lecture 31 macroeconomic analysis 2003 golden rule of saving and capital accumulation

Lecture 3 1

Macroeconomic Analysis 2003

Golden Rule of Saving and Capital Accumulation

Lecture 3 2

Saving and Investment Ratios Across the World 1984

I/Y = 0.5966(S/Y) - 5.9608

R2 = 0.1297

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00

Investment ratio

Sav

ing

Rat

io

Series1

SI Global

Lecture 3 3

How does a higher saving rate affect the level of output in the steady state?

11

sksyS

22ky

1y

L

Kk

222

sksyS 22kni

2y

1k 2k

Low saving country

High saving country

Saving rate affects level of income but not

the growth rates

Lecture 3 4

How does the technological advancement affect the per capita capital and per capita output in the steady state?

11

sksyS

22ky

1y

L

Kk

222

sksyS

22kni

2y

1k 2k

Primitive Technology

Advanced Technology

11ky

Lecture 3 5

Golden Rule for Saving and Capital Accumulation

ky

L

Yy

L

Kk

sksyS

kni

KssKg

C-max

nMPK

nk 1

Lecture 3 6

Golden Rule of SavingW h a t i s t h e s a v i n g r a t e t h a t m a x i m i s e s c o n s u m p t i o n ?

iyc ( 1 ) knyc ( 2 )

knycMax ( 3 )

01

nkdk

c ( 4 )

nk 1 ( 5 ) nMPK ( 6 )

P u r p o s e o f a l l e c o n o m i c a c t i v i t i e s i s c o n s u m p t i o n . T h ec a p i t a l s t o c k w h e r e t h e s l o p e o f p r o d u c t i o n f u n c t i o n( m a r g i n a l p r o d u c t o f c a p i t a l ) e q u a l s t h e s l o p e o f t h ei n v e s t m e n t r e q u i r e m e n t l i n e ( d e p r e c i a t i o n p l u s t h e g r o w t hr a t e o f t h e p o p u l a t i o n ) a s g i v e n i n ( 6 ) .

Lecture 3 7

T a k e 1 1 d i f f e r e n t s a v i n g r a t e s , s = 0 , 0 . 1 , 0 . 2 , … … . , 1 . 0 .A n d c a p i t a l s t o c k l i k e : 1 , 4 , 9 , 1 6 , 2 5 , 3 6 , 4 9 , 6 4 , 8 1

LKY 5.0 i n p e r c a p i t a t e r m s5.05.0 ky

A s s u m e 05.0 , 5.0 , A = 0 . 5

T h e n c a l c u l a t e c o n s u m p t i o n , m p k a n d m p k – d a s f o l l o w i n gs - r a t e k y d k c S a v i n g

sm p k m p k - d

0 . 1 1 . 0 0 0 . 5 0 0 . 0 5 0 . 4 5 0 . 0 5 0 . 2 5 0 0 0 . 2 0 0 00 . 2 4 . 0 0 1 . 0 0 0 . 2 0 . 8 0 . 2 0 . 1 2 5 0 0 . 0 7 5 00 . 3 9 . 0 0 1 . 5 0 0 . 4 5 1 . 0 5 0 . 4 5 0 . 0 8 3 3 0 . 0 3 3 30 . 4 1 6 . 0 0 2 . 0 0 0 . 8 1 . 2 0 . 8 0 . 0 6 2 5 0 . 0 1 2 50 . 5 2 5 . 0 0 2 . 5 0 1 . 2 5 1 . 2 5 1 . 2 5 0 . 0 5 0 0 0 . 0 0 0 00 . 6 3 6 . 0 0 3 . 0 0 1 . 8 1 . 2 1 . 8 0 . 0 4 1 7 - 0 . 0 0 8 30 . 7 4 9 . 0 0 3 . 5 0 2 . 4 5 1 . 0 5 2 . 4 5 0 . 0 3 5 7 - 0 . 0 1 4 30 . 8 6 4 . 0 0 4 . 0 0 3 . 2 0 . 8 3 . 2 0 . 0 3 1 3 - 0 . 0 1 8 80 . 9 8 1 . 0 0 4 . 5 0 4 . 0 5 0 . 4 5 4 . 0 5 0 . 0 2 7 8 - 0 . 0 2 2 2

F o r t h i s p a r a m e t r i c c o n f i g u r a t i o n 5 0 p e r c e n t s a v i n g r a t e m a x i m i s e s c o n s u m p t i o n .

A Numerical Example for the Golden Rule of Saving

Lecture 3 8

Saving rate

C-max = 1.25

Con

sum

ptio

n

s*=1.25

y=2.5

k = 25

y = 0.5*k0.5

s1 s2 s4 s5

How High Should be the Saving Rate? Saving Rate that Maximises Consumption

Lecture 3 9

Investment Ratio in OECD Countries:Average 1980-2000

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

Austra

lia

Austri

a

Belgium

Canada

Denmar

k

Finlan

d

Franc

e

Germ

any

Greec

e

Icela

nd

Irelan

dIta

ly

Japa

n

Luxe

mbo

urg

Nether

lands

New Zea

land

Norway

Portu

gal

Spain

Sweden

Switzer

land

United K

ingdom

United S

tate

s

Lecture 3 10

Variation in the Saving Ratio Across OECD Countries: Average 1980-2000

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00A

ustr

alia

Aus

tria

Bel

gium

Can

ada

Den

mar

k

Fin

land

Fra

nce

Ger

man

y

Gre

ece

Icel

and

Irel

and

Ital

y

Japa

n

Luxe

mbo

urg

Net

herla

nds

New

Zea

land

Nor

way

Por

tuga

l

Spa

in

Sw

eden

Sw

itzer

land

Uni

ted

Kin

gdom

Uni

ted

Sta

tes

Lecture 3 11

Average Saving Rate in Growth Disaster Countries (1980-2000)

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

CAFRChad

Ghana

Haiti

Mada

gasc

ar

Nicara

guaNige

r

Senega

l

Sierra

Leo

ne

Venezu

ela, R

B

Zambia

Series1

Lecture 3 12

Investment Ration in Growth Miracle Countries: Average 1980-2000

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

China HongKong,China

Ireland Korea,Rep.

Japan Malta Portugal Singapore Thailand

Lecture 3 13

Population by Age and Gender in the UK in 2000How Does it Affect Saving and Investment?

0500

1,0001,5002,0002,5003,0003,5004,0004,5005,000

in '0

00

femalemale

Lecture 3 14

Population by age and Gender in India in 2000What is the prospect of Saving and Investment?

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

in '0

00

FemaleMale

Lecture 3 15

Intertemporal budget constraint:

23.19505.1

100100

112

12

1

r

CC

r

ww

Optimal consumptions

11.10095.1

23.195

11

C

86.99)05.112.10095.011

112

rrCC

If the interest rate is 10 percent 9.190

1.1

100100

9.971

9.1901

C

3.102)1.19.9795.0112 rCC

Optimal Saving and Consumption in Two Period Model

Lecture 3 16

A Three Period Optimal Consumption-Saving Model

3ln

32ln

21ln

3,

2,

1CCCCCCUMax

S u b j e c t t o :

1 . 21

31

2121

31

21

r

W

r

WW

r

C

r

CC

2 . ( 1W , 2W , 3W ) = ( 1 2 0 , 1 2 0 0 , - 1 2 0 )3 . ( 1C 0 , 2C 0 , 3C 0 )

W h a t i s t h e o p t i m a l c o n s u m p t i o n i n e a c h p e r i o d (1

C , 2

C ,

3C ) i f 1

21 a n d 0

21 rr ?

Lecture 3 17

Four Optimisation Conditions

21

31

213ln32ln21ln,3,2,1 r

C

r

CCCCCCCCL F

o u r f i r s t o r d e r c o n d i t i o n s :

( 1 ) 01

1

1

CCL

1

1C

( 2 ) 01

2

2

1

rCCL

rCC

11

1

2

2

rC

C 1

21

2 rCC 1212

( 3 ) 02

113

3

1

r

CCL

211

1

3

3

rCC

213

1

3 rC

C 21

313rCC

( 4 ) 0

21

31

21

r

C

r

CCL

13121

CCC

Lecture 3 18

Consumption and Savings in Three Periods

O p t i m a l C o n s u m p t i o n i n p e r i o d 1 : 321 1

C ;

O p t i m a l C o n s u m p t i o n i n p e r i o d 2 :

321

121212

rrCC

O p t i m a l C o n s u m p t i o n i n p e r i o d 3 :

321

21321313

rrCC

O p t i m a l s a v i n g i n p e r i o d 1 : 280400120111

CWS

O p t i m a l s a v i n g i n p e r i o d 2 : 4001200222

CWS

O p t i m a l s a v i n g i n p e r i o d 3 : 400120333

CWS

Lecture 3 19

Policy Issues:Tax, Saving and Consumption

• What is the impact in consumption and saving in the above model– If there is a 20 percent tax on interest income?– If there is a 20 percent subsidy in it?– What sort of tax system is better for increasing the

ratio of saving? Does a higher rate of VAT promote saving or consumption?

– Does a higher rate of tax on labour income encourage or discourage saving?

– Does a higher rate of tax on pension income increase saving or consumption?

Lecture 3 20

Factor Shares Across Production Sectors in the UK (ONS)

-

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Sh

are

Labour share

Capital share

Which sectors are hit hard when the labour income is taxed more heavily than the capital income?

Do workers in the Service sector lobby for Higher capital income tax?

Lecture 3 21

Agri Mining Manf EGW Construc

Distribution

Transport

Fin.Serv

Pub.Adm.

Ed/health

Other TotalGDP

Maxgrwth

Mingrwth

1983 -0.065 -0.130 0.056 0.124 0.129 0.104 0.091 0.136 0.144 0.072 0.058 0.072 0.144 -0.130

1984 0.336 -0.734 0.071 -0.181 0.105 0.126 0.160 0.106 0.111 0.126 0.052 0.040 0.336 -0.734

1985 -0.086 2.451 0.100 0.091 0.027 0.100 0.056 0.131 0.055 0.100 0.075 0.125 2.451 -0.086

1986 0.056 -0.029 0.128 0.053 0.048 0.120 0.089 0.170 0.053 0.122 0.146 0.109 0.170 -0.029

1987 0.033 -0.103 0.096 -0.003 0.226 0.082 0.082 0.052 0.058 0.096 0.113 0.077 0.226 -0.103

1988 -0.027 -0.116 0.104 -0.023 0.222 0.132 0.107 0.072 0.094 0.158 0.124 0.100 0.222 -0.116

1989 0.162 -0.030 0.097 -0.019 0.198 0.109 0.099 0.171 0.055 0.180 -0.081 0.113 0.198 -0.081

1990 0.100 -0.098 0.036 0.013 0.065 0.099 0.081 0.163 0.089 0.124 0.110 0.083 0.163 -0.098

1991 -0.014 0.116 -0.034 0.309 -0.088 0.079 0.056 0.046 0.044 0.145 -0.035 0.036 0.309 -0.088

1992 0.063 0.010 0.012 -0.044 -0.079 0.010 0.008 0.106 0.092 0.121 0.084 0.041 0.121 -0.079

1993 0.064 -0.265 0.057 -0.052 0.059 0.018 0.122 0.056 0.035 0.055 -0.005 0.043 0.122 -0.265

1994 -0.027 -0.412 0.041 -0.018 0.068 0.091 0.052 0.137 0.010 0.073 0.041 0.061 0.137 -0.412

1995 0.250 0.132 0.062 -0.080 0.007 0.092 0.072 0.062 0.038 0.041 0.102 0.061 0.250 -0.080

1996P 0.021 0.101 0.036 -0.003 0.094 -0.013 0.027 0.044 0.017 0.004 0.060 0.027 0.101 -0.013

Source: www.statistics.gov.uk

Which Sectors are important for a higher economic growth in the Yorkshire and

Humberside region? (annual growth rates)

Lecture 3 22

Sectoral compositon of Imports in UK and EU

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 Agr

i

2 M

ininn

g

3 M

nfcs

4 Elec

tricit

y

5 Con

struc

tion

6 Dist

ribut

ion

7 Tr

ansp

ort

8 Fi

nSer

v

9 Edu

catio

n

10 O

ther

1 EU

2 UK

Why is the Manufacturing Sector So Important for Economic Growth?

Lecture 3 23

Sectoral Composition of Exports in the UK and the EU

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 Agr

i

2 M

ininn

g

3 M

nfcs

4 Elec

tricit

y

5 Con

struc

tion

6 Dist

ribut

ion

7 Tr

ansp

ort

8 Fi

nSer

v

9 Edu

catio

n

10 O

ther

1 EU

2 UK

Lecture 3 24

Exercises• Calculate the saving rate consistent with the

golden rule

• Study of Relative income levels across regions in the UK

• Study of economic growth in Hulls and Humberside

• Which are the leading sectors of Economic Growth in the UK and in the Yorkshire and Humberside?