Macroeconomic analysis of technological change

Merit course – 2006� Production functions� Innovation and employment

Production functions

Figure 1. Isoquants showing all possible combinations of production factors that willyield a fixed amount of output

� Today’s substitution possibilities are yesterday’s technological innovations

Characteristics of the production function

� Returns to scale� Decreasing marginal returns� These are crucial assumptions in modern

economic theory (e.g., without decreasing marginal returns a supply curve would not be upward sloping)

� Traditional economics does not provide a clear theory of these assumptions would hold; can technology provide the answer?

Engineering production functions

� Hollis Chenery, Vernon Smith in 1950s and 1960s

� An example: heat transferH1�H0�HL.H1�H0�HL.

HL�Tout�Tin

K� tkS

,HL�Tout�Tin

K� tkS

,

H1�H0�Tout�Tin

K� VkS 2

.H1�H0�Tout�Tin

K� VkS 2

.

H1�H0�280

0.01381�0.000595V.H1�H0�

2800.01381�0.000595V

.

V�St To raise the heat output level, we may use insulation of the pipe, or produce more heat as input; these two alternatives are substitutable production factors

The isoquantsIsoquants for the heat transmission process

0

10

20

30

40

50

60

70

0 5000 10000 15000 20000 25000 30000 35000 40000

Heat input (BTU/hr)

insu

latio

n m

ater

ial (

cubi

c fe

et)

output=5000 BTU/hr

output=15000 BTU/hr

output=10000 BTU/hr

Functional forms of production functions

� Cobb Douglas (widely used):� Constant Elasticity of Substitution (CES):

� Elasticity of substitution:

� σ = 1 for Cobb-Douglas, 1/(1+ρ) for CES

���

���

���

���

�����

�����

��

��

���

���

���

��� ��

����

==σ

βα���� =

ρρρ ���� −−− += ����� ��

Substitutability and localized technological change

Figure 3. Isoquants shifting under the influence oflocalized technological change

Localized technological change (Atkinson & Stiglitz)

A bias of technological change

Figure 4. Technological change shifts the isoquant down: neutral technological progress(left), capital saving technological progress (middle) and labour saving technologicalprogress (right)

Bias of technological change (labour-saving or capital-saving)

Biased technological change – Hicks’mathematics

�

�

�

�

�

��

�

���

∂∂−∂∂= ��

� For Cobb-Douglas a change in A is neutral (B=0)

� For CES, a change in AK or AL is non-neutral (unless both change in the same proportion)– The CES is a more flexible form than the Cobb-

Douglas

Endogenous bias (Kennedy’s model)

Figure 5. Kennedy’s model of an endogenous bias of technology

Growth accounting

� Tinbergen/Abramovitz/Solow:

� A measure of technological change or a measure of our ignorance?

dQdt

�dAdt

f�AfKdKdt

�AfLdLdt

.dQdt

�dAdt

f�AfKdKdt

�AfLdLdt

.

Q� A�AfKK

QK�

AfL L

QL.Q� A�

AfKK

QK�

AfL L

QL.

A�Q��L L��K K.A�Q��L L��K K.

Figure 6. Substitution and technological change in theproduction function

Growth accounting results (Solow)

TFP growth for the Netherlands, 1921-2002

80

90

100

110

120

130

140

150

1920 1940 1960 1980 2000

Endogenous technological change –R&D

Non-military R&D as a % of GDP

1.0

1.5

2.0

2.5

3.0

3.5

EU

Japa

n

US

OE

CD

Total R&D as a % of GDP

1.0

1.5

2.0

2.5

3.0

3.5

EU

Japa

n

US

OE

CD

R&D researchers as a % of total employment

4

5

6

7

8

9

10

11

EU

Japa

n

US

OE

CD

% R&D financed by businesses

50

55

60

65

70

75

EU

Japa

n

US

OE

CD

Q�AR �K 1��L �,Q�AR �K 1��L �,

BERD and productivity

0.00

0.50

1.00

1.50

2.00

2.50

1950 1960 1970 1980 1990 2000 2010

France United Kingdom Japan United States

Country αααα ρρρρ

France 0.860 (0.000) -0.031 (0.273)

United Kingdom 0.421 (0.023) 0.395 (0.067)

Japan 0.478 (0.000) 0.155 (0.000)

United States 0.521 (0.000) 0.237 (0.000)Table 1. Estimations results for the equation including business R&D as a production factor,1959 - 1999.

Issues – Ned Ludd and the Army of Redressers

Ricardo: “The opinion, entertained by the labouring class, that the employment of machinery is frequently detrimental to their interests, is not founded on prejudice and error, but is conformable to the correct principles of political economy”

The demand for labour - Two types of innovation

� Process innovation: technology replaces labour? Compensation mechanisms:– Lower prices, expanded demand (general

equilibrium)– Demand for machinery (investment)

� Product innovation: expanding demand– New products substitute old ones?

Labour markets and unemployment

� Keynesians and neoclassicals: flexible wages or sticky wages?

� We focus mainly on demand for labour (fall leads to either unemployment or wage pressure)

Models - Katsoulacos

� Process innovation and the demand for labour

� Product innovation (supply-side of the labour market)

� Structural issues (skills bias)

Process innovation and the demand for labour

� Restrictive assumptions:– Homothetic demand– One production factor: homogenous labour– Two sectors/goods

� Setting: investigate the impact of a change in the labour coefficient (productivity) in one industry

Goods markets

� Profit maximization in goods market

� Totally differentiation this w.r.t. time:

pi (1�1�ii

)�wai, where �ii���Qi

�pi

pi

Qi

.pi (1�1�ii

)�wai, where �ii���Qi

�pi

pi

Qi

.

p1�(�11�1) a1(�22�1�e22)�e12(�22�1) a2

(�11�1�e11)(�22�1�e22)�e12e21

,

p2�(�22�1) a2(�11�1�e11)�e21(�11�1) a1

(�22�1�e22)(�11�1�e11)�e21e12

,

p1�(�11�1) a1(�22�1�e22)�e12(�22�1) a2

(�11�1�e11)(�22�1�e22)�e12e21

,

p2�(�22�1) a2(�11�1�e11)�e21(�11�1) a1

(�22�1�e22)(�11�1�e11)�e21e12

,

Consumers – Utility function

� Ces functional form:

� Leads to demand functions:

� With price elasticities:

� Because of homothetic demand:

U� C��1�

1 �C��1�

2

�

��1,U� C

��1�

1 �C��1�

2

�

��1,

Q di �

Y

p �i A, where A�p 1��

1 �p 1��2 ,Q d

i �Y

p �i A, where A�p 1��

1 �p 1��2 ,

�ii���(��1)si, �ij�(��1)sj (i�j), where si�piQi

Y�

11� (pi /pj)

��1�ii���(��1)si, �ij�(��1)sj (i�j), where si�

piQi

Y�

11� (pi /pj)

��1

�11��12��22��21�1

e11��e12��12�21

�11

, e22��e21��21�12

�22

.

�11��12��22��21�1

e11��e12��12�21

�11

, e22��e21��21�12

�22

.

Model closure

� Differentiate demand function:

� Which leads to:

� Hence everything depends on relative elasticities η11 and η22

Li� aj�Q di � ai��iipi��ij pj.Li� aj�Q di � ai��iipi��ij pj.

L�a1

(�22��11) (�222��11�22��12 (�22��11))

(�11��22)(�22�11��21�11��21�22).L�a1

(�22��11) (�222��11�22��12 (�22��11))

(�11��22)(�22�11��21�11��21�22).

Model conclusions

� Process innovation leads to an increase in overall demand for labour if the sector where the innovation takes place has a high price elasticity

� But in the model, price elasticity is an endogenous variable, it depends on the share of a sector in GDP

� With persistently higher process innovation in a sector, the share of this sector in GDP will grow, and hence it’s price elasticity will decline, hence the impact of process innovation eventually becomes negative

Product innovation and the demand for labour

� A similar setup, but– Labour productivity fixed and constant between

sectors– Number of goods/sectors is n, and expands as a

result of product innovation– Labour supply is modeled explicitly

Model – consumers and workers

� Ces utility function

U� C��1�

1 �C��1�

2 �..�C��1�

n

�

��1.U� C

��1�

1 �C��1�

2 �..�C��1�

n

�

��1.

Vj = U - ω j, where ω j is worker j’s disutility from workwhen Vj < 0 (U < ωj), worker j will make the rational decision not totake a job

ωj is a random variable distributed uniformly between 0 and � , withtotal density equal to N (the number of workers)ωj is a random variable distributed uniformly between 0 and � , withtotal density equal to N (the number of workers)

Model solution

� Demand functions become:

� Profit maximization condition becomes:

� This leads to:

� Substituting in the utility function leads to:

Q di �

Y

p �i A, where A�p 1��

1 �p 1��2 � ..�p 1��

n .Q di �

Y

p �i A, where A�p 1��

1 �p 1��2 � ..�p 1��

n .

�d���(��1)

n, �c�

(��1)n

,�d���(��1)

n, �c�

(��1)n

,

p(1� 1�d

)�w.p(1� 1�d

)�w.

wp�

(��1)(n�1)� (n�1)�1

.wp�

(��1)(n�1)� (n�1)�1

.Each workers that has a job receives w income, which is spent on the ngoods. Thus, the budget constraint is w = npC*, where C* is the quantityconsumed of each good

V ��n

1��1 (��1)(n�1)� (n�1)�1

,V ��n

1��1 (��1)(n�1)� (n�1)�1

,

Labour supply

� V*determines labour supply:

� This derivative is always positive, but it is declining in θ

L ��N�

n1��1 (��1)(n�1)�(n�1)�1

.L ��N�

n1��1 (��1)(n�1)�(n�1)�1

.

�L �

�n�

N�

�n�

��1 (1�1/n)�n2����1 (��1)

(�n���1)2.�L �

�n�

N�

�n�

��1 (1�1/n)�n2����1 (��1)

(�n���1)2.

Conclusions (in words!)

� Product innovation (increasing number of products) always leads to a higher labour supply

� The extent two which this happens declines with the elasticity of substitution between the products

� In the limit, when products become complete substitutes, there is no effect on labour supply (product innovations completely substitute old products)

Structural unemployment

� Industries (Schumpeter’s creative destruction)

� Skills (skills-bias of technological change and the skills-premium)

A model of the skills-bias (structural unemployment)

� A ces production function with skilled and unskilled labour (homogenous output):

� Profit maximization:

� Labour demand functions:

Q�T �s(As Ls)��1� ��u (AuLu)

��1�

�

��1.Q�T �s(As Ls)

��1� ��u (AuLu)

��1�

�

��1.

�Q�Li

�AiT��

��1i 1�

�j

�i

AjLj

SiLi

��1�

1��1

�wi

p, i, j� s,u (i� j)�Q

�Li

�AiT��

��1i 1�

�j

�i

AjLj

SiLi

��1�

1��1

�wi

p, i, j� s,u (i� j)

Li��

�

��1j �

�

i T �A ��1i AjLj

(wi/p)��1�A ��1i �

�

i T ��1�

��1

.Li��

�

��1j �

�

i T �A ��1i AjLj

(wi/p)��1�A ��1i �

�

i T ��1�

��1

. si��Q�Li

Li

Q�

(Ai T)��1��

i

(wi/p)��1.si�

�Q�Li

Li

Q�

(Ai T)��1��

i

(wi/p)��1.

Model solution

� From this one may derive:

– Then, demand for skilled labour will always increase

– But demand for unskilled labour is ambiguous, only when elasticity of substitution is high it may increase

Lu��/ssT�(�/ss�1)� As�Ls,

Ls��/su T�(�/su�1)�Au�Lu,

Lu��/ssT�(�/ss�1)� As�Ls,

Ls��/su T�(�/su�1)�Au�Lu,

Lu>0 iff �/ss (T� Au)> Au� As,

Ls>0 iff �/su (T�As)> As� Au.

Lu>0 iff �/ss (T� Au)> Au� As,

Ls>0 iff �/su (T�As)> As� Au.

Suppose that all three rates of innovation (T, As,Au ) are positive, butthat innovation primarily replaces unskilled technical change, i.e.,Au> As .

Suppose that all three rates of innovation (T, As,Au ) are positive, butthat innovation primarily replaces unskilled technical change, i.e.,

Conclusions

� With a skills-bias of technological change, unskilled labour is at a disadvantage (unemployment or skills-premium)

� But this depends on how easy unskilled labour may substitute for skilled labour