Essays on outsourcing, technological adoption and unemployment

1.2.3 Job Matching and Creative Destruction Dynamics 1.2.4 Optimization Behaviour Across the Firm and the Economy 1.2.5 Wage Bargaining Curve 1.3 Steady-State Analysis and Changes in Hum

ESSAYS ON OUTSOURCING, TECHNOLOGY ADOPTION AND

UNEMPLOYMENT

BY TAN CHIH WEI, RANDY (B SOC SCI., HONS., 2003)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SOCIAL SCIENCE

DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE

2005

ACKNOWLEDGEMENTS

Much has happened during the past 2 years of my candidature here while doing

this course, the most significant of which is the Lord’s guiding hand in bringing me into

confession of my sins and acceptance of Christ I recalled my feeling of being upset at

my final exam for Mathematical Economics 2 and how worried I was about missing out

on a 2nd upper I was discussing this with my then, and now current, supervisor Dr Ho Kong Weng and he somehow shared the Gospel with me Through my supervisor, who

has assisted me in the understanding of the Gospel and explained some things in the

Bible which I could not understand, the Lord has helped me to understand more of His

revealed will Looking back, it is interesting to think about how the Lord has shut the

doors in my futile search for a job after completing my Honours in Economics and

opening the door of a research scholarship and I am indeed indebted to the Lord for

opening this door and shutting the others, convicting me of my sins and enabling me to

embrace Christ as my and the only Saviour I would also like to express my sincere and

heartfelt appreciation to Dr Ho for his efforts and valuable time in sharing with me the

word of God as well

I would like to express my heartfelt appreciation to Dr Ho for his supervision and

a free hand in the process of doing this thesis as well as in the tutorial classes I have

conducted for his module and research assistance rendered and his valuable and creative

inputs throughout Admittedly, I have a tendency of wanting things my own way and I

would express my sincere apologies for the offence and unpleasantness caused Much

i

has been learnt whilst working with him in that I have learnt to be more open and critical

in my thought process, as well as how to help students learn and not excessively

spoon-feeding them These, and other lessons and attributes which I may have unintentionally

omitted, have certainly made it a great privilege for me to have worked with Dr Ho I

must again thank him for the valuable assistance, time and opportunity cost incurred in

helping me throughout the 3 years of supervision for my Honours and Masters theses

My sincere appreciation to Ms Sagi Kaur for her help in the administrative

assistance rendered for the departmental graduate presentation I conducted and the

summer meeting of the North American Economics and Finance Association held at the

80th Western Economics Association conference I would also like to thank Mdm Foo and Mdm Woo for their assistance in the printing of the transparencies and handouts for

the above-mentioned events Financial assistance from NUS for the attendance and

presentation at the conference is acknowledged I would also like to thank the rest of the

administrative staff for the handling of the administrative and teaching matters

I would like to thank the Lord for His providential hand in guiding me through the

research programme, without which the completion of the coursework and thesis would

have been impossible I would also like to thank A/P Zeng Jinli and A/P Zhang Jie for

sharing some research techniques during the Honours and Masters classes respectively,

which have certainly been useful during the course of my research work Comments for

a shortened version of the first chapter from those who attended my presentation at the

Graduate Students’ Seminar on 27 June 2005 and Professor Daniel Mitchell at the 2005

Summer Meeting of the North American Economics and Finance Association held during

the 80th Western Economic Association conference is also much appreciated Finally, I would also like to thank the following for the constant encouragement and friendship:

Shirley Fong, Daniel Soh, Enrico Tanuwidjaja, Grace Yong, Kelvin Foo, Koh Phuay

Leng, Oh Boon Ping, Yvonne Yau, Qiao Zhuo, Feng Shuang, Luckraz Shravan, Nicholas

Sim, Terence Cheng, Kuhan Harichandra, Swee Eik Leong, Gabriel Wong, Koo Ping

Shung, the Economics Graduate Students Society committee of 2004, students whom I

have taught or who I have come into contact with as a tutor for Econometrics 2 or

Macroeconomic Analysis 2 during the academic year 2004/05, everyone over at Pilgrim

Covenant Church and friends from my secondary and college days My sincere apologies

go out to those whom I have omitted unintentionally Any remaining errors or omissions

in this thesis is mine and views expressed in this thesis do not necessarily represent those

of the Department of Economics, National University of Singapore, or any of the

above-named or group of individuals

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ABSTRACT

This thesis is made up of two distinct essays In the first essay, titled

“Technology Adoption and Unemployment”, a model with employment of workers as an

investment decision within a small open economy is used to examine the relationship

between technology adoption and employment Human capital plays a crucial role in the

technology adoption and, subsequently employment of workers It is shown that as

human capital level increases, level of technology adopted within the economy increases

There exists a threshold level of human capital beyond which employment falls, which

equivalently translates into higher unemployment in our model Two opposing effects

are in place here as human capital increases An increase in human capital enables better

use of existing technology and reduces job loss However, this also has a positive impact

on the adoption of technology, thus raising the technology adoption aspect of creative

destruction which raises job loss at an increasing rate and thus reduces employment The

latter effect dominates the former upon breaching the threshold, thus leading to the

increase in unemployment We have therefore a non-monotonic relationship between

level of technology adopted and employment and hence human capital and employment

The second essay, titled “Integration versus Domestic Outsourcing: An

Exploratory Study”, considers a two-country model of production of the service good that

differs in quality The firm in each country competes with each other in price and in

quality Constrained by local provision of the service good, the firm faces the choice of

either adopting the integrated mode of production or outsourcing the intermediates

domestically There exists a threshold level of human capital whereby integration

(outsourcing) is adopted when human capital level is below (above) the threshold As

human capital increases, the cost of outsourcing the intermediate decreases relative to

wage cost, thus the firm is able to reduce the per unit employment sufficiently and yet

produce a sufficiently high quality of the product at a low price-to-quality ratio The

endogenous quality choice in our model thus allows for an extra avenue of response

towards increased competition

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1.2.3 Job Matching and Creative Destruction Dynamics

1.2.4 Optimization Behaviour Across the Firm and the Economy

1.2.5 Wage Bargaining Curve

1.3 Steady-State Analysis and Changes in Human Capital 20

1.3.1 Steady State Equilibrium

1.3.2 Parameterization

1.3.3 Simulation Results

1.3.4 Changes in the Human Capital Level of the Economically Active

1.4.1 Matching Parameters

1.4.2 Wage Setting Parameters

1.4.3 Rate of Global Technological Progress

2.3.3 Changes in the Human Capital Level of the Northern Economy

2.4.1 Price Charged by the Southern Firm

2.4.2 Quality of the Southern Firm’s Service Good

2.4.3 Cost of Outsourcing Manual Component

2.4.4 Wage Cost

2.4.5 General Productivity Level

2.6 Modifying the Cost of Outsourcing 106

LIST OF TABLES

Table 1.1: Parameter values used for base case 22

Table 1.2: Summary of slopes of demarcation curves and approximate 23

corresponding range of values of h

Table 1.3: Simulation results for baseline case 25

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Table 1.4: Summary of outcomes of comparative statics exercise of an 37

increase in respective parameters in 1.4.1 to 1.4.5

Table 1.5: Simulation results for (a) ε = 0.2 and (b) ε = 0.3 39

Table 1.6: Simulation results for (a) δ = 0.5 and (b) δ = 0.7 39

Table 1.7: Simulation results for (a) 10% fall in χ (=0.144) and 41

(b) 10% rise in χ (=0.176)

Table 1.8: Simulation results for (a) γ = 1.1 and (b) γ = 1.7 41

Table 1.9: Simulation results for (a) 5% fall in ψ (=0.95) and 42

Table 2.1: Parameter values used for initial numerical analysis 80

Table 2.2: Comparison of roots obtained with H N = 0.5 81

Table 2.3: Numerical results under both forms of production for 83

different values of H N

Table 2.4: Numerical results under both forms of production for 90

different values of H N with a 20% fall in price charged by

the Southern firm

Table 2.5: Numerical results under both forms of production for 94

different values of H N with a 20% increase in the quality of

the Southern firm’s service good

Table 2.6: Numerical results under both forms of production for 97

different values of H N with a decrease in the cost of

outsourcing (10% fall in ρ and 10% fall in δ)

Table 2.7: Numerical results under both forms of production for 100

different values of H N with a 15% increase in the base wage

rate

Table 2.8: Numerical results under both forms of production for 102

different values of H N with a 20% increase in general per unit

productivity

Table 2.9: Numerical results under both forms of production for

different values of H N with a change in the productive share 104

of the organizational component (β=1/3)

Table 2.10: Summary of outcomes of comparative statics exercise of an 110

increase in respective parameters in sections 2.3.3 and 2.4

under the relevant production mode

LIST OF FIGURES

Figure 1.1: Demarcation curves for low level of human capital (h=0.25) 23

Figure 1.2: Demarcation curves for high level of human capital (h=0.7) 24

Figure 1.3: Effect of an increase in h when h is below the threshold level 31

of human capital

Figure 1.4: Effect of an increase in h when h is above the threshold level 33

of human capital

Figure 2.1: Graphs of the first-order conditions around the intersection 84

point for H N =0.7 and H N=0.72

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1 TECHNOLOGY ADOPTION AND UNEMPLOYMENT

1.1 Introduction

Human capital is known to have played a crucial role in the development process

of many economies The development of a more highly-skilled workforce through improved educational and training opportunities have helped to enhance the employability of workers at the individual level and reduce unemployment at the aggregate level The presence of skilled labour would, in turn, be a crucial factor in the firm’s technology adoption decision, as implementation of newer and better technologies

is often infeasible without the presence of more highly-skilled workers

Whilst it is true that firms may find it difficult to adopt new technologies, which usually raise productivity, without the availability of skilled workers (for example, see Haskel and Martin (1993); a mathematical exposition on the capital-skill complimentarily

is found in Lloyd-Ellis and Roberts (2002)), increases in the human capital of workers actually present firms with the opportunity to implement a higher level of technology to replace workers For example, strikes by port workers from the United States over the proposed retrenchment of workers involved in jobs that will be lost as a result of automation is just one of many similar situations that have taken place throughout history.1 The job of ticket conductors to punch bus tickets and collect payment was made redundant with the introduction of various technologies to collect bus fares and dispense bus tickets, enabling bus services to be run as one-man-operations One good example

will be that of Singapore, where such a change has occurred in the late 1970s IT professionals have also found themselves becoming redundant as new variants of computer technology become more intelligent Highly-skilled journalists may no longer require a cameraman to accompany them in news reporting should future technological developments result in improved versions of the videophone Thus, technological progress could potentially have destructive effects on employment, with serious repercussions on job creation within the economy as well

The above discussion leads to the following question: does improved skill profile amongst the economically active result in increased employment? More importantly, with the availability of better-skilled workers to work with better technology, will firms take advantage of this to reduce the use of workers in the production process?

This paper attempts to study the relationship between technology adoption and unemployment in a general equilibrium analysis More importantly, our model considers how the level of human capital within a small open economy affects the choice of technology implemented by firms, which subsequently affect the employment situation within the economy

The underlying difference between the small open economy and the large economy is its inability to play a significant role in pushing the world technological frontier Any advancement in the small open economy’s technology frontier is due to its ability to adopt technologies quickly from the leading nations Eaton and Kortum (1996) did an empirical study to assess the proportion of a nation’s growth that can be attributed

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to its own research efforts and found that such efforts within major economies, namely United States, Japan and Germany, form a significant proportion of their growth Nahuis and van de Ven (1999) further postulated that efforts that concentrate on the adaptation of technology are more appropriate for the small nations based on the empirical outcomes from Eaton and Kortum (1996) Computations by Howitt and Mayer-Foulkes (2002) revealed that 80% of the global R&D expenditure can be attributed to 5 countries, this figure rising to 95% with the inclusion of another 6 countries, thus suggesting that most other nations are embarking on technology adoption rather than being at the forefront of the global technological frontier Therefore, unlike previous works that incorporate the research and development sector, this paper assumes that such a sector does not exist directly in the small open economy, that is, the small open economy concentrates solely

on the adoption of technology

There have been a myriad of reasons presented regarding the technology adoption decisions of firms These include the degree of willingness of workers to learn new skills associated with such technologies, the age profile of such workers, asymmetric information, availability of credit, externalities associated with network, market power and learning, the required human capital level for implementation of a given technology and the level of human capital available within the economy (see, for example, Besley and Case (1993), Basu and Weil (1998) and Canton, de Groot and Nahuis (2002)) We focus on the cost issues associated with the availability of human capital in the implementation of a particular technology To illustrate, suppose the United States has developed a modern farming technology With many studies showing that new variants

of technology are often skill-biased2, it is likely that such a technology is more suitable for farmers in the United States and other nations that share similar levels of human capital than the lowly-developed nations since they will be in a better position to make productive use of that technology

The availability of human capital plays a crucial role in the implementation of higher levels of technology, which often comes at a price Firms thus face both implicit and explicit costs associated with such implementation Explicit costs arise from the effective per unit cost of implementation of such technologies for a given level of human capital, which would generally include the purchase and installation of that unit as well as the additional training required to help workers gain proficiency in using that particular technology Implicit costs may arise from the failure to harness fully the productive capabilities of such technologies, such as the potential opportunity cost incurred to train the workers during working hours as well as the possibility of damages caused resulting from improper use of that state-of-the-art technology Acemoglu and Zilibotti (2001) highlighted that the mismatch between skill level and technology results in large differences in productivity between the North and LDCs and that such skill shortages play a key role in a multinational firm’s decision not to introduce such technologies in the latter group of countries Also, empirical studies by Bartoloni and Baussola (2001) on the determinants influencing technology adoption decisions of Italian manufacturing firms have revealed that the human capital level of a firm’s employees does play an important role towards the firm’s decision on whether to adopt a certain technology.3

2 Empirical evidence on the skill-biased nature of technological innovations can be found in Berman, Bound and Machin (1998), Machin and van Reenen (1998) and Morrison Paul and Siegel (2001)

3 An indirect manner in which higher levels of technology can have a negative impact on employment would be that such technologies can actually allow firms to reorganize existing job scope to facilitate greater multi-tasking, subject to the availability of workers with the desired level of human capital Lindbeck and Snower (1996) noted that technological advances have enabled firms to move from the Tayloristic structure to one that is more holistic They

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In our paper, the employment of workers is seen as an investment decision by the firms due to the presence of labour market frictions, similar to that by Yashiv (2000) Labour flow within the economy is determined by job creation and job destruction Conventional job matching technology (see Pissarides (2000)) dictates that the rate of job match is determined by the unemployment and vacancy rates Our paper takes on a different approach by considering this probability as a function of human capital level amongst the economically active and the level of unemployment This suggests that from the firm’s point of view, it is the skill profile and the availability of workers that will determine whether a suitable applicant or interviewee can be matched to a position that has been vacated due to job destruction or created due to various factors In our paper,

we assume that these factors are taken into consideration in the firm’s decision in selecting the number of interviewees for consideration A wage bargaining curve, which

is dependent on the human capital of the workers and the level of employment within the economy, is also introduced to endogenize the wage rate

External and internal technological factors play the main role in the determination

of job destruction Our paper employs an implication resulting from the creative destruction effect arising from an increase in the pace of technological progress As discussed in Aghion and Howitt (1994), growth is driven by the increase in knowledge and that this knowledge is embodied via state-of-the-art technologies Thus, a more rapid increase in knowledge will translate into higher growth rates and higher job-turnover

gave the example of how increased use of computers in disseminating information within firms has enabled greater complementarities across different tasks that were, in the past, clearly segregated This would imply that firms can

rates, with a more rapid introduction of new technologies leading to greater job destruction Given the inability of the small open economy to shift the world technological frontier, one can thus postulate that such effects are beyond the control of a small open economy Should the rate of creative destruction increase, the additional value of introducing a relatively higher level of technology diminishes, since the time available for the firm to recover various costs is reduced, which also reduces the profitability of the firm’s production and will subsequently influence the firm’s decision

on job creation On the whole, these will create a negative impact on job-loss within the small open economy To endogenize overall job-loss, we incorporate the role of domestic technology and human capital This is in view of the increasingly worker-replacing capability of newer technologies that can be used in the production process with the availability of better-trained workers in the workforce

Our model uncovers an interesting result regarding the non-monotonic relationship between technology adoption and employment under the onslaught of increasing levels of human capital Using appropriate parameters for our numerical simulation, we find that while increases in human capital encourage adoption of higher levels of technology and raises the sum of future discounted profits of an additional worker, wages and interview rate, such increases can only raise employment up to a threshold level of human capital Employment falls, or equivalently in our model, unemployment rises upon the economy’s human capital level exceeding the threshold The adjustment process in the short run that brings about the above long-run outcome can

be summarized as follows On the one hand, we have a job creation effect whereby having higher-skilled workers means that it is easier to find workers and that you can

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make better use of existing technology, which would contribute positively towards future discounted profits and thus reducing job loss or promoting employment However, we have the job destruction effect where the presence of higher-skilled workers promotes adoption of better technologies, thus raising the technological aspect of creative destruction and job loss, reduces total future discounted profits (which is a negative influence on job creation as well) and thus reduces employment Before crossing the threshold, the former effect dominates the latter Recalling that the employment decision

of the firms is likened to that of an investment decision, increases in human capital level that are below the threshold would actually result in the long-run outcome of higher employment on the whole since there exist future gains in terms of higher total future discounted profits by employing additional workers However, upon crossing the threshold, the latter effect dominates Thus, having additional workers over and above the optimal level of employment will result in future losses in terms of lower total future discounted profits from having these surplus workers, which will thus necessitate the laying off or reduction in the optimal level of employment amongst the firms Hence, we have this non-monotonic relationship between unemployment and technology adoption and also unemployment and human capital Various comparative statics analysis will be carried out to study the effect on employment, technology adoption, threshold level of human capital, the sum of discounted future profits of an additional worker, wages and interview rate upon changes in job matching, wage setting, global technological progress, productivity and cost parameters

The majority of existing literature has uncovered the relationship between human capital and technology, human capital and unemployment and technology and

unemployment Regarding the first instance, Nelson and Phelps (1966) showed that human capital plays a crucial role in learning and technological diffusion Acemoglu (1997b) showed that an increase in human capital may or may not raise the level of technology adopted Chander and Thangavelu (2004) found that higher investment in education by workers can provide the incentive for entrepreneurs to adopt better technology Empirical findings by Papageorgiou (2003) based on World Bank data revealed that post-primary education contributes significantly towards technology innovation and adoption whilst primary education contributes towards final output production Hollanders and Weel (2002) found a positive relationship between skill upgrading and R&D intensity in manufacturing based on an empirical study of six OECD countries

Several writers have examined the issue of the relationship between technology and unemployment, without incorporating the issue of human capital Using a model of frictional unemployment, the findings in Postel-Vinay (2002) do show that an increased pace of technological progress raises equilibrium unemployment via job obsolescence However, the model does not feature any underlying mechanism that motivates firms to adopt higher levels of technology The findings by Aghion and Howitt (1994) suggest that higher exogenous growth rate of leading technology can raise or lower unemployment, depending on the rate of growth and that higher endogenous growth arising from an increase in innovation size will strictly raise unemployment Hoon (1993) found that the effect of an increase in the level of technology on unemployment is entirely transient in that unemployment rises only in the short run However, increased pace of technological progress will raise unemployment In an empirical study,

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Danninger and Mincer (2000) found that an increase in the pace of technology has an uncertain short-run impact on unemployment but can result in a fall in unemployment in the long run as less skilled workers receive training Nakanishi (2002) found in an empirical study on Japan that there exists a negative relationship between IT capital and labour and further indicated that the impact has increased during recent times

Other writers have also studied the relationship between human capital and unemployment An increase in education capital is found to reduce unemployment by Davis and Reeve (2003), regardless of whether the economy is closed or open Empirical studies by Richardson and van der Berg (2001) and Chan and Suen (2003) on evaluating the effectiveness of training policies on employability of workers indicate that such policies have a minimal impact on enhancing labour market performance Nickell (1979) has also found that there exists only a very limited impact of the number of years of schooling from 13 years and above on unemployment rate

Acemoglu (1997a) has attempted to incorporate all the above aspects He found that, subject to the extent of exogenous productivity increase, firms may or may not adopt better technology If the former is carried out, the firm will thus help enhance the human capital of the workers Such an outcome raises the proportion of skilled workers within the workforce and would also lead to a reduction in unemployment The findings here seem to imply that increase in human capital is driven by technology adoption and that unemployment falls as a consequence His finding differs significantly from ours in that

we view the presence of human capital to be the driving force behind technology

adoption and that unemployment may or may not decrease depending on the strengths of the job creation and job destruction effects

To summarize, the above literature suggests that raising human capital level may

or may not result in implementation of higher level of technology Faster technological change or implementation of higher level of technology need not necessarily raise equilibrium unemployment The relationship between human capital and unemployment cannot be clearly established Our contribution is to integrate the aspects of human capital and global technological advancement into a framework of unemployment and technology adoption arising from changes in the former aspect, which is presently sorely lacking in existing literature

The rest of this chapter is organized as follows Section 1.2 describes the various aspects of the model and the optimization process Steady-state and comparative statics analysis of changes in human capital is carried out in section 1.3 We consider changes

in other parameters in section 1.4 Section 1.5 provides a general discussion of the implications of the outcomes obtained Section 1.6 concludes this chapter

1.2 The Model

The economy consists of a collection of identical firms indexed from 0 to 1 that are producing the final good The population consists of economically active agents that

can also be indexed from 0 to 1, with L t of these employed Each agent is assumed to

possess an exogenous amount of human capital h, h∈(0,1], that is not technology-specific,

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with the difference in level of human capital determining the degree of proficiency with a given technology.4 It is also assumed that agents would not be looking for another job when employed

Each firm produces a single, all-encompassing final good of unitary price that is identical across all firms, and operates within a perfectly competitive environment Firm

i employs L it of workers, and adopts a unit level of technology i

1.2.1 The Production Process

The firm requires a combination of technology, human capital and labour for final-good production Each of the firms in the economy takes on the Cobb-Douglas production function which satisfies the usual Inada conditions:

technology and labour are seen as complementary in the production process.5 We augment human capital to technology rather than to labour in view of our assertion that technology can only be an effective component of production through the implementation

of available knowledge Rewriting the above production function to allow human capital

to augment labour would suggest that the total amount of effective workers increases at a diminishing rate.6 B represents a productivity parameter that is exogenous to the firm

Each firm also faces an exogenous per unit cost of technology q/h, which includes

the cost of the physical unit of that technology as well as training costs, with this cost component decreasing in the human capital level of the economically active This suggests that the availability of a better-trained workforce will help lower the cost of adopting a particular level of technology In the process, each infinitesimal improvement

in human capital presents firms the opportunity to make changes to existing work practices and job scope of workers, which could lead to adjustments in employment, to take advantage of possible use of higher levels of technology For simplicity, the total cost associated with technology implementation can be seen as a whole, rather than being subjected to depreciation, upon the assumption that firms actually rent their machines from an agency that supplies machines equipped with a given technology Thus,

6 We may also rewrite the above production function as i( i, ) ( )i ( ( ) )

increases at a diminishing rate with respect to an increase in human capital

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interviewing prospective applicants of job vacancies of b units of final good per

interviewed applicant We also assume that firms face search costs which are increasing

in the number of interviews conducted.7 In the process, the firm thus also needs to decide

on the number of candidates D it to be considered for an interview In this paper, we

assume that the cost of selecting the candidates follows the specific quadratic form bD it 2,

where b>0

1.2.3 Job Matching and Creative Destruction Dynamics

The probability that the interviewee would be able to secure the job is dependent

on the average human capital level within the economy and the economy’s

unemployment level u t , which would be equivalent to (1-L t ) From the firm’s perspective,

a higher unemployment rate would mean a higher probability of finding that suitable worker if there is a larger pool of unemployed workers to choose from This can be seen

as a measure of tightness of the labour market The average level of human capital is included as it is in general easier for firms to find the suitable worker within an economy with more better-skilled workers Thus, the number of successful job interviewees that

7 Search costs can increase at an increasing rate through the tasks that can be undertaken due to loss of working time in the process of interviewing prospective applicants, which can otherwise be used to raise output in a more than proportionate manner For example, the time taken to interview five candidates consecutively to fill up extra vacancies

are offered employment can be written as ς(h)u t ε D it , where ς(h) is a function that

generates a probability attributed to the human capital component in the selection process,

with ς’(h)>0 and ς’’(h)<0 to indicate the diminishing role of human capital in determining the right candidate for the job For simplicity, we let ς(h)=h ε , where ε∈(0,1] With δ∈(0,1], the advantage arising from the presence of more unemployed workers

diminishes These assumptions can be seen in view of the fact that while the chances of finding that worker are higher with a larger pool to choose from or with improved skill level, it is likely that there exists more workers that can be seen to be similar, thus not

necessarily presenting the firm with more choices ε + δ < 1 would suggest that there

exists overall diminishing probability of a successful match, with the opposite and equality situations indicating overall increasing and neutral probability of successful match respectively

Within the small economy, firms face external pressures associated with the pace

of technological development, which is denoted as z, with z∈(0,1] The level of

technology adopted plays a role in the firm’s employment decision For a given level of technology, the availability of a higher level of human capital would reduce job loss as workers are now more capable of working with the given technology, which can be seen

as an incentive for firms to retain workers On the other hand, for a given level of human capital, the use of higher levels of technology will raise job loss as the workers available are now not only less capable of coping with the new technology, but also encounter technology that can increasingly replace workers These are sufficient to deter firms from keeping such workers In this model, we suggest ( )i h

t

A to be a plausible specific form to capture the technological impact of creative destruction associated with the level

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of technology implemented within the firm Collectively, the job loss rate would be

( )i h

t

z A This can be seen as a measure of the extent of the impact of technology on

workers A higher z would mean that keeping up with technological progress would be

costly in the sense that the time available for the firm to obtain sufficient profits when using that level of technology decreases The inverse of ( )i h

t

z A can be seen as a measure

of the duration of a job match The number of workers losing their jobs at a firm at a given time period would be ( )i h

1.2.4 Optimization Behaviour Across the Firm and the Economy

Each firm attempts to maximize its discounted profits over an infinite time horizon in the following manner, subject to the net employment function in (2):

( ) ( )2 0

w =w Summing up all similar instantaneous profit functions would give

us the economy’s profit function, as well as the economy’s level of employment and total umber of candidates considered for the job Thus, the economy-wide optimization, which is the sum of all firm’s profit function, c

ely The current-value Hamiltonian can be written as follows, where λ t is the tate variable and is a measure of the sum of discounted future profits of an additional worker:

co-t , w t and D t are the economy’s employment rate, wage rate and interview rate respectiv

The following are the first-order and transversality conditions obtained based on the ove Hamiltonian:

side of (9) can be seen as the marginal benefit of having, or investing, in an additional worker, which constitutes of the current marginal product of labour and the net discounted future profit The right-hand side of (9) would denote the marginal cost of having, or investing, in this additional worker, with wage cost making up the current cost and the shadow-price weighted future labour turnover and interest forgone constituting future costs The first term of the right-hand side of (10) would be the economy’s overall job creation whilst the economy’s overall job loss is represented by the second term of the right-hand side of (10) The usual transversality condition is represented by (11) We

ewrite equations (7) and (8) to obtain the following expressions of D t and λ t, with the latter obtained from

attributed to technology We substitute equations (7’) and (8’) into (9) and (10) The

Equation (7’) would suggest that the number of vacancies is positively related to the total discounted future profits of an additional worker and unemployment rate It is useful to note that equation (8’) measures the total future discounted profits of employing

an additional worker in terms of the difference between marginal product and marginal cost of technology, adjusted for the marginal impact of technology on creative destruction The numerator term in (8’) can be seen as the net marginal benefit of technology adoption whilst the denominator is the marginal creative destruction

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time derivative of (8’) is taken and set to be equal to (9) to obtain the partial differential

equation that would implicitly define the dynamic equation for A t The following

ynamic equations for L t and A t are as follows:

1

2 1 2

2

12

βδ

1.2.5 Labour Supply Curve

firm i faces an overall labour supply curve that is as follows:

human capital level Thus, a higher value of ψ would indicate that workers would expect their wages to increase at a higher rate with an increase in human capital γ can be seen

as a measure of ease of finding jobs Here, one would expect γ to be larger than 1

because workers would envisage that it would be easier to find jobs when the economy’s

employment, L t, is high and would want to escalate their wage demands, with the opposite occurring when the economy’s employment is low No numerical restriction is laced regarding the sums of the exponents We will substitute (14) into (13) for the m

d Changes in Human Capital

.3.1

The demarcation curves associated with (12) and (13) can be obtained through

setting the respective time derivatives of A t and L t to be zero as follows:

p

dyna ic equation of A t

1.3 Steady State Analysis an

( )2 ( )

2 1

02

illing up a vacancy relative to the level of human capital The low value of ε suggests

per unit level cost of technology, q been s as 0.14 that of r unit c of

unemployment within the economy in finding the right candidate (ε and δ respectively),

we have arbitrarily set these values to be 0.15 and 0.6 respectively We have adopted the view that there exists overall diminishing probability of job match because it is in general harder to differentiate workers when the availability of workers and skill level increases The parameterization suggests that the availability of workers plays a larger role towards f

human capital is rapidly diminished at fairly lo

Table 1.1: Parameter values used for base case

interviewing a candidate, b, as 0.1 The productivity parameter B has been arbitrarily set

to be 0.5 and the world interest rate r is taken to be 4% (i.e r=0.04) We assume the rate

of global technological progress to be at 7% (i.e z=0.07).8 This translates to an average lifetime of (1/0.07) = 14.29 years before the current set of key technologies are completely replaced by a new set of key technologies The parameters associated with wage setting behaviour, χ, ψ and γ, have been set as 0.16, 1 and 1.4 respectively Values

of h ranging from 0.2 to 0.95 were considered against the above baseline values of other

arameters For ease of interpretation, the parameter values have been set in a manner

s between 0 and 1.9

p

such that the solution of A t lie

1.3.3 Simulation Results

Numerical simulations reveal the existence of a unique non-zero saddle-path

stable solution (L t * , A t *) upon the intersection of the two demarcation curves based on their graphical outputs It is found that the slopes of the two demarcation curves around

the intersection point do change as the value of h increases, from the case of an

downward-sloping A&t =0 and upward-sloping L&t =0 to an upward-sloping A 0

t =

upward-sloping L&t =0 to an upward-sloping A&t =0 and a downward-sloping L&t =0

The third case occurs for the biggest range of values of h Table 2 provides a summary of the approximate range of values of h where the respective graphical solutions are

8 This rate can be better estimated by first considering the lifetime associated with various key technologies A relevant weighted measure pertaining to each key technology is imposed to find the estimated lifetime of the group of technologies The inverse will then yield the rate of global technological progress

9 The value of L t will automatically lie between 0 and 1 due to the appearance of (1-L t ) in the dynamic equation for L t

22

obtained In addition, the slope for A&t =0 becomes steeper when downward-sloping and

becomes gentler and then steeper when upward-sloping as h increases Saddle-path

stable solutions also exist for all the above situations For given values of human capital

h, we can obtain the graph consisting of the above demarcation curves in Figures 1 and 2

corresponding to situations 1 and 3 A brief explanation of the above observations will

e given in the next sub-section ulation outcome for the baseline scenario will be

alues of h

Slope

presented in the next sub-section in view of the comparative statics analysis for h

le 1.2: Summary of slopes of demarcat

v and approximate corresponding range of

s of demarcation curves L&t = 0 and A&t = 0 Approximate range of values of h

Upward, Downward (Situation 1) [0.20000, 0.29613]

Upward, Upward (Situation 2) (0.29613, 0.31700]

Downward, Upward (Situation 3) (0.31700, 0.95000]

Figure 1.1: Demarcation curves for low level of human capital (h=0.25)

Figure 1.2: Demarcation curves for high level of human capital (h=0.7)

1.3.4 Changes in the Human Capital Level of the Economically Active

We now consider how the economy makes its transition as the skill profile of the labour force is enhanced and the eventual steady-state outcome While the subsequent discussion deals with the impact of employment, the impact on the economy’s unemployment rate can be inferred easily Before subsequent analysis on the

comparative statics exercise for h, we first look at the outcome of a selected simulation

e and consider the implications associated with the slopes of the demarcation

Table 3 presents the numerical solutions for the baseline case, with the values of h

The values of A t , D t , w t and λ t are found to be increasing

roughout with an increase in h However, the outcome associated with employment, L t,

Proposit n 1: There exists a threshold level of h man capi al level h reshold suc that the

level of technology used, A threshold, is assoc ated wit the maximum a tainable

employm nt level L threshold

Proof: See section 1.7.1

Table 1.3: Simulation results for baseline case

0.20000 0.895310 0.044147 0.163266 0.02741 0.165563 0.037504 0.033578 0.037813 0.25000 0.911224 0.069944 0.181805 0.035118 0.172680 0.035999 0.032803 0.047827 0.30000 0.921649 0.101480 0.197979 0.042819 0.179301 0.035238 0.032477 0.057823 0.31700 0.924360 0.113485 0.203033 0.045431 0.181529 0.035117 0.032460 0.061216 0.35000 0.928728 0.138608 0.212286 0.050493 0.18588

0.40000 0.933599 0.181149 0.225047 0.058131 0.19269

0.29613 0.920981 0.098838 0.196798 0.042223 0.178794 0.035275 0.032487 0.057050

8 0.035053 0.032555 0.067793

0 0.035143 0.032732 0.077732 50000 0.939085 0.281580 0.246759 0.073262 0.207455 0.035344 0.032997 0.097494 60000 0.940913 0.400583 0.264277 0.088154 0.224205 0.037145 0.034882 0.117063 0.61000 0.940948 0.413398 0.265828 0.089628 0.226000 0.040431 0.038042 0.119008

Two issues arise as a result of an increase in h First, the graphs of the two

demarcation curves have experienced an upward shift around the intersection Second, the slopes of the demarcation curves around the intersection point have changed Accountability of these two issues would allow us to provide an intuitive explanation behind the existence of a threshold level of human capital In the subsequent discussion,

we compare the vertical shifts of the two loci at a given level of L t Appendix B provides the mathematical intuition for the subsequent discussion

We first consider the demarcation curve for L&t =0 The transition of the slope

from being upward-sloping to downward-sloping for this demarcation curve around the intersection indicates the prominence of employment level and its interaction with the

technological impact of creative destruction effect on overall job loss At low levels of h,

employment levels are not sufficiently large enough to have an impact on overall job loss The rate of job loss actually falls during this stage, based on our simulation results Thus

firms appear to complement the use of workers with technology At higher levels of h,

employment levels are now sufficiently large enough such that subsequent increases in employment and the higher creative destruction impact of technology arising from further increases in human capital combine to increase overall job loss by a large extent Since

an increase in either technology level or employment will escalate overall job loss, thus the downward-sloping nature of the graph will suggest a trade-off between the two to suppress job loss as there are costs associated with the replacement of workers The downward-sloping demarcation curve can thus be viewed as depicting the substitution

quation (14), an increase in h at a given L t actually reduces job loss rate and raises the

t and L t In terms of the upward shift of the

e

26

chances that the firm can find the required worker It also raises the sum of discounted

future profits that the firm can obtain by employing that worker (increase in λ t) Thus the demarcation curve can no longer pass through the old saddle-path equilibrium as the marginal benefits of using higher levels of technology at a given employment level would outweigh the overall marginal cost of creative destruction Thus, for a given level of employment, a higher level of technology is used, shifting the demarcation curve upwards In the process, increasing the level of technology implemented would raise creative destruction and cost of technology implementation whilst reducing the marginal benefits gained from the use of improved chnology With higher human capital levels, the slope thus becomes steeper due to the greater combined impact of employment of workers and creative destruction effect of technology

The transition of the slope of the demarcation curve of A&t =0 is more

complicated Our findings indicate that the slope transitions from being negative to positive around the intersection point, with the slope subsequently becoming gentler up to

a certain value of h The slope remains positive but becomes steeper beyond that value of

h Simulation results indicate that the extent of job loss arising from implementation of technology (i.e A

te

t h ) falls prior to that value of h and rises subsequently This seems to suggest that when h is low, firms are still conservative in the use of technology despite the availability of better-trained workers, which may account for the slope When h is

beyond that particular value, the slope of A&t =0 around the intersection becomes positive

A quantitative way to account for the upward-sloping nature of the demarcation curve

around the intersection would be to look at (8) Suppose, for a given L t, we increase the level of technology to be adopted According to the dynamics, this would suggest that

the marginal benefit of having higher technology is higher than the marginal cost of

adopting it (i.e LHS < RHS in (8)) Mathematically, this would mean the fall in λ t A t h-1

(note that λ t changes as A t or L t changes) is such that the overall impact to the second term

on the left-hand side of (8) falls by a larger extent compared to the right-hand side of (8)

To restore this to equality, employment level must be raised Mathematically, this would

ean the rise in λ t L t is such that the overall impact to the second term on the left-hand

ent

On the other hand, a rising share of costs ttributed to wage payments due to rising employment may also play a role in

ase inrg

m

side of (8) increases by a larger extent compared to the right-hand side of (8) We can therefore view this demarcation curve as depicting the complem arity between A t and

L t The slope also becomes steeper as h increases Two possibilities may play a role in

this On the one hand, firms have become more willing to make use of technology with the availability of better-trained workers

Graphically, we can think of the shifts in the various demarcation loci as tracing a particular effect in place A shift in the demarcation curve of L&t =0 (for a given A&t =0

locus) can be seen as tracing the complementarity between labor and technology, whilst a shift in the demarcation curve for A&t =0 (for a given L&t =0

locus) can be seen as

e substitution between labor and technology

tracing th

28

The issue of the threshold level of human capital arises from the differing extents

of vertical shift in the demarcation curves, with the graph of A&t =0 shifting by a lesser

extent than L&t =0 for levels of h below the threshold level leading to increased

employment, which we denote a scena io 1, and vice-versa for levels of h above the

threshold leading to decreased employment, which we denote as scenario 2 It would be more intuitive to explain the situation by considering the effects of an unanticipated change in the level of human capital with the use of the phase diagram We also discuss the changes occurring under an anticipated change The adjustment process in the short run would differ depending on whether the change is anticipated or unanticipated, but the underlying intuition leading to the long-run unemployment outcome will be similar

We first look at scenario 1 Under the unanticipated case, an increase in h will

lead to an immediate upward jump in the level of technology implemented to a point directly above the level of employment before the shock along the new saddle path In this scenario, we find that both t

A& and L& t are positive, with the latter further suggesting that there is still room to employ more workers This occurs as the benefits associated with ease of finding workers and the ability to make better use of existing technology, which favour job creation, outweigh the costs associa d with the technological and overall job loss impact of creative destruction through adoption of better technologies, which favour job destruction As the optimal solution should continue to lie along the demarcation curve, having higher levels of technology at the same time is optimal, with the rationale being that the technological impact of creative destruction is still not sufficiently large enough and that acquiring more workers to work with better technology raises overall undiscounted profits and contributes positively to the net discounted future

te

profit of an additional worker (i.e λ&t >0) The movement in the north-east direction

suggests the presence of a complementary effect that is stronger than that of the substitution effect, thus raising the level of technology adopted and employment With

an anticipated change, a jump in the level of technology implemented that is lower than that of the instantaneous case occurs We find that A& t and L& t will be positive and negative respectively The economy actually experiences a fall in employment, whilst experiencing increasing levels of technology implemented along its adjustment trajectory until it reaches the saddle path, whereby the economy will experience increasing employment and level of technology adopted until it arrives at the equilibrium point Here, firms make the adjustment to implement better technology and releasing existing workers prior to the increase in the average skill-profile workers since the overall higher ost of technology implementation m kes it not optimal to employ the existing number of orkers to work with the better technology as the net discounted future profit of having the additional worker is negative Once the changes actually tak effect, firms will, at this point, actually seek to hire workers to plementation costs fall and output increases, with positive net discounted future profits from employing additional workers, until arrival at saddle-path equilibrium Again, the complementary effect is much stronger relative to the substitution effect, thus resulting in higher level of technology adoption and employment, the latter surpassing the previous level of employment The net effects arising from the short run adjustment process under either type of change would thus be the positive effects of an increase in human capital on job creation outweighing the negative effects of the same increase on job destruction

w

e work with better technology as im

30