1

Department of Economics

Uppsala University

Master Thesis, D-level

Author: Mahmoud Rezagholi

Supervisor: Per Johansson

Autumn semester 2006

The Effects of Technological Change

on Productivity and Factor Demand

in U.S. Apparel Industry 1958-1996

- An Econometric Analysis

2

Acknowledgement

I would like to especial thanks to my supervisor Per Johansson for worthy comments, and

Apostolos Bantekas for a great useful guidance in econometrics and production theory.

Abstract

In this dissertation I study substantially the effects of disembodied technical change on the

total factor productivity and inputs demand in U.S. Apparel industry during 1958-1996. A

time series input-output data set over the sector employs to estimate an error corrected model

of a four-factor transcendental logarithmic cost function. The empirical results indicate

technical impact on the total factor productivity at the rate of 9% on average. Technical

progress has in addition a biased effect on factor augmenting in the sector.

Keywords: technological progress, total factor productivity, technical bias effect, factor

effectiveness, transcendental logarithmic cost function, input demand function.

Autoregressive process, and Likelihood Ratio Statistic Test.

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CONTENTS

1. Introduction ....................................................................................................................................................... 1

2. Theories, Definitions and Measuring of Technological Change.................................................................... 3

2.1 Embodied and Disembodied technological change................................................................................... 3

2.2 measurement of technical change .............................................................................................................. 4

2.3 Separation problem with exogenous disembodied technological effect .................................................. 5

3. Earlier Empirical Works .................................................................................................................................. 8

4. Development of Factor Price and Factor Intensity in U.S. Apparel Industry 1958-1996 ........................... 9

5. Econometric Modelling................................................................................................................................... 11

5.1 The Transcendental Logarithmic Cost Function ................................................................................... 11

5.2 Derivation of Estimate Formulas and rules to interpret........................................................................ 13

5.3 Adjustment of the econometric model and the choice of estimation method ....................................... 17

5.4 The effect of Auto correlation and the first-order autoregressive stochastic process ......................... 18

5.5 Statistic Test of Restricted and Unrestricted Models............................................................................. 20

6. Estimations and Empirical Results................................................................................................................ 23

6.1 the estimated parameters.......................................................................................................................... 24

6.2 The Elasticities of Substitution................................................................................................................. 25

6.3 Returns to Scale......................................................................................................................................... 26

6.4 The Elasticity of Output ........................................................................................................................... 27

6.5 The Technological Effect on Total Cost .................................................................................................. 28

6.6 The Technological Effect on Total Factor Productivity, TFP ............................................................... 29

6.7 Technical Bias and the Technological Effect on Factor Demand.......................................................... 30

About slowdown in productivity growth....................................................................................................... 32

7. Summary and Conclusion .............................................................................................................................. 34

Bibliography ........................................................................................................................................................ 34

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1. Introduction

We know that the level of output changes over time, but we have experienced that even output

per man-hour varies too over time. Why? Changes in the level of domestic product are due to

either growth in inputs as labour forces or improvement in the factor’s effectiveness. In the

absence of any technological change, all changes in the level of output would bias depend on

changes in the quantities of production factors. Long run economic growth is associated with

technological progress in the both neo-classical growth models, which treated technological

change as exogenous, and even in the endogenous growth models 1.

What is technology? The production sector is presumed to supply two forms of goods:

“conventional” goods as capital goods and consumer goods, and besides goods in the form of

“ideas” and “inventions” in order to increase the level of output. 2. The fundamental unit of

technology is the technique (set of instructions) or production methods that factor inputs to the

production process are transformed into output. Technology in form of “idea” or “technique”

is associated with a fixed cost (research cost), increasing returns to scale and imperfect

competition (market inefficiency). Market efficiency requires that price of output to be equal

to marginal cost. But the firms don’t want sets price equal to marginal cost when average cost

due to existence of a fixed cost is greater than marginal cost. Technological categories as

public goods (non-rival and mostly non-excludable) can also result to increasing returns to

scale and imperfect competition. 3

According to Mokyr (2005), technology has developed faster and more geographically

dispersed after the Industrial Revolution than had been experienced by any economy before. 4.

During the last decades we have experienced that the technological growth has accelerated

based on rapid development on science as electronic, communications, automation technique,

chemistry and so on. Which factor is lied behind this accelerated technological progress? The

answer is that the technology is knowledge, and knowledge naturally is “sustainable” 5, and

“mostly cumulative and evolutionary” 6. In this study, I will, in addition to estimate technical

1See Mokyr (2005) ”long term economic growth and the history of technology” p. 4

2 See Gomulka (1990) ”the theory of technological change and economic growth” p. 3

3 See Jones (2002) ”introduction to economic growth” p. 83-86.

4 See Mokyr p.58

5 Mokyr, p.58

6 Mokyr, p. 11

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effects, empirically test the hypothesis about accelerated technical growth in The U.S.

Apparel industry during 1958-1996.

Technical change can be viewed as a shift upward in the isoquant map of a production

function, not by increasing quantities of inputs, but by an increase of factor effectiveness. In

the general production function Y = F (Xi, t), where Xi stand for inputs, the “disembodied”

technology of production is given by F (t) and assumed to be independent of capital

accumulation. In the traditional Cobb-Douglas production function Y = Ka

(AL)1-a

, A is an

index of technology. New advanced technologies allow an efficient combining of input,

giving us more or better output. Technological evolutionary trend is according to Mokyr the

determinant force behind ”phase transition” from a slow-growth to a rapid-growth steady

state. 7

As I pointed earlier there are two well-known growth models: the neo-classical (Solow)

model and the endogenous model, which both define and discuss the technology evolution

and its effect on economic growth. According to neo-classical growth model, technology is

treated as an exogenously given and cost free factor, which its evolution determines by an

exogenously law. As a contrast opinion the endogenous growth model considers technology

as a result of investment in the research and development (R&D) sector, and market forces

guide its development. Both models suffer of some shortages. A cost free and exogenous

technology is the lack of the neo-classical (Solow) growth model. The endogenous model

suffers on the contrary of endogeneity and omitted variables. With these concepts I mean that

it is unclear which factors, as explanatory variables, determine the development of technology

as a dependent variable. For example if investment in R&D sector determine development of

technology, we observe in the real world that technological growth also determine the level of

investment in the sector. In addition there are always both economical and non-economical

factors which are omitted in endogenous growth models. I have treated technology as

exogenous, consistently with the neo-classical approach, to empirically analyse the effects of

technological progress; i.e. time evolution represents technological progress in my study.

The purpose of this article is to empirically investigate effects of technological progress on

Total Factor Productivity (TFP), on total cost, and on factor demand in U.S. Apparel industry

7 See Mokyr (2005) p. 33-35

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from 1958 to 1996. The input-output data materials used for this study are a time series data

respecting U.S. Apparel industry over the time interval 1958 to 1996, developed by professor

Dale W. Jorgenson (2000) from Harvard University. The aggregate data materials that is

called KLEM-data set, contains information on the value and the price of four input (Capital,

Labour, Energy and non-energy intermediate Material) and the value and price of output. All

prices in the KLEM-data set are in real prices. It does mean that there is no trend in the

development of input prices due to inflation effect. All prices are normalized to unity in 1992.

I have applied these data materials to a four-factor transcendental logarithmic (translog) cost

function. My chosen method in this empirical study is to estimate parameters of a translog

cost function in an equation system by using a three stage least square (3SLS) estimator.

2. Theories, Definitions and Measuring of Technological Change

2.1 Embodied and Disembodied technological change

Technical progress is embodied if it is a result of new equipment or new skills, and is called

disembodied if output increase as a result of improvement in productivity of old equipment

(and existing skills) when quantity of inputs remain unchanged. Characteristic of disembodied

technological change is thus factor augmentation. I begin with the introduction of three well-

known definitions of disembodied technological change:

Exogenous technology can enter in a capital-labour production function in three possible

ways:

Y = A* F (K, L) [Hicks neutral technology] (2.1)

Y = F (A*K, L) [Solow neutral technology or “Capital augmenting”] (2.2)

Y = F (K, A*L) [Harrod neutral technology or “Labour augmenting”] (2.3)

Where A stand for effectiveness, and Y, K, and L represent output, capital and labour

respectively.

There are thus three well-known definitions of bias in technological change. In order to

distinction between labour- and capital effectiveness, I rewrite the usual neo-classical

production function including disembodied technological change as follows:

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Y = F (K, L, t) = G {(1+bt) K, (1+at) L} (2.4)

Where t denotes time that indicate the level of technology, bt and at stand for capital- and

labour effectiveness respectively. If bt = 0 and at > 0, technological change is purely labour

augmenting (Harrod neutral). If at = 0 and bt > 0, technological change is contrary purely

capital augmenting (Solow neutral). The technological change is Hicks neutral if at = bt = 0.

Harrod-neutral assume a constant K/Y ratio, Solow-neutral suppose a constant L/Y, and in

Hicks neutrality K/L ratio has to be constant.

Induced technical change establishes a functional relationship between the rate of labour

augmenting at and capital augmenting bt, that is called invention possibility frontier. The slope

is negative, and it does mean that an increase in the rate of capital augmenting involve

automatically a decline in the rate of labour augmenting, and vice versa. Factor augmenting is

restricted by the invention possibility frontier, and the frontier is stationary (don’t shift over

time) 8. Induced technical change is of disembodied type.

According to embodied technological change, new and old machines (like new and old skills)

are affected by technical progress at different rates. In spite of theoretical accuracy, empirical

analysis of such models can convey difficulties in identifying embodied from disembodied

technical progress. 9 However, long run equilibrium rates of growth in models with embodied

technical change is identical with models based on disembodied technological change. 10

2.2 measurement of technical change

The traditional method of measuring technological change derived from the Cobb-Douglas

production function Y = t Kα

Lβ, is called the Solow residual and is introduced as follows:

∆t ∆Y ∆K ∆L = - α + β

t Y K L

(2.5)

8 See Burmeister and Dobell (1993) in ”mathematical theories of economic growth” p. 89

9 Burmeister and Dobell (1993), p. 90

10 Burmeister and Dobell (1993), p. 93

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Where α and β are capital- and labour income share respectively. Equation (2.5) is usually

used in estimation of the rate of technological progress. The capital and labour income share

is defined as α = rK/PY and β = wL/PY, where P, r and w are stand for the prices of output,

capital and labour respectively. The relative factor income share can be derived from above

formulas as α/β = rK/wL ratio. The technological growth index can also be defined as a

percentage change in relative factor income shares over time as follows:

( )( ) ( )wL wL ln

rK rKrKI = = wL t t

∂ ∂⋅

∂ ∂(2.6)

The formula gives us the following outcomes in three assumptions regarding those three

mentioned definitions:

1) According to Hicks definition, the capital-labour ratio is assumed be constant. In this case

the technological change is Hicks labour saving, Hicks neutral, and Hicks capital saving,

if I < 0 , I = 0 and I > 0 , respectively.

2) If the capital-output ratio remained unchanged the technological change is Harrod labour

saving, Harrod neutral, and Harrod capital saving if I < 0 , I = 0 and I > 0 , resp.

3) The technological change is Solow labour saving, Solow neutral, and Solow capital saving

whether respectively I < 0 , I = 0 and I > 0 under the assumption that the labour-output

ratio is constant.

2.3 Separation problem with exogenous disembodied technological effect

A change in an input-output ratio is partly a response to a relative change in factor prices, and

partly a response to an introduction of a new technology. The main problem in studies of

technological change is to distinguish and to separate these two effects on factor ratio or

factor intensity. These two effects are called substitution effect and technological bias effect

respectively. The first concept measures by elasticity of substitution (σ) and the last concept

measures by Hicksian or Harrodian definitions. Separation of these two effects is difficult due

to insufficient empirical evidence.

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Hicks measure the substitution effect and technological bias effect in term of changes on

factor ratio. Hicks measuring of the effects can in its capital-labour functional form introduce

as the following formulas:

( )( )

KL

L

K

K lnL

σ = P ln

P

∂

∂(2.7)

( )KL

K lnL

B = t

∂

∂(2.8)

The Hicksian elasticity of substitution (2.7) measures the effect of a relative change in the

factor price on the corresponding factor ratio. The Hicksian bias in the technological change

(2.8) measure the effect of technological change on a factor ratio under assumptions such as

fixed output and fixed corresponding factor price ratio. According to Hicks definition the

technological change has been biased in the direction of saving inputs. We say that

technological progress is Hicks-neutral, Hicks capital saving (labour using), or Hicks labour

saving (capital using) depending on whether BKL = 0, BKL < 0, or BKL > 0 respectively, and if

factor ratio K/L remain unchanged.

Harrod and Solow measure the technological bias effect in term of changes on input-output

ratio under assumption that output and the price of factor j are fixed. Harrod- and Solow

measurement of technical change can in its combination form be introduced as the following

formula:

( )j

i

X lnY

B = t

∂

∂; Where j = K, L (2.9)

Xj for Harrodian bias is the capital input, and for Solow definition of technical bias is the

labour input. We define technological progress as Harrod (Solow)-neutral, Harrod (Solow)

factor saving or Harrod (Solow) factor using, depending on whether Bi = 0, Bi < 0, or Bi > 0

respectively, and if factor/output ratio (factor intensity) is constant.

Hicks measure the effect of technological bias for each pair of factors, but we have only one

measure of this effect for each factor with Harrod- and Solow definition. If we have Capital,

Labour and Energy in our production function, technological change may be energy-saving

10

relative to capital (given PE/PK, the ratio E/K would decline over time) but energy-using

relative to labour (given PE/PL, the ratio E/L would be increasing over time). 11

The difficulties in measuring technical effect are even more complicated since the impact of

technological progress must be distinguished from scale of economies too. The optimal factor

demand and input intensity may change in response not only to technological change and

corresponding factor prices but also to the scale of output. Scale of economies is the third

force which affect factor ratio Xi / Xj and factor intensity Xi / Y via changing the total cost.

The effect of technical progress can be overestimated if it does not separate from substitution

effect and the impact of scale economies. These three different effects on Xi / Xj and Xi / Y

will be separated in this empirical analysis in order to avoid overestimation of technological

effect.

There are two theories about estimation of exogenous disembodied technological change:

Diamond-McFadden impossibility theorem, and simultaneous theorem. 12

According to the

first theorem it is impossible to estimate effects of technological change and elasticities of

substitution at the same time. Estimating process must perform in two steps. First the

elasticities of substitution estimates from a cost function under assumption that constant rate

of technological progress prevail. Second step is using these elasticities to estimate the effect

of technical change. 13

According to the second theorem, the substitution effect, scale effect,

and the technical effect can be estimated simultaneously. Sato (1982) showed that technical

effect could be distinguished from the impact of scale economies by choosing a non-

homothetic model to estimate 14

. Simultaneous estimation of substitution effect, scale effect,

and non-neutral technical effect, in an arbitrary cost function, can separate these three effects.

Berndt and Khaled (1979), Stevenson (1980), Jorgenson (1986), Försund and Hjalmarsson

(1979) and W. H. Greene (1983) use simultaneous estimation approach. In this study I have

applied the simultaneous estimation and cost function approach in order to distinguish and

separate the technical effect from the impacts of substitution and scale economies on the

11

See Gomulka, p. 12612

See Woodward and Greene (1983) in ”developments in econometric analyses of productivity” edited by A.

Dogramaci, chapter 5-6, p. 101-102, and 121-122.

13 Woodward (1983), p. 102.

14 Woodward, p. 101.

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optimal factor ratio. The advantages with cost function approach will be discussed later in

chapter 5.

3. Earlier Empirical Works

Kavanaugh and Ashton (1995) have estimated the technological effect on fossil fuel-fired

electricity production in U.S. during period 1979-1989. Their empirical research is based on

production function approach. They find technical change to be capital augmenting at the rate

of 1,8% per year. The composite rate of technical change is found to be 0,7% per year.

By estimation of a translog production function over Indonesian manufacturing under 1993-

2000, Margono and Sharma (2004) have found that the average technological growth was

55,87% and average technical efficiency was 3,22%. For the food and textile sector the total

factor productivity was growing during 1991-1995 by the rate of 5,7% and 3,6% respectively,

while chemical and metal product had a growth rate about –0,3% and 6,9% respectively.

Woodward (1983) employed cost function approach to find out factor augmenting due to

technical change in U.S. manufacturing during 1948-1978. The result is that labour

augmenting and capital augmenting, of course with different rates, slows down from 2,89% to

0,91% and from 0,68% to 0,31%, respectively.

Greene (1983) estimated a three-factor translog cost function based upon time series of cross

section data set over 114 firms in U.S. electric power industry observed during 5 years 1955,

1960, 1965, 1970, and 1975. The empirical result shows that total cost of production reduces

in average by a rate of 2,5% per year due to technological change. Technical change has been

fuel- and labour saving but capital using.

Jin and Jorgenson (2005) have studied empirically the technical bias effect on production

factors in 35 sectors of U.S. economy during 1958-2004. The econometric model is a price

function in translog functional form, giving the price of output as a function of the input

prices and the level of technology. Technical bias is found out to be capital using for

Government Enterprises, Coal Mining and Communications. The biases are capital saving for

Trade, Electric Utilities, and Transportation Equipment. The technical change is labour saving

for Motor Vehicles and Coal Mining, while labour using for Metal Mining and Construction.

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The technical bias for energy is large and energy using for Petroleum Refining, but energy

saving for Petroleum and gas Mining. The technical bias is material saving for Government

enterprises, Petroleum Refining, metal Mining, and motor vehicles.

4. Development of Factor Price and Factor Intensity in U.S. Apparel

Industry 1958-1996

The prices of inputs are assumed to be exogenous given in the cost function approach. Factor-

output ratios (factor intensities) are also the basic economic issues in analysis of technical

effect on productivity and factor augmenting. Before introduction of the econometric model

of technical change, it is necessary to give an economic view of U.S. Apparel industry during

1958 to 1996. In order to replay this inquiry I want to show graphically the developments in

factor prices and input intensities in the sector as follows:

Diagram (4.1)

Development of Factor Prices in U.S. Apparel Industry

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1958 1965 1972 1979 1986 1993

Year

Pri

ce

In

de

x Capital Price

Labour Price

Energy Price

Material Price

13

Diagram (4.2)

Note that all prices are normalized in year 1992. The first diagram (4.1) gives us a foundation

to study the change rate of input prices in the sector. All prices are increasing on the whole

during the time interval, but not at the same rate. The slope of capital price curve is more

variable in direction than the slopes for other factor prices during the period, though the trend

is upward on the whole. Further we can see that the rates of change in input prices are greater

from 1974 to 1990. This can be partly due to increase in the energy price that has the greatest

growth rate during 1974-1990.

Diagram (4.2) shows the development in factor intensities (factor-output ratios) in the sector.

The direction of the movements in factor intensities is different. The capital intensity slope is

upward (increasing), while the slopes of material intensity and labour intensity are downward

(decreasing). Concerning energy intensity the trend is upward until 1972, and downward after

that. Development of factor intensities can be due to three forces: Technical progress, Output

elasticity, and price substitution effect. The substantial question is that in witch direction these

forces affect the factor intensities.

Development of Factor Intensities in U.S. Apparel

Industry

0

0,2

0,4

0,6

0,8

1

1,2

1958 1965 1972 1979 1986 1993

Year

In

ten

sit

y In

dex

Capital Intensity

Labour Intensity

Energy Intensity

Material Intensity

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5. Econometric Modelling

5.1 The Transcendental Logarithmic Cost Function

I suppose that the production technology in the U.S. Apparel industry, represented by a

monotonic, concave, continuous and twice-differentiable production function as:

Y = f (K, L, E, M, t) (5.1)

Where Y, K, L, E, M stand for output, capital, labour, energy and material respectively. The

technological progress is represented by t. The production function above shows the

maximum output witch can be produced in the sector from the input combination. The dual

cost function can be derived from (5.1) by using the duality principle and by assuming that

firms in the apparel industry minimise the cost of production:

C = g (PK, PL, PE, PM, Y, t) (5.2)

Where C stand for the total cost, and PK, PL, PE, PM for the price of capital, labour, energy and

material respectively. I assume that the sector’s cost function apart from envelope property

has certainly following properties: cost function is non-decreasing in both output and factor

prices. The cost function is linear homogenous, continuous and concave in the price of inputs.

In this study I have chosen the cost function approach (5.2), rather than the production

function (5.1) for three reasons. The first is that the costs of production input are always

exogenously given. Second reason is that cost minimizing with cost function approach is a

weaker assumption than output maximising with production function approach. The final

reason is that both elasticities of substitution and technological effect on the total cost and

factor demand can be measured easily with estimated parameters of a cost function.

The difficult decision now is the choice of functional form for the cost function (5.2). The

choice of functional form (specification) is very important because the empirical results can

vary depending on this choice. Cobb-Douglas specification constrains the elasticity of

substitution between any pair of inputs to be equal to one. It also constrains the technological

change to be Hicks-neutral, being therefore unsuitable for my aims. Cobb-Douglas cost

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function can not be an appropriate specification in empirical studies regarding specially

estimation of technological effects.

The transcendental logarithmic (translog) cost function is a second-order Taylor’s series

approximation of quantities and factor prices in logarithmic form to an arbitrary cost function.

Econometricians in production with complicated technology usually apply the transcendental

logarithmic cost function. The general (non-homothetic) functional form of translog cost

function can be formulated as:

ln C = α0 + 1

n

∑ αi · ln Pi + ½1

n

∑1

n

∑ αij · ln Pi · ln Pj + βY · ln Y + ½ βYY · (ln Y)2 +

1

n

∑ βiY

· ln Pi · ln Y + γt · t + ½ γtt· t2 +

1

n

∑ γit · t · ln Pi + γYt · t · ln Y (5.3)

Where i,j = K, L, E, M. A well-behaved cost function requires to be symmetric of the second-

order terms, and linear homogenous in input prices. These requirements can be formulated as

follows:

αij = αji (symmetry condition),

1

n

∑αi = 1, 1

n

∑ αij =1

n

∑ αji = 1

n

∑ βiY = 1

n

∑ γit = 0 (homogeneous condition) (5.4)

For an efficient estimation of the translog cost function I must obtain the optimal factor

demand functions by employing the envelope theorem and Shepherd’s Lemma in order to

build a system of equation. Cost minimizing input demand functions or cost share equations

can be obtained by differentiating logarithmically the general translog cost function (5.3) with

respect to factor prices:

i

lnC

lnP

∂

∂ =

i

C

P

∂

∂· iP

C =

iiPX

C ⇒ Si = αi +

1

n

∑ αij · ln Pj + βiY · ln Y + γit · t (5.5)

Where Xi is the optimal input and Si is the optimal factor demand or share of production cost,

and sum of the shares is always equal with unity, i.e. 1

n

∑Si = 1 (5.6)

16

There are no predetermined restrictions as constant elasticity of substitution (CES), constant

return to scale (CRS), or various neutrality of technical progress with this specification. But

all possible restrictions may be tested statistically. In additional, the translog cost function has

a flexible functional property so that with imposing different assumptions it can transform to

almost any specification. The translog cost function gives me the possibility to estimate the

effect of technological change on factor demand and factor effectiveness (technical bias).

Estimating of the effects of technological change by translog cost function has another

advantage in my study. The hypothesis of accelerated technological growth in OECD-

countries after the Second World War 15

can be tested empirically by the translog functional

form of cost function. Transcendental logarithmic cost function gives me thus the possibility

to estimate the rate of acceleration (deceleration) in technical progress in U.S. Apparel

industry during 1958-1996.

5.2 Derivation of Estimate Formulas and rules to interpret

As was discussed in section 2.3 the effects on factor ratio or factor intensity can be due to a

relative change in the corresponding factor price. This substitution effect can be measured by

Allen-Uzawa partial elasticities of substitution as follows:

2i j ij

ij

i j i j

C ( C / P P )σ 1+

( / P ) ( C / P ) S SC

α⋅ ∂ ∂ ∂= =

∂ ∂ ⋅ ∂ ∂(5.7)

Where αij is the estimated parameter from translog cost function (5.3), and Si , Sj is the optimal

cost share (5.5). The rules of thumb to interpret of Allen-Uzawa elasticity of substitution is as

follows: if σij is positive, the correspondent inputs Xi and Xj are said to be price-substitutes,

while a negative value of σij, claims price-complements between the inputs. The degree of

weakness/strength of substitutability or complementarity between production factors

determine as the following rules: σij > 0,5 indicate strong substitutability between

correspondent inputs Xi and Xj , while 0 < σij < 0,5 indicate a weak substitutability between

15

See Gomulka p. 155

17

the factors Xi and Xj . The condition -0,5 < σij < 0,5 exhibits unclear relation between inputs

Xi and Xj , and σij < -0,5 indicate a legible complementarity between the correspondent inputs.

Notice that the partial elasticities of substitution are symmetrical, i.e. σij = σji. The standard

error (SE) of σij can be calculated by the below formula:

ijij

i j

SE ( )SE (σ ) =

S S

α(5.8)

Economies of scale is defined from the cost function (5.2) as the ratio of marginal cost to

average cost according to the following formula;

C / Y lnCε = =

C / Y lnY

∂ ∂ ∂

∂(5,9)

Values of ε less than one mean scale economies, and values greater than one imply

diseconomies. In the case of ε = 1 we have constant scale economies. According to the above

formula, economies of scale from the translog cost function (5.3) is equally:

ε = βY + βYY· lnY + 1

n

∑βiY· lnPi + γYt ·t (5.10)

In the case of constant scale economies the average cost reaches its minimum, and in this

case, the optimal output can be obtained. Solving (5.10) for lnY* (the optimal output in

logarithm) and differentiating it with respect to time gives:

n

Y iY i Yt

* i=1

YY

1- β - β ln P - γ t

ln Y = β

⋅ ⋅∑⇒

*Yt

YY

lnY γ = -

t γ

∂

∂(5.11)

This magnitude is called scale efficiency and measures the technical effect on the optimal

output in logarithm. Thus efficient scale grows by a rate of - γYt / βYY.

The returns to scale µ can be defined as follows:

18

C / Y ln Y ln Cµ 1/

C / Y ln C ln Y

∂ ∂ = = =

∂ ∂ ∂ ∂ (5.12)

In terms of the parameters of the transcendental logarithmic cost function (5.3) the returns to

scale are given by below formula:

µ = (βY + βYY· lnY + 1

n

∑βiY· lnPi + γYt ·t)-1

(5.13)

If the value of µ is greater than one, then the underlying production technology display

increasing returns to scale (IRS). If the value of µ is on the contrary less than one, decreasing

returns to scale (DRS) is prevailed, and in the case of µ is equal to unity the underlying

production technology exhibit constant returns to scale (CRS).

Changes in the level of output affect on the input demand and this effect can be calculated as:

2iY

iY

i i i

Y C βe = = ε +

X P Y S

∂⋅∂ ∂

(5.14)

eiY > 1 indicate decreasing returns to input i, while eiY < 1 suggest increasing return to input i.

If eiY = 1, we have constant returns to factor i, and if eiY < 0 we say that input i is an inferior

production factor.

Technological progress has two important indicators. The first indicator is the primal total

factor productivity or the dual cost diminution, and the other indicator is the technical bias

effect on input saving. The primal total factor productivity as an index of technological

change is obtained by differentiating the primal production function (5.1) with respect to time,

i.e. θ = ∂ lnY/ ∂t. The rate of cost diminution due to technological progress may be obtained

by partial derivation of the translog cost function (5.3) with respect to time:

λ = - (∂ lnC / ∂t) = - (γt + γtt· t + 1

n

∑ γit · ln Pi + γYt · ln Y) (5.15)

19

The rate of primal total factor productivity growth θ is related to dual cost diminution λ

through economies of scale ε (or the returns to scale µ) as follows:

θ = λ / ε = λ · µ (5.16)

λ = - (∂ lnC / ∂t) does not measure the net technological effect. The effect of scale economies

is included in this measurement method. It must thus be divided with ε in order to find out the

net effect of technical change. If the underlying production technology characteristics by

constant return to scale; i.e. ε = µ = 1, this case leads to θ = λ.

The bias of technical change (factor augmenting) is obtained by differentiating cost share

equations with respect to time:

∂ Si / ∂t = γit (5.17)

The estimated parameters γit reflect the technical bias. The rules to interpret these estimated

parameters are as follows: γit greater than zero suggest that technical change be input i-using,

while γit less than zero indicate contrary that technical progress has a saving effect (factor

augmenting) on input i. If γit is equal to zero technical change is of course input i-neutral.

The effect of technical progress on factor demand can be calculate based on index of technical

bias as:

2it

it

i i i

1 C γe = = - λ

X P t S

∂⋅∂ ∂

(5.18)

The estimated value of technological effect on input demand interprets as follows: if eit is

positive, the entering of new technology leads to increasing in demand for input i. If eit is in

contrast negative, this mean that the entering of new technology results in decreasing of

demand for input i due to technical effect on the factor augmenting.

The second order differentiation of the translog cost function (5.3) with respect to time give

us parameter γtt that indicate the acceleration or deceleration of technological progress. If γtt >

20

0, the technical progress is accelerated, while in the condition γtt < 0, the technology is

growing at a decelerated rate.

5.3 Adjustment of the econometric model and the choice of estimation method

As I have pointed before in section 5.1 an efficient estimation requires derivation of cost

minimizing input demand equations (5.5) from the translog cost function (5.3) in order to

build a system of equation. 16

By applying linear homogeneity restrictions (5.4) and using linear independent principal (5.6)

I can eliminate the cost share equation for material input and reduce the number of parameters

to estimate from 28 to 21. The parameters to material cost share equation estimates indirectly

by applying the homogeneity restrictions (5.4). In this way I minimise the probability of

multicollinearity problem, witch usually appear in regression equations with a great number

of explanatory variables. The system of regression equations prepared to estimate is

introduced as follows:

LnM

C

P

= α0 + αK · ln K

M

P

P

+ αL · ln L

M

P

P

+ αE · ln E

M

P

P

+ ½ αKK · ln

2

K

M

P

P

+ ½ αLL ·

ln

2

L

M

P

P

+ ½ αEE · ln

2

E

M

P

P

+αKL · ln K

M

P

P

· ln L

M

P

P

+ αKE · ln K

M

P

P

· ln E

M

P

P

+ αLE ·

ln L

M

P

P

· ln E

M

P

P

+ βY · lnY + ½ βYY · (lnY)2 + βKY · ln K

M

P

P

· lnY + βLY · ln L

M

P

P

· lnY +

βEY · ln E

M

P

P

· lnY + γt · t + ½ γtt · t2 + γKt · t · ln

K

M

P

P

+ γLt · t · lnL

M

P

P

+ γEt · t · lnE

M

P

P

+

γYt · t · lnY + εt (5.19)

Where εt is the error term. If we now differentiate the above equation with respect to the

price ratio i

M

P

P

logarithmically the following value share equations for Capital, Labour,

and Energy yields:

16

See Berndt (1996), ”the practice of econometrics” p. 470

21

SK = αK + αKK · ln K

M

P

P

+ αKL · ln L

M

P

P

+ αKE · lnE

M

P

P

+ βKY · lnY + γKt · t + εKt

SL = αL + αKL · ln K

M

P

P

+ αLL · ln L

M

P

P

+ αLE · ln E

M

P

P

+ βLY · lnY + γLt · t + εLt

SE = αE + αKE · ln K

M

P

P

+ αLE · ln L

M

P

P

+ αEE · ln E

M

P

P

+ βEY · lnY + γEt · t + εEt

(5.20)

Where εKt, εLt, and εEt, stand for error terms. The above system of equations can now verify

that the symmetry- and homogeneity conditions (5.4) are satisfied.

Cost share equations (5.19) don’t include parameters βY, βYY, γYt, and for this lack,

estimation of scale economies is not obtained by estimating (5.20) alone. To estimate scale

economies and so return to scale, the translog cost function (5.19) must be added to the

system of equations.

The equation (5.19) and (5.20) will be estimated simultaneously for reason of efficiency.

Separate estimation may lead to different estimated value for the same parameter.

Note that if there are n factor share equations, only n-1 of them are linearly independent with

symmetry –and homogeneity restrictions imposed. The choice of witch n-1 share equations

is directly estimated may affect the parameter estimates depending on witch estimation

procedure is employed. The Three-Stage Least Square estimator (3SLS) has a property so

that it is indifferent to the choice of witch n-1 equations is directly estimated. 17

5.4 The effect of Auto correlation and the first-order autoregressive stochastic process

A basic assumption in the econometric literatures is that the error terms are distributed

normally and independent of each other. Time series regression analyses usually suffer of

autocorrelation (serial correlation). In the regression based upon time series data, one must be

sure that the disturbance term relating to any observation is not influenced by the disturbance

term of any other observation. The disturbances must also be independently distributed from

17

Berndt (1996), p. 471-474

22

each other. It does mean that the covariance between any pair of error terms must be zero. If

this covariance is non-zero, then the disturbances are said to be autocorrelated. The presence

of autocorrelation in the error terms leads to inefficient estimation and unreal estimated

coefficients. Thus, no empirical analysis should be based on the results of an uncorrected

regression. Autocorrelation as the dependent disturbances of regression can be viewed as

follows:

Yt = α + βXt + εt (1) ; where εt = ρεt-1 + ut (2)

The error εt is depended on the previous error εt-1. Now the question is how we can eliminate

the effect of autocorrelation. Gujarati (2003) has explained four standard methods for

discovery of autocorrelation in regression, as Graphical Method, The Runs Test, Durbin-

Watson test, and the Breusch-Godfrey (BG) test. 18

. The well-known Durbin-Watson (d) test is

defined by d = ∑ (et-et-1)2 / ∑et

2. Where et and et-1 (residuals) are the differences between the

actual and estimated Y values. There is no positive autocorrelation if 0 < d < dL, and no

negative autocorrelation exist whether 4-dL < d < 4. If condition dU < d < 4-dU is fulfilled, then

there is no existence of autocorrelation (positive or negative) in the regression. Usually the

value of Durbin-Watson (d) calculates by the econometrically software. But for a system of

equations, this value for each individual equation can not determine whether there is

autocorrelation in the regression. A practical method is to first derive the corrected

(autoregressive) model from autocorrelated disturbances, and then by Likelihood Ratio

Statistic test determine which of these two models is accepted. If the autoregressive model

will be accepted, it exhibit that autocorrelation existed in the regression. Now I experience the

first-order autoregressive procedure (AR1) in a simple regression. The last period regression

equation of equation (1) can be written as:

Yt-1 = α + βXt-1 + et-1 (3)

Both sides of equation (3) multiplies with the autocorrelation coefficient ρ, giving us:

ρYt-1 = αρ + βρXt-1 + ρet-1 (4)

18

See Gujarati (2003), “basic of econometrics”, p. 462-474

23

Equation (4) subtracts from equation (1) in order to arrive at independently distributed

residuals. This mathematical operation lead us to the below equation:

Yt-ρYt-1 = α(1-ρ) + β(Xt-ρXt-1) + ut (5)

Equation (5) represent regression equation (1) corrected for serial autocorrelation of the first

order as called the first-order autoregressive stochastic process.

The translog cost function (5.19) and input demand equation (5.20) exact like equation (5)

will be transformed to the autoregressive model in order to eliminate the unwilling effect of

autocorrelated disturbances on my empirical result. Note that the symmetry- and homogeneity

condition (5.4) require that the error terms from cost share equations must sum to zero at each

observation. Condition 1

n

∑εit = 0 must also be satisfied.

5.5 Statistic Test of Restricted and Unrestricted Models

First I would like to perform a Likelihood Ratio (LR) statistic test whether the autoregressive

model is rejected or not. The value of log-likelihood estimates first for both restricted and

unrestricted model (here for non corrected autocorrelation regression model and the first-order

autoregressive process), and then these values computes as follows:

Λ = -2 ln (LR / LU) = 2 (LU - LR) (5.21)

Where LR is the log-likelihood value of the restricted model and LU is the log-likelihood value

of the unrestricted specification. Λ is χ 2-distributed with (r) degrees of freedom equal to the

number of imposed restrictions. If Λ is greater than the critical value, then the unrestricted

model can not reject. Here there is one restriction (the autocorrelation coefficient ρ) and the

critical value for one degree of freedom is 3.842. The estimated values of log-likelihood for

non-corrected specification and autoregressive model are 618.074 and 648.555 respectively.

The calculation shows me that I can not reject the unrestricted model as the first-order

autoregressive specification.

24

In section 5.1 I discussed about the flexibility property of translog cost function that can

reduce to almost any specification with imposing different restrictions. Now I am going to

explain all possible restrictions based on various economic theories- and hypothesis. The

validity of restrictions will be tested by the above mentioned procedure test, LR statistic test. I

can obtain twelve specifications based on different hypothesis.

1. General (non homothetic) Specification

The first model is a general functional form (non-homothetic) of transcendental logarithmic

cost function (5.19). This unrestricted specification can reduce to many constrained models by

imposing different restriction regarding technological progress combined with other economic

theories:

2. Homothetic Specification

Homothetic hypothesis emphasises that the level of output has no effect on demand of inputs.

The general model of translog cost function (5.19) can transform to the homothetic

specification if βiY = 0.

3. Homogeneous Specification

The homogeneity restriction occurs if the underlying production function has the property of a

constant degree in output; i.e. the slopes of the isoquants of a homogeneous production

function are independent of the level of output. This assumption requires that βiY = βYY = γYt

= 0. With imposing of this restriction the degree of homogeneity (the return to scale) is equal

to 1/ βY, and computes simply with estimation formula (5.13).

4. Constant Return to Scale (CRS) Cost Function

The linear homogeneity in output (constant return to scale) occurs if in additional to previous

restrictions, even βY = 1.

5. Hicks Neutral Technical Change Cost Function

A famous economic theory in production technology is the Hicks-neutral technical change. It

does mean that technical change has no effect on factor augmenting and input demand. This

25

assumption requires that all parameters that indicate technical bias in the translog cost

function (5.19) are equal to zero; i.e. γit = 0.

6. Homothetic Hicks Neutral Technical Change Cost Function

A combination of the previous restriction, Hicks neutral technical change, and homothetic

specification (model 2) can be theoretically possible in the Apparel’s cost function if in the

general specification (5.19) condition βiY = γit = 0 is satisfied. This specification does mean

that neither the level of output nor the technical progress has effect on input demand in the

sector.

7. Homogeneous Hicks Neutral Technical Change Cost Function

A composite model of homogeneous specification and Hicks neutral technical change can be

occur if in addition to the previous specification, the condition βYY = γYt = 0 holds.

8. (CRS) Hicks Neutral Technical Change Cost Function

If U.S. Apparel’s translog cost function supposed to be linear homogeneous (constant return

to scale) and Hicks neutral technical change simultaneously, the following condition must be

satisfied: βiY = γit = βYY = γYt = 0, and βY = 1.

9. Non Technological Progress (NTP) of the general functional model

Now I suppose that technological progress has no effect on input-output quantities in the U.S.

Apparel industry. This assumption (NTP) requires that all parameters concerning technology

effects in the translog cost function are equal to zero; i.e. γt = γtt = γit = γYt = 0. Three constrain

specifications: homothetic restriction, homogeneous restriction, and model with constant

return to scale (CRS), can be combined with this assumption, building the following

specifications:

10. Homothetic specification of (NTP)

This specification occurs if the model 2 (homothetic specification) is composite with the

previous restriction (NTP); i.e. βiY = γt = γtt = γit = γYt = 0.

26

11. Homogeneous specification of (NTP)

If the restriction of non-technological progress (NTP) has the property of a constant

homogeneity degree in output, this specification will appear. Conditions βiY = βYY = γt = γtt =

γit = γYt = 0 must be satisfied.

12. CRS specification of (NTP)

I consider here a very strong assumption that U.S. Apparel industry’s cost function has

constant return to scale as property, and simultaneously technical progress has no effect on

quantities of the input-output relation. The previous condition plus βY = 1 must be fulfilled.

6. Estimations and Empirical Results

In the table below we can see that in all cases Λ > χ2 (0.05). Thus all restricted specifications

and their underlying economic theories are rejected by Likelihood Ratio (LR) statistic test.

The autoregressive general (non-homothetic) translog functional form of cost function is not

rejected in U.S. Apparel production by that test procedure.

Table 6.1: LR-test results

LU = 648.555 Λ= 2 (LU – LR) Restrictions χ2 (0.05)

(Model 1)

Model 2 14.196 3 7.815

Model 3 16.562 5 11.071

Model 4 22.754 6 12.592

Model 5 38.768 3 7.815

Model 6 44.400 6 12.592

Model 7 46.986 8 15.507

Model 8 68.614 9 16.919

Model 9 42.030 6 12.592

Model 10 38.498 9 16.919

Model 11 38.036 10 18.307

Model 12 39.884 11 19.675

The empirical results from the estimation of the via LR-test accepted specification will be

presented in this section. Estimated parameters of the equation system (5.19) and (5.20), and

the inferences of calculated economic issues concerning the technological effects on U.S.

Apparel production, presents in the subsections. All tables and graphs are available in its own

subsection. Note that all results and its conclusions regarding technical change are based on

estimated values of the parameters that theirs validity are confirmed by LR test. If the

27

unconstrained specification can not be rejected by LR test, it implies that all parameters in the

equation system (5.19) and (5.20) have a significant effect on the costs of production in the

sector. In this case I don’t worry much about some insignificant estimated parameters by

3SLS at the usual level of significance. Finally I must emphazise that my conclusion are

based on approximately estimation of parameters. Neither a perfect model nor a perfect

estimation method exists yet.

6.1 the estimated parameters

All estimated parameters of Model 1, are presents in the table below:

Table 6.2: estimated parameters of U.S. Apparel industry 1958-1996.

Parameters Estimate Parameters Estimate

(Standard Error) (Standard Error)

α0 42.2777 αEM -0.005

(40.788) (0.0041)

αK 0.5758* βY -5.905

(0.1150) (7.022)

αL 1.0596** βYY 0.5921

(0.4973) (0.6137)

αE 0.0652 βKY -0.0448*

(0.0448) (0.0101)

αM -0.7006 βLY -0.076***

(0.5343) (0.0445)

αKK 0.0494* βEY -0.004

(0.0026) (0.0034)

αLL 0.1699* βMY 0.1248

*

(0.0550) (0.0478)

αEE 0.0093* γt 0.0799

(0.0023) (0.1268)

αMM 0.1897* γtt 0.00179

(0.0625) (0.00169)

αKL -0.0152*** γKt 0.0033

*

(0.0084) (0.0006)

αKE -0.00216* γLt 0.0039

(0.0007) (0.0027)

αKM -0.0321* γEt -0.0004

(0.0092) (0.0004)

αLE -0.0022 γMt -0.0068**

(0.0037) (0.0031)

αLM -0.1526* γYt -0.0122

(0.0580) (0.0098)

ρ* = 0.9746 with standard error 0.012 R

2(for Total Cost) = 0.995

R2 (for Capital Cost) = 0.986 R

2 (for Labour Cost) = 0.888

R2 (for Energy Cost) = 0.953

* Denote different from zero at the 1% level of significance

** Denote different from zero at the 5% level of significance

*** Denote different from zero at the 10% level of significance

28

The generalized R2 measure in the system of equation can be computed as follows:

�2 E ́E

R = 1 - y ́y

(5.21)

Note that the coefficient of determination R2 for individual function in a system of equation

can not value the regression specification. According to Brendt 19

single-equation R2 measures

are not appropriate in an equation system context. Incidentally, the generalized R2

in the

equation system of U.S. Apparel industry cost function (Model 1) is approximately equal to

0.965.

6.2 The Elasticities of Substitution

I have chosen the Allen-Uzawa definition as the measurement method of substitution effect. I

previously discussed that like technological progress, a relative change in input prices affects

the optimal input ratio. Allen-Uzawa (partial) elasticities of substitution between production

factors, and theirs standard error (SE), are estimated and presented for the year 1960, 1970,

1980, 1990 and 1996 in the table below:

Table 6.3: Allen-Uzawa partial elasticities of substitution between the pair of inputs in U.S. Apparel industry

1959-1996.

Year σKL σKE σKM σLE σLM σEM

(SE) (SE) (SE) (SE) (SE) (SE)

1960 -0.500 -12.16*

-0.380 -0.566 0.216 -0.573

(0.834) (4.333) (0.398) (2.671) (0.298) (1.307)

1970 -0.100 -5.326*

-0.038 -0.024 0.199 -0.054

(0.612) (2.083) (0.299) (1.746) (0.304) (0.876)

1980 0.333 -1.658***

0.075 0.550 0.254 0.319

(0.371) (0.875) (0.267) (0.767) (0.284) (0.566)

1990 0.531**

-1.352***

0.334***

0.420 0.216 0.102

(0.261) (0.774) (0.192) (0.989) (0.298) (0.746)

1996 0.437 -2.371**

0.263 0.259 0.227 -0.059

(0.313)

(1.110) (0.213) (1.264) (0.294) (0.880)

* Denote different from zero at the 1% level of significance.

** Denote different from zero at the 5% level of significance.

*** Denote different from zero at the 10% level of significance.

19

Berndt (1996), p. 468

29

The estimate values of Allen-Uzawa substitution elasticities between various pair of inputs

show us an expected legible price complementarity between capital input and energy input

during the selected years. Concerning price substitution possibility between capital and

labour, there is no clear relation between these two inputs under the selected years except

1990 that a weak substitutability between capital and labour exist. No clear price relation

between capital-material, labour-energy, labour-material, and energy-material prevails.

The estimation of various technological effects on the U.S. Apparel production under 1958-

1996 will be presented in separate subsections.

6.3 Returns to Scale

As I showed in the section 5.2 return to scale (µ) is the inversion of scale economies (ε).

Applying the correspondent formulas these mutual related economic issues could be estimated

for the time interval. The estimated values of ε and µ presents in the table below:

Table 6.4: scale economies ε and the return to scale µ in U.S. Apparel industry 1959-1996.

Year ε µ Year ε µ

1959 0.944 1.059 1978 1.001 0.999

1960 0.929 1.076 1979 0.968 1.033

1961 0.925 1.081 1980 0.951 1.051

1962 0.946 1.057 1981 0.931 1.074

1963 0.964 1.037 1982 0.921 1.085

1964 0.978 1.022 1983 0.923 1.083

1965 0.990 1.010 1984 0.921 1.085

1966 0.997 1.003 1985 0.895 1.118

1967 1.012 0.988 1986 0.880 1.136

1968 1.023 0.977 1987 0.923 1.083

1969 1.036 0.966 1988 0.900 1.111

1970 0.997 1.003 1989 0.868 1.152

1971 1.013 0.987 1990 0.842 1.187

1972 1.050 0.952 1991 0.830 1.205

1973 1.063 0.940 1992 0.860 1.162

1974 1.011 0.989 1993 0.868 1.152

1975 0.968 1.033 1994 0.875 1.143

1976 0.983 1.018 1995 0.870 1.149

1977 0.999 1.001 1996 0.840 1.191

Above empirical results indicate a weak scale economies and increasing return to scale in

U.S. Apparel industry for the most of years in the interval. This conclusion means that the

long run average cost of the sector’s production mostly has been above its long run marginal

30

cost. While in the periods 1967-1969 and 1971-1974 decreasing return to scale prevails.

Under the years 1966, 1970, 1977, and 1978 the apparel production characterizes

approximately by constant return to scale. The following diagram shows the movements in

returns to scale graphically:

Diagram (6.1)

The efficient scale in U.S. Apparel industry grows by a proportional rate of - γYt / βYY = 2.1%.

Technical progress has thus affected the optimal output in the sector at a constant rate of

2.1%. This magnitude assumed be unchanged and is valid for the selected interval 1958-1996.

6.4 The Elasticity of Output

Apart from relative factor price and technical progress, a change in the optimal factor ratio

and input demand can be duo to a change in the level of output. The effect of this change on

factor demand in U.S. Apparel for the year 1960, 1970, 1980, 1990, and 1996 is estimated by

formula (5.14), presented in the table below:

Table 6.5: the effect of output on input demand (eiY) in U.S. Apparel 1959-1996.

Year eKY eLY eEY eMY

1960 -0.362 0.668 0.089 1.115

1970 0.049 0.736 0.447 1.188

1980 0.229 0.744 0.648 1.175

1990 0.340 0.632 0.456 1.074

1996 0.258 0.622 0.362 1.061

Development of Returns to Scale in U.S. Apparel

Industry

0,6

0,7

0,8

0,9

1

1,1

1,2

1,3

1958 1965 1972 1979 1986 1993

Year

Retu

rns t

o S

cale

31

From the table above we see that eMY is greater than unity in the selected years. It imply that

U.S. Apparel industry has decreasing return to input material; i.e. one percentage change in

output demand is met by a more than one percent change in using of intermediate material.

eKY , eLY, and eEY are less than unity in the selected years. These outcomes exhibit that the

sector has increasing returns to inputs capital, labour, and energy; i.e. a relative change in

output is met by a smaller relative change in using of capital, labour, and energy. In the year

1960, input capital is an inferior production factor in the sector.

6.5 The Technological Effect on Total Cost

The effect of technical change on total cost of production (λ) in the U.S. Apparel industry is

estimated by formula (5.15) and presents in the table below. This effect exhibits the rate of

cost diminution due to technical progress. A positive value of λ indicate that the using of new

technology involve a reduction in the total cost of production.

Table 6.6: the rate of cost diminution due to technical progress in U.S. Apparel 1959-1996.

Year λ Year λ Year λ

1959 0.114 1972 0.094 1985 0.071

1960 0.112 1973 0.094 1986 0.069

1961 0.110 1974 0.092 1987 0.068

1962 0.108 1975 0.088 1988 0.067

1963 0.107 1976 0.087 1989 0.064

1964 0.106 1977 0.085 1990 0.062

1965 0.104 1978 0.084 1991 0.060

1966 0.103 1979 0.082 1992 0.059

1967 0.102 1980 0.080 1993 0.058

1968 0.100 1981 0.078 1994 0.056

1969 0.099 1982 0.076 1995 0.055

1970 0.097 1983 0.074 1996 0.053

1971 0.096 1984 0.073 - -

The rate of cost diminution is positive over the time interval, and it does mean that the

technical progress for U.S. Apparel industry exhibit a reduction in the total cost. On average

technical change has reduced the total cost of production in the sector at a rate of 8%. Further

we can see in the table that technological effect on cost reduction is diminishing; i.e. the rate

of cost diminution due to technical change has a property of diminishing over time. It is

beginning with 11.4% and finishing at 5.3%. I illustrate the diminishing property of technical

effect on total cost in the follow diagram:

32

Diagram (6.2)

As I previously discussed, the parameter γtt shows acceleration or deceleration in

technological growth. This magnitude has an approximate estimate value of 0.0018, which

exhibits an acceleration of technological progress in the sector by a weak rate of 0.18%.

6.6 The Technological Effect on Total Factor Productivity, TFP

As I discussed in section 5.2, the rate of cost diminution does not measure the net effect of

technical change. The rate of total factor productivity growth (θ) as a primal index of

technological progress is estimated by dividing (λ) with scale economies (ε), presented in the

following table.

Table 6.7: the rate of total factor productivity growth in U.S. Apparel industry 1959-1996

Year θ Year θ Year θ

1959 0.121 1972 0.090 1985 0.080

1960 0.120 1973 0.088 1986 0.078

1961 0.119 1974 0.091 1987 0.074

1962 0.115 1975 0.091 1988 0.074

1963 0.111 1976 0.089 1989 0.074

1964 0.110 1977 0.085 1990 0.074

1965 0.105 1978 0.084 1991 0.073

1966 0.103 1979 0.085 1992 0.068

1967 0.100 1980 0.085 1993 0.066

1968 0.098 1981 0.084 1994 0.064

1969 0.096 1982 0.083 1995 0.063

1970 0.097 1983 0.081 1996 0.063

1971 0.095 1984 0.079 - -

Cost Diminution due to Technical Progress in U.S.

Apparel Industry

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

1958 1965 1972 1979 1986 1993

Time Evolution

Th

e R

ate

of

Co

st

Dim

inu

tio

n

33

From the table above we can see that the rate of total factor productivity growth is

diminishing in the sector from 12.1% in the first year to 6.3% at the end of time interval. The

growth of total factor productivity is becoming slower over time. There are some explanations

about slowdown or diminishing rate of total factor productivity growth on the whole, that I

will discuss it later. Slowdown in total factor productivity is showed graphically in the below

diagram:

Diagram (6.3)

Compare the above diagram with diagram (6.2). The difference between curves exhibits the

effect of scale economies. The net effect of technical change (the rate of total factor

productivity growth) is not so different with the rate of cost diminution. The reason is that the

effect of scale economies is not great due to prevail of constant or a weak increasing return to

scale during the time interval.

6.7 Technical Bias and the Technological Effect on Factor Demand

Parameters γit exhibits a general index to bias effect on factor augmenting. The test of Model 5

(Hicks neutral technical change) by Likelihood Ratio statistic test demonstrated a rejection of

this restriction (table 6.1). Inequity γit ≠ 0 (biased technical change) can not be rejected by

LR-test, and technical progress has therefore a significant bias effect on production factors in

The Slowdown in Total Factor Productivity Growth in

U.S. Apparel Industry

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

1958 1965 1972 1979 1986 1993

Time Evolution

Th

e R

ate

of

To

tal

Facto

r P

rod

ucti

vit

y

34

U.S. Apparel industry. From table 6.2 we can observe that the estimated value of parameters

γKt and γLt is positive; i.e. the technical change uses factors capital and labour in U.S. Apparel

industry during 1959-1996. But technical progress in the sector is both energy- and material

saving. These results are constant and are valid for the whole time period under investigation.

In order to study technical bias effects on production factors carefully, I have estimated the

effect of technical progress on factor demand (eit) by applying the formula (5.18), presented in

the table below:

Table 6.3.5: technical bias effect on factor demand in the U.S. Apparel industry 1959-1996

Year eKt eLt eEt eMt Year eKt eLt eEt eMt

1959 0.003 -0.100 -0.196 -0.124 1978 -0.027 -0.073 -0.124 -0.096

1960 -0.016 -0.098 -0.193 -0.122 1979 -0.021 -0.072 -0.118 -0.094

1961 -0.018 -0.096 -0.187 -0.120 1980 -0.027 -0.070 -0.110 -0.093

1962 -0.022 -0.095 -0.190 -0.119 1981 -0.031 -0.067 -0.107 -0.090

1963 -0.001 -0.094 -0.186 -0.118 1982 -0.031 -0.066 -0.104 -0.089

1964 0.000 -0.093 -0.182 -0.116 1983 -0.034 -0.062 -0.105 -0.086

1965 -0.033 -0.091 -0.187 -0.115 1984 -0.028 -0.062 -0.104 -0.085

1966 -0.032 -0.090 -0.175 -0.113 1985 -0.022 -0.061 -0.099 -0.084

1967 -0.026 -0.089 -0.170 -0.112 1986 -0.027 -0.060 -0.098 -0.081

1968 -0.026 -0.088 -0.167 -0.111 1987 -0.026 -0.057 -0.104 -0.080

1969 -0.020 -0.086 -0.161 -0.110 1988 -0.023 -0.055 -0.106 -0.078

1970 -0.026 -0.084 -0.150 -0.107 1989 -0.025 -0.053 -0.102 -0.076

1971 -0.016 -0.083 -0.146 -0.106 1990 -0.025 -0.051 -0.099 -0.075

1972 -0.032 -0.081 -0.155 -0.105 1991 -0.024 -0.049 -0.098 -0.073

1973 -0.008 -0.081 -0.140 -0.104 1992 -0.023 -0.048 -0.101 -0.071

1974 -0.005 -0.079 -0.129 -0.102 1993 -0.020 -0.046 -0.102 -0.070

1975 -0.036 -0.076 -0.127 -0.099 1994 -0.018 -0.045 -0.103 -0.068

1976 -0.031 -0.075 -0.122 -0.098 1995 -0.013 -0.044 -0.099 -0.067

1977 -0.033 -0.074 -0.121 -0.097 1996 -0.010 -0.042 -0.099 -0.065

We see in the table above that except eKt for the years 1959 and 1964, all estimated value are

negative. These outcomes exhibit that the introduction of new technology causes factor

augmenting and reduces also the input demand for U.S. Apparel industry over the time under

study. Capital demand has been reduced on average by a rate of 2%. Labour demand reduces

at a diminishing rate. The rate of labour augmenting and labour demand reduction declines in

regularity from 10% to 4.2% over the time. Demand reduction for inputs energy and material

is diminishing too. The rate of energy demand reduction and material demand reduction due

to technological progress in U.S. Apparel industry declines regularly from 19.6% to 9.9%,

and from 12.4% to 6.5%, respectively. The diminishing effect of technical progress on factor

effectiveness in the sector can be showed in follow diagrams:

35

Diagram (6.4)

The curve of technical effect on capital augmenting is so variable in direction of its

development. The slowdown in capital effectiveness can be observed under 1962-1964, 1965-

1969, 1975-1979, and 1986 to 1996. For the periods 1958-1962, 1964-1965, 1969-1970,

1971-1972, 1974-1975, and 1979-1983, the rate of capital effectiveness has increased. The

slowdown in technical progress on energy effectiveness is observed regularly from 1958 to

1980 except temporary for periods 1965-1966 and 1971-1972. After that the effect of

technological progress on energy demand and energy effectiveness is approximately constant

(vary in a very small range). The regularly slowdown in technical effect on labour augmenting

and material augmenting can be seen obviously during the period 1958-1996.

About slowdown in productivity growth

The presented results regarding the rate of total factor productivity growth and technological

bias effect on input demand, in the last section, indicate a slowdown in productivity growth.

This phenomenon has observed in the recent econometric studies of productivity and

technical change 20

. There is some reasoning around the slowdown in productivity.

Woodward (1983), Nordhaus (1997), and several researcher, have named some reason as;

increasing expenditure of pollution control, lagging capital formation, energy price shocks,

change in demographic composition of the labour force, and declined investment in R&D

20

See Woodward (1983), p. 94-98, Nordhaus and more researchers in ”The economics of productivity”, edited

by Edward N. Wolff (1997), volume 2, part IV.

Biased Technical Effect on Factor Demand

-0,02

0,01

0,04

0,07

0,1

0,13

0,16

0,19

0,22

1958 1965 1972 1979 1986 1993

Time Evolution

Th

e R

ate

of

Facto

r

Eff

ecti

ven

ess

Capital Augmenting

Technical Change

Labour AugmentingTechnical Change

Energy AugmentingTechnical Change

Material Augmenting

Technical Change

36

sector, for slowdown in productivity growth. 21

Each of these reasons explains a part of the

slowdown in productivity. Siegel empirical study (1979) suggested that 83% of the slowdown

from 1948-1965 to 1965-1973 is explained by pollution control efforts, and 58% of that from

1965-1973 to 1973-1978, is because of increase in energy prices. 22

Varieties in empirical

results concerning the factors behind slowdown in productivity are depending on the model

specification. They suffer of misspecification and omitted variable. Depending on witch

variable that appears in the model as explanatory (independent), slowdown in productivity

may be bias affected of that variable in regression. 23

Among all possible reason to

productivity slowdown, pollution control approach and increasing in energy price are more

discussed as main causes to this phenomenon. The rationale of pollution control approach is

that the capital equipment has some difficulty in adapting to this control. 24

The second reason

is easier to understand. Due to complementarity between capital and energy (see table 6.3 of

this article), an unusual rise in energy price lead to reduction in the effective use of both

energy and capital in production, resulting in slower growth in productivity. U.S. economy is

often said to be very sensitive to energy price shocks 25

. The question is that whether the

higher energy prices under 1970s really cause the slowdown in productivity growth in U.S.

Apparel industry. Development of energy prices in diagram (4.1) obviously shows that the

price was increasing during 1970s. But the slowdown in total factor productivity growth is not

limited to this decade. From diagrams (6.3) and (6.4) we can not observe a dramatic

slowdown in the rate of productivity –and factor effectiveness growth under 1970s.

21

Woodward (1983), p. 94-98, Edward N. Wolff (1997), volume 2, chapter 20-28.

22 Woodward, p. 96

23 Woodward, p. 96

24 Woodward, p. 97

25 See Jorgenson (1998), ”growth”, volume 1, p. 299.

37

7. Summary and Conclusion

I employed a transcendental logarithmic cost function to analyse econometrically the effects

of technological progress on productivity and factor demand in U.S. Apparel industry during

1958-1996. The empirical results showed that the total factor productivity was growing at the

rate of 9% on average. The declined growth rate in the total factor productivity from 12.1% to

6.3%, is consistent with observed slowdown in technical bias effect on input saving (factor

augmenting) for labour (from 10% to 6%), for energy (from 19.6% to 9.8%), and for

intermediate material (from 12.4% to 8.1%). No regular slowdown is observed in technical

bias effect on capital saving. Capital demand decline due to technical effect by 2% on

average. Technical change in U.S. Apparel industry is biased energy saving; i.e. technological

progress has larger effect on energy input than the other inputs. The estimated value of

parameter γtt exhibits an acceleration of technological progress in the sector by a rate of

0.18%. The effect of technical progress on the optimal output in U.S. Apparel industry has

found out to be 2.1%. The efficient scale in the sector grows also by a constant rate of 2.1%

for the whole time interval.

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