PRODUCTION FUNCTION AND THEORIES OF TFP

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PRODUCTION FUNCTION AND THEORIES OF TFP

• By
• Ir. Mah Lok Abdullah
• Malaysia
• Tehran, December 2004

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TFP terms used
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ORIGIN AND TFP DEVELOPMENT

• 1940s concept on TFP unheard. It was thought o/p
  growth was attributed fully by
• quantitative increase in L K.
• 1942 first empirical measure of TFP by an
  economist Jan Timbergen. He computed TFP
• by taking the residual difference between output
  weighted contribution of L K. His
• studies compared TFP for France, Germany, U.K,
  US for period 1870 to 1914. ( In the case
• of US at least ¾ of economic growth was due to
  increase efficiency in the
• use of productive I/ps.)
• 3. After world war II(1950s 60s) many
  significant studies appeared.
• 1950s major contributors of TFP studies e.g
  Jacob Schmookler, Solomon Fabricant,
• John Kendrick Moses Abramovitz.
• 1957 Robert Solow became the first economist to
  use production function framework
• in growth analysis as this become the
  theoretical basis of understanding the concept.
  He
• include technical change to represent any
  kind of shift in the production function, which
• capture all qualitative changes in labour and
  capital inputs, systems and technology.
• 1960s major contributor Edward Denison, John
  Kendrick, Dale Jorgenson
• In 1961 Kendrick introduced the neutral term of
  TFP.

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Among Important Contributors to Measurement of TFP

• Macro Kim Lau (1994)
• Young (1994)
• Krugman (1994)
• Sarel (1997)
• National Productivity Report, Malaysia
• Journal of Productivity Analysis

• Sectoral

Jorgenson, D.W, Gollop, F, Fraumeni, B.
(1987) Nishimizu and Hulten (1977) National
Productivity Report, Malaysia Journal of
Productivity Analysis

• Manufacturing Todd (1985), Oguchi, N. et al
  (2000)
• Leung (1998)
• Wong and Tok(1994)
• Kim Han (2001)

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• TFP Studies in Malaysia for Manufacturing Sector
  

Maisom Arshad (1992) Maisom, Mohd Ariff and
NorAini (1993) Gan and Robinson (1993) Zarina
Shariman (1994) Choong Tham (1995) Tham
(1996) Rokiah Alavi (1996) Rauzah (2000) Lee
Maisom (2001) Noeline Maisom (2001) Roslina,
Wahab Maisom (2001) Oguchi el at.,
(2002) National Productivity Report (1993-2004),
Malaysia
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Past Studies on Sources of growth for the
Malaysian Economy

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Past Studies on Sources of growth for the
Malaysian Economy

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Importance of TFP Growth
Output per worker
New per worker Production function
P2
F(t1)
Y/L2
TFP
F(t0)
Y/L1
Initial per worker production function
P1
Y/L0
P0
Y Output L Labour K Capital Y/L
Productivity K/L Capital intensity
K/L0
K/L1
Capital labour ratio
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• An increase in productivity may be obtained by
  two
• different means.
• The production function remains unchanged but
  capital intensity increases (movement from P0 to
  P1).
• Increase in capital intensity from K/L0 to K/L1
  raises productivity from Y/L0 to Y/L1.
• 2. A higher volume of production can be
  obtained with the same amount of labour and
  capital (movement from P1 to P2, TFP improvement)
• Productivity increases from Y/L1 to Y/L2, at
  the same capital intensity, K/L1.

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The economist view on TFP Is explained using
the PRODUCTION FUNCTION FRAMEWORK Two
InputsK,L Y f ( K, L ) The function relates
the size of output (Y) to the quantity Of inputs
used- capital (K) and labour (L). It defines the
Maximum output achievable with any given
quantity of Inputs. The resulting shifts of
the production function can be presented by Y
f ( K,L,t ) Thus implying that the same input
quantities yield a Different output at different
points of time Assuming neutral technical
progress ( Solow, 1975) Y T (t) . K, L
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DERIVING THE SOURCES OF ECONOMIC GROWTH
Differentiating with respect to time and dividing
by Y . . . Y/Y T/T ?Y/?K . K/Y
. K/K .
?Y/?L . L/Y. L/L Assuming competitiveness
equilibrium and constant Return to scale . .
. . Y/Y
T/T wK . K/K wL . L/L OR Using the
residual method . . . . T/T Y/Y
- ( wK. K/K wL. L/L )
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Linkages between the Key Economic Variables of
the Economy The GDP-Labour Productivity Link
Consider Labour Productivity
P GDP Y
Total Employed Labour Force L
or Total Man-Hours Equation Labour
Productivity

Output Unit of labour Input
GDP No of workers or man-hour
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So, P Y / L
Y P L
(1) Mathematically, this equation can be
expressed in terms of growth in the variables.
The growth equation is
Ygr Pgr Lgr (2) In other words, over
time, GDP growth (Ygr) is the sum of labour
productivity growth (Pgr) and the growth of
employed labour force (Lgr).
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• The Labour Productivity TFP Link
• Labour productivity is determined by the nature
  of and changes in the production process.
  Improvements (either quantitative or qualitative)
  in the production process will increase labour
  productivity.
• Quantitative Improvements
• In the form of higher capital intensity
• Qualitative Improvements
• Encompassing organisational improvements,
  technological advancements and rising quality of
  the labour force, in other words, TFP.

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• The mathematical derivation of this relationship
  starts with a production function. Through a
  series of mathematical manipulations, an equation
  relating the growth rates of labour productivity
  (P), capital intensity (K/L) and TFP (A), can be
  derived, as follows
• Pgr Agr b(K/L)gr (3)
• The coefficient b show how much productivity
  will grow for every percentage change in capital
  intensity.
• Agr Pgr b(K/L)gr (4)

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• The TFP GDP Link
• The link between TFP and GDP is through labour
  productivity. Taking equation (2) and (3)
  together
• Ygr Pgr Lgr
• (Agr b(K/L)gr) Lgr
  .. (5)
• From this, we can derive the equation that
  underpins the growth accounting framework.
• Ygr Agr aLgr bKgr . (6)
• Where a is measured as the share of labour
  in output or GDP
• while b is measured by the share of capital
  share in output or GDP.

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Growth of GDP, TFP, Capital and Labour ()
Malaysia
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Contribution of TFP, Capital and Labour to GDP
Growth ()
Malaysia
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?
How to capture the effect of qualitative things,
which are not quantifiable?

• At the economy level, there are two ways of
  estimating TFP
• Growth accounting framework
• Regression

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Growth Accounting Framework
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• - based on Cobb Douglas Production Function
• Is based on the notion that the growth in the
  non-measurable (or qualitative) factor is just
  the difference between overall output growth and
  the increase in measurable factor inputs.
  
• Equation

TFP growth GDP growth Weighted growth in
factor inputs
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• The weight of the factor input reflects the
  contribution of that particular factor to overall
  output growth. This weight is the factors share
  of total output.
• Example
• Assuming in a country, about 42 of its total
  output goes to labour as wages, while the
  remaining 58 goes to capital in form of interest
  and profits. This means that the weights assigned
  are 0.42 to labour and 0.58 to capital.
• Therefore,

TFP growth GDP growth (0.42 X labour gwt.
rate)
(0.58 X capital gwt. rate)
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Regression

• Establishes a statistical relationship among
  output (GDP), measurable factor resources (like
  labour and capital) and qualitative factors
  group.
• Equation

GDP Weighted factor input levels TFP

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• The weight are estimated. To overcome the
  non-measurability of the qualitative factors, a
  proxy, usually a time trend is used. After a
  regression exercise, an equation like the
  following may be obtained
• GDP (a X labour) (b X capital) (c X
  time)
• where a, b, c are correlation coefficients.
  TFP growth is given by the coefficient of the
  time variable, c.

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Sources of TFP Growth
HIGHER PRODUCTIVITY
CI
TFP
Capital Structure
Demand Intensity
Quality of Labour
Economic Restructuring
Technical Progress
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Major Determinants

• Changes in Quality of Labour/workforce is
  commonly used in growth accounting to refer to
  variables that affect the production capacity of
  workers. A component of labour quality is human
  capital investment, mainly in education and
  skills upgrading. Training as proxy to indicate
  the effect of change of education level on TFP
  which will be reflected through the wage rate.
  Other growth studies use the age-sex composition
  of workforce as a proxy for labour quality, as it
  reflects experience on the job.

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Major Determinants

• Changes in capital structure Investment in
  productive investment such as machinery and
  equipment yields immediate output as compared to
  infrastructure, plant and buildings which have
  longer lag time. Hence, composition of total
  capital has an impact on the short term or medium
  term growth of TFP. User cost approach were used
  to analyse for the changes of efficiency of
  capital composition.

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Major Determinants

• Economic Restructuring Productivity growth of
  sector depends on the maturity and resource
  availability ( both capital and labour ). As
  workers move from lower productivity sector to
  higher productivity sector, the overall
  productivity of the country will improve. We see
  the effects of shifts of employment and capital
  movement from sector to sector which affects
  aggregate TFPG.

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Major Determinants

• Demand intensity This affect TFPG through
  economies of scale that come with the growth in
  domestic and international markets.
  Business/cyclical fluctuation affects capacity
  utilisation rates that also affect TFPG in short
  term. High fluctuation indicates increased
  capacity due to high demand for output. A
  recession may result in underutilisation.
  Therefore, we have to discount for this
  fluctuation effect to get the true TFPG.

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facilitates restructuring
Interdependence Among TFP
Determinants
facilitates technical progress
facilitates restructuring
Education Training
Economic Restructuring
necessitates continuous skills upgrading
increases investments in mach. equipment

facilitates
restructuring
facilitates technical progress
necessitates continuous skills upgrading
necessitates appropriate invt. in mach. equip.
Technical Progress
Capital Structure
facilitates technical progress
accelerate technical progress
sustain high demand
accelerates restructuring
Demand Intensity
sustain high demand
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THANK YOU