Technology grows at a rate g > 0 and increases productivityof labor (otherwise Kaldor's stylized facts would be violated):
At+1 = (1+ g)AtVery often we use a Cobb-Douglas production function:
Yt = Kαt (AtLt)
1−α
Like other neoclassical prod. functions, it exhibits constant returnsto scale – doubling inputs K and L doubles the amount produced:
(λKt)α(At · λLt)1−α
= λαλ1−αKαt (AtLt)
1−α= λYt
33
Firms
Perfectly competitive firms maximize their profit:
maxKt,Lt
Kαt (AtLt)
1−α − rkt Kt − wtLt
where rk denotes the rental rate on capital.
FOCs:
Kt : αKα−1t (AtLt)1−α − rkt = 0 −→ rkt = α
YtKt
Lt : (1− α) Kαt A1−α
t L−αt − wt = 0 −→ wt = (1− α)
YtLt
Total factor payments are equal to GDP:
rkt Kt + wtLt = αYtKtKt + (1− α)
YtNtLt = αYt + (1− α) Yt = Yt
34
Factor shares
Calculate the fraction of GDP that is paid to each factor:
wtLtYt
=(1− α)
YtLt
· Lt
Yt= (1− α) and rkt Kt
Yt=
αYtKt
· Kt
Yt= α
Cobb-Douglas function implies constant sharesof labor and physical capital in income.
Confronting with the US data, we can obtain α ≈ 13 and (1− α) ≈ 2
3 .
35
Households
Own factors of production (capital and labor)and earn income from renting them to firms.
Each households supplies one unit of labor: Lt = Ntand population grows at a rate n:
Nt+1 = (1+ n)Nt
Capital accumulates from investment It and depreciates at rate δ > 0:
Kt+1 = It + (1− δ) Kt
Income of households is consumed or saved (invested):
Yt = wtLt + rkt Kt = Ct + St = Ct + It
Households don't optimize, save a constant fraction s of income:
It = sYt and Ct = (1− s) Yt
36
GDP per worker
Usually we are most interested in GDP per worker (or per capita), y:
yt ≡ YtLt
=Kαt (AtLt)
1−α
Lt= At
(KtAtLt
)α
≡ Atkαt
where k is capital K divided per effective unit of labor (AL).
Clearly, GDP per worker increases due to improvements intechnology and due to capital accumulation.
The production function exhibits diminishing marginal returns tocapital. GDP per worker increases with k, but the size of the increasefalls with k.
It is also useful to define output per effective unit of labor y:
yt =ytAt
= kαt
37
Capital accumulation
Capital accumulates according to:
Kt+1 = sYt + (1− δ) Kt
And capital per effective labor according to:
Kt+1 = sYt + (1− δ) Kt | : AtLtLt+1Lt
At+1At
Kt+1At+1Lt+1
= s YtAtLt+ (1− δ)
KtAtLt
(1+ n) (1+ g) kt+1 = syt − δkt
kt+1 =skα
t + (1− δ) kt1+ n+ g+ ng ≈ skα
t + (1− δ) kt1+ n+ g
The growth rate of capital per effective labor equals:
kt+1 − kt =skα
t − (δ + n+ g) kt1+ n+ g
gk ≡ ∆kt+1kt
=kt+1 − kt
kt=skα−1
t − (δ + n+ g)1+ n+ g 38
Balanced growth path (steady state)
Variables per effective labor converge to their steady state values.If kt+1 = kt = k∗ (or, equivalently, gk = 0) then:
s(k∗)α−1
= δ + n+ g
k∗ =
(s
δ + n+ g
) 11−α
y∗ =
(s
δ + n+ g
) α1−α
Along the balanced growth path (BGP) variables per workergrow together with increases in technology:
y∗t = Aty∗ −→
∆y∗t+1y∗t
=∆At+1At
= g
And aggregate variables like aggregate capital and GDP growat the sum of rates of increase in population and technology.
39
Comparative statics
Solow-Swan model predicts that the BGP level of GDP per worker:
y∗t = At
(s
δ + n+ g
) α1−α
is higher in countries with higher investment share of GDP sand higher technology level A,and lower in countries with higher population growth rate n.
40
Investment share of GDP s vs GDP per worker y
0 10 20 30 40 50
Average investment share of GDP, 1950-2014 (%)
1000
2000
5000
10000
20000
50000
100000
200000
GD
Pp
erw
orke
rin
2014
(2011
US
D)
Investment rate vs GDP per worker
41
Population growth rate n vs GDP per worker y
−2 −1 0 1 2 3 4 5
Average population growth rate, 1950-2014 (%)
1000
2000
5000
10000
20000
50000
100000
200000
GD
Pp
erw
orke
rin
2014
(2011
US
D)
Population growth rate vs GDP per worker
42
Transitional dynamics
We are also interested in the determinants of growth ratesin GDP per worker outside of the BGP.
Start with growth rates of GDP per effective labor:
∆yt+1yt
≈ log(yt+1yt
)= log
(kαt+1
kαt
)= α log
(kt+1kt
)≈ α
∆kt+1kt
∆yt+1yt
≈ α[skα−1
t − (δ + n+ g)]
To obtain the growth rate of GDP per worker,add the growth rate of technology g:∆ytyt
= α[skα−1
t − (δ + n+ g)]+ g = α
[skα−1
t − (δ + n)]+ (1− α)g
An increase in s or a decrease in n temporarily increases the growthrate of GDP per worker. Note that even if higher g decreases k∗,it increases the rate of growth of GDP per worker. 43
Investment share of GDP s in “growth miracle” countries
1950 1960 1970 1980 1990 2000 2010
Year
0
10
20
30
40
50
60
70
Inve
stm
ent
shar
eof
GD
P(%
)Investment rates in “growth miracle” countries
Taiwan
South Korea
Singapore
Hong Kong
44
Factor payments once again
Using k∗ as capital per effective labor along the BGP,let us revisit factor prices:
rk∗t = αKα−1
t (AtLt)1−α= α
(k∗)α−1
w∗t = (1− α) Kα
t A1−αt L−α
t = (1− α)At(k∗)α
The model predicts that along the BGP the interest rates are constantwhile hourly wages increase at the same rate as GDP per hour:
1950 1960 1970 1980 1990 2000 2010
102
6× 101
2× 102
3× 102
4× 102
Ind
ex19
60=
100
Real compensation vs GDP per hour in USA
Real mean hourly compensation
Real GDP per hour
45
Convergence
Solow-Swan model predicts that if countries have access to thesame technology and share the same steady state, then ones thatare poorer should grow faster:
0
γk
k∗ k
46
Convergence: USA
We can observe convergence across individual states in USA:
Barro and Sala-i-Martin (1991)Convergence across States and Regions
47
Convergence: “West”
We can observe convergence across “Western” countries (+ Japan):
1000 2000 5000 10000
GDP per capita in 1870 (2011 USD)
1.25
1.50
1.75
2.00
2.25
2.50
An
nu
algr
owth
rate
,18
70-2
013
(%)
AUSBEL
CAN
CHE
DEUDNK
ESP
FIN
FRA
GBR
ITA
JPN
NLD
NOR
PRT
SWE
USA
Convergence across “Western” countries
48
Convergence: OECD
We can observe convergence across initial OECD members:
104 2× 104 3× 104 4× 104
GDP per worker in 1960 (2011 USD)
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
An
nu
algr
owth
rate
,19
60-2
014
(%)
AUT
BEL
CAN
DNK
FRA
DEU
GRC
ISL
IRL
ITA
LUX
NLD
NORPRT
ESP
SWE
CHE
TUR
GBR
USAAUS
FIN
JPN
NZL
Convergence across initial OECD members
49
Convergence: conditional/club, but not absolute
In general it is not true that poorer countries grow faster:
1000 2000 5000 10000 20000 50000
GDP per worker in 1960 (2011 USD)
−2
0
2
4
6
8
An
nu
algr
owth
rate
,19
60-2
014
(%)
ARG
AUS
AUTBEL
BFA
BGD
BOL
BRA
BRB
CAN
CHECHL
CHN
CIVCMR
COD
COLCRI
CYPDEU
DNK
DOM
ECU
EGY
ESP
ETH
FINFRA
GBR
GHA
GRC
GTM
HKGIDN
IND
IRL
IRNISL
ISR
ITA
JAM
JOR
JPN
KEN
KOR
LKA
LUX
MAR
MDG
MEX
MLI
MLT
MOZ
MWI
MYS
NER
NGA
NLD
NOR
NZL
PAK
PERPHL
PRT
ROU
SEN
SGP
SWE
SYR
THA
TTO
TUN TUR
TWN
TZAUGA URY
USA
VEN
ZAFZMB
No convergence across all countries
50
Conditional convergence
But countries grow faster the further away they are from their ownsteady state:
DZA
ARG
AUS
AUT
BGD
BRB
BEL
BENBOL
BWA
BRA
BDICMR
CAN
CAF
CHL
CHN
COLCOG
CRICIV
CYP
DNKDOM
ECU
EGY
SLV FJI
FINFRA
GAB
GMBGHA
GRC
GTM
HTI
HND
HKG
ISL
INDIDN
IRN
IRL
ISR
ITA
JAM
JPN
JORKEN
KOR
LSOLUX
MWI
MYS
MLI
MRTMUS
MEX
MAR
MOZ
NAMNPL
NLD
NZL
NIC
NER
NORPAKPANPNG
PRY PER
PHL
PRT
ROM
RWASEN
SGP
ZAF
ESP
LKA
SWE
CHESYR
TWN
TZA
THA
TGO
TTO
TUR
UGA
GBRUSA URY
VENZMB
ZWE
−0.02
0.00
0.02
0.04
0.06G
row
th r
ate
of G
DP
per
wor
ker,
196
0−−
2008
0.25 0.50 0.75 1.00 1.25 1.50Deviation from steady state in 1960, log scale
Jones and Vollrath (2013)Introduction to Economic Growth
51
Speed of convergence
The model implies a relationship between the distance from steadystate and the current rate of growth:
∆yt+1yt
≈ (1− α) (δ + n+ g)︸ ︷︷ ︸β
(log y∗t − log yt)
Econometric studies both on individual countries and states withinUSA find that β ≈ 0.02, meaning that it takes about 35 years to closehalf of the gap between the current income level and its steady state.
Given sensible parameter values: α = 0.33, δ = 0.05, n = 0.01,g = 0.02, the model generates β = 0.053, implying that it would takeabout 13 years to close half of the gap, a very unrealistic number.
Adding human capital allows the model to assign lower weightto raw labor and be consistent with slow convergence.
52
Human capital augmented Solow model
The production function that accounts for human capital:
Yt = Kαt (AtHt)
1−α
Ht = h (ut) Lt
where u are average years of schooling. Benchmark empiricalestimates on returns to schooling are expressed via the h function:
lnh (u) =
0.134 · u if u ≤ 40.134 · 4+ 0.101 · (u− 4) if 4 < u ≤ 80.134 · 4+ 0.101 · 4+ 0.068 · (u− 8) if u > 8
The estimates capture the empirical regularity that schooling boostsindividuals' wages. Wages contain not only rewards to raw labor, butalso to human capital. Empirical estimates of the income share of``broad capital'' are consistent with convergence factor β ≈ 0.02.
53
Human capital augmented Solow model
The production function that accounts for human capital:
Yt = Kαt (AtHt)
1−α
Ht = h (ut) Lt
Human capital generates level effects for GDP per workeralong the BGP:
yt = Ath (ut)(
sδ + n+ g
) α1−α
54
Human capital per capita h vs real GDP per worker y
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Index of human capital per worker in 2014
1000
2000
5000
10000
20000
50000
100000
200000
GD
Pp
erw
orke
rin
2014
(2011
US
D)
Human capital level vs GDP per worker
55
Fit of human capital-augmented Solow model
Suggests that poor countries ``should'' be richer:
DZA ARG
AUS
AUT
BGD
BRBBEL
BEN
BOL
BWA
BRA
CMR
CAN
CHLCHN
COL
COG
CRI
CIV
CYPDNK
DOM
ECU
EGYSLV
FJIFINFRA
GAB
GMB
GHA
GRC
GTMHTI
HND
HKGISL
IND
IDNIRN
IRLISRITAJAM
JPN
JOR
KEN
KOR
LSO
MYS
MLI
MRT
MUSMEX
MAR NAM
NPL
NLDNZL
NIC
NER
PAK
PAN
PNG
PRYPER
PHLPRT
ROM
RWA
SEN
SGP
ZAF
ESPLKA SWECHE
SYR
TWN
TZA
THA TTO
TUR
UGA
GBR
USA
URY
VENZMB
0.02
0.05
0.10
0.20
0.30
0.50
0.75
1.00
Pre
dict
ed s
tead
y st
ate
valu
e of
rel
ativ
e Y
/L
0.02 0.05 0.10 0.20 0.30 0.50 0.75 1.00Relative Y/L
Jones and Vollrath (2013)Introduction to Economic Growth
56
Solow residual: accounting for technology differences
There are also significant differences in technology across countries:
DZA
ARG
AUS
AUT
BGD
BRB
BEL
BEN
BOL
BWABRA
CMR
CAN
CHL
CHN
COL
COG
CRI
CIV
CYP
DNK
DOM
ECU
EGYSLV
FJI
FINFRA
GAB
GMB
GHA
GRC
GTM
HTI
HND
HKGISL
IND
IDN
IRN
IRL
ISR
ITA
JAM
JPN
JOR
KEN
KOR
LSO
MYS
MLI
MRT
MUS
MEX
MAR
NAM
NPL
NLD
NZL
NIC
NER
PAK
PAN
PNG
PRY
PER
PHL
PRT
ROM
RWA SEN
SGP
ZAF
ESP
LKA
SWECHE
SYR
TWN
TZA
THA
TTO
TUR
UGA
GBR
USA
URYVEN
ZMB
0.05
0.10
0.20
0.30
0.50
0.75
1.001.25
1.75
Rel
ativ
e A
0.02 0.05 0.10 0.20 0.30 0.50 0.75 1.00Relative Y/L
Jones and Vollrath (2013)Introduction to Economic Growth
57
Takeaway
• Long run growth stems from improvements in technology.• Countries can achieve higher balanced growth paths if theyaccumulate more physical and human capital.
• Just as important as accumulation is technology adoption.• Did not touch on “deep” causes of growth – we treated manychoice variables as exogenous parameters:
• Countries with low s may not protect private ownership properlyor have underdeveloped financial system.
• Countries with high n may have high mortality rates incentivizingfamilies to have many children in hopes that at least some surviveinto adulthood to be able to support their (then old) parents.
• Countries may have high u because they are already richand children do not have to work there.
• Groups of interest within a country may obstruct technologyadoption if they have a monopoly over the old technology.
58