lecture 4 - macroeconomic analysis of technological change
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Macroeconomic analysis of technological change
Merit course – 2006� Production functions� Innovation and employment
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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
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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?
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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
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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
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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 ���� −−− += ����� ��
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Substitutability and localized technological change
Figure 3. Isoquants shifting under the influence oflocalized technological change
Localized technological change (Atkinson & Stiglitz)
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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)
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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
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Endogenous bias (Kennedy’s model)
Figure 5. Kennedy’s model of an endogenous bias of technology
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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
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Growth accounting results (Solow)
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TFP growth for the Netherlands, 1921-2002
80
90
100
110
120
130
140
150
1920 1940 1960 1980 2000
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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 �,
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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.
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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”
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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?
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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)
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Models - Katsoulacos
� Process innovation and the demand for labour
� Product innovation (supply-side of the labour market)
� Structural issues (skills bias)
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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
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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
,
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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
.
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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).
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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
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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
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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)
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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
,
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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.
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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)
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Structural unemployment
� Industries (Schumpeter’s creative destruction)
� Skills (skills-bias of technological change and the skills-premium)
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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)
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�
��1.
�Q�Li
�AiT��
��1i 1�
�j
�i
AjLj
SiLi
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1��1
�wi
p, i, j� s,u (i� j)�Q
�Li
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��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.
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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.,
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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