Entrepreneurial networking, international outsourcing and wage inequality

ENTREPRENEURIAL NETWORKING, INTERNATIONAL OUTSOURCING AND WAGE INEQUALITY KOH PHUAY LENG (B.Soc. Sci.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SOCIAL SCIENCE DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE 2006 i ACKNOWLEDGEMENTS First and foremost, I will like to express my heartfelt gratitude and thanks to Dr Ho Kong Weng, for his great patience and guidance in the development of the paper. In particular, his valuable insightful comments, directions and explanations have enabled me to smoothly complete this thesis. I will also like to thank Dr Chang Youngho for his supervision and comments on the dissertation. Secondly, I will like to thank my family members and Mr. Yan Cheok Kin for their constant support and encouragement throughout the entire process. I am especially thankful to my younger brother, Mr. Koh Chee Hui for proof reading my thesis. Special thanks to Miss Tan Teck Kiah for her valuable help and patience in the use of MATLAB. I will also like to grab the opportunity to thank Mr. Lin Zhiming and Mr. Kelvin Foo for their comments and help respectively. In addition, here’s a big thanks to all other good friends who have given me their great support and help in one way or another. Koh Phuay Leng August 2006 ii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS i TABLE OF CONTENTS ii SUMMARY iv LIST OF TABLES vi LIST OF FIGURES vii LIST OF SYMBOLS xii 1. 1 2. INTRODUCTION THE MODEL 2.1 2.2 2.3 2.4 2.5 3. A Simple Static Model The production process 2.2.1 Firms Choosing To Adopt Vertical Integration 2.2.2 Firms Choosing To Engage In Outsourcing Activities Profit Functions Optimization Behavior Across The Economy 2.4.1 Firms Engaging In Vertical Integration 2.4.2 Firms Engaging In Outsourcing Activities Equilibrium 2.5.1 Threshold Level of Managerial Ability 2.5.2 Labor Market Equilibrium 7 7 8 8 9 10 11 11 13 15 15 17 DYNAMIC MODEL 20 3.1 3.2 3.3 3.4 3.5 3.6 20 21 23 25 26 27 30 34 The Model Baseline Steady-state System Parameterization Simulation Results Welfare Of The Domestic Country Comparative Statics Analysis 3.6.1 Cost Before Quality Adjustment, ρ 3.6.2 Changes In Parameters Affecting Networking Of Both Types Of Entrepreneurs 3.6.2.1 A Decrease In Inverse Of Networking Efficiency In Outsourcing Mode, k1 3.6.2.2 A Decrease In Inverse Of Networking Efficiency In Vertically Integrated Mode, k 2 3.6.3 Changes In Parameters Affecting Both Local And Foreign Labor Markets 3.6.3.1 An Increase In Human Capital In The Local Labor Market, H 3.6.3.2 An Increase In Human Capital In The Foreign Labor Market, h 3.6.4 Change In Parameters Related To Efficiency Of Training 34 39 44 44 47 51 iii 3.6.4.1 A Decrease In Entrepreneurial Overload In Training Unskilled Labor, α 3.6.4.2 A Decrease In Entrepreneurial Overload In Training Skilled Labor, γ 3.7 4. 3.6.5 A Change In Parameter Relating To Matching Ability, b Comparison With Previous Literature Results GENERAL DISCUSSION 51 54 57 61 68 5. CONCLUSION 69 6. BIBLIOGRAPHY 72 7. APPENDIX A 74 iv Summary The recent phenomenon of international outsourcing has taken place over the past few years. Based on OECD data, it is observed that the United States and the United Kingdom have experienced an upward trend on wage inequality over the years. Previous studies have linked the reason behind such a trend to the evolution of technology either due to international outsourcing or skilled-biased technical change. In this paper, we investigate the impact of international outsourcing on both wage inequality and entrepreneurs’ decision to outsource or perform in-house production. In addition, we postulate that technology evolves over time due to spillover effects by networks formed among firms undertaking integrated and outsourcing modes of production. Such an evolution of technology will affect the wage inequality between skilled and unskilled workers and the welfare of entrepreneurs versus domestic workers. We construct a simple dynamic model for a small, developed and open economy whereby the equilibrium organization of firms changes due to the formation of networks among domestic firms that undertake vertical integration and those that are engaged in outsourcing activities. The growth of integrated productivity and network knowledge stocks over time contributes to the growth of a common aggregate stock, which has spillover effects on the domestic economy in the next period. There exists a unique threshold level of entrepreneurial ability below (above) which firms elect to do vertical integration (international outsourcing). We show that in the long run, slightly more than half of the entrepreneurs will choose to do vertically integrated production. Although a static model without the evolution of the various stocks is inadequate in explaining the impact of networking on the domestic economy, it is able to explain the impact of other exogenous parameters adequately. We show that a reduction in the cost of manual components, an increase in foreign human capital and efficiency of matching firms with overseas supplier will increase the fraction of firms choosing to do outsourcing v and subsequently affect wage inequality. In addition, we investigate the impact of networking on GDP over time and find that an increase in outsourcing activities will benefit the welfare of entrepreneurs while decreasing the welfare of domestic workers. Furthermore, one of our striking results is that an increase in outsourcing activities is not necessary beneficial to the domestic economy throughout all cases. An increase in the ability of the entrepreneurs to match domestic firms to overseas supplier will result in a lower GDP in the long run. vi LIST OF TABLES 1 Parameter Values Used for Baseline Static Model 2 Parameter Values Used for Baseline Simulation 3 Baseline Steady State Values 4 Baseline Values for Various Components of GDP 5 Summary of Comparative Statics Results for Baseline Static Model 6 Summary of Comparative Statics Results for Dynamic Model 7 Summary of Outcomes of Comparative Statics Exercise for an Increase in Selected Parameters 8 Summary of GDP Outcomes of Comparative Statics Exercise for an Increase in Selected Parameters 9 Comparison with Previous Literature Results (1) 10 Comparison with Previous Literature Results (2) vii LIST OF FIGURES 1-1 Percentage Ratio of Volume of Exports and Imports Between U.S Parent Companies and Their Foreign Affiliates and Total Volume of U.S Exports and Imports 2-1 Profits of Integration and Outsourcing Firms 3-1 Evolution Of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease in ρ 3-2 wts Evolution of Wage Gap u for 1% Decrease in ρ wt 3-3 Evolution of GDP for 1% Decrease in ρ 3-4 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Decrease in ρ 3-5 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Decrease in ρ 3-6 Evolution of Total Unskilled Labor Income for 1% Decrease in ρ 3-7 Evolution of Total Skilled Labor Income for 1% Decrease in ρ 3-8 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Decrease in ρ 3-9 Evolution Of Threshold Level Of Entrepreneurial Ability mt* for 1% Decrease in k1 3-10 Evolution of Common Aggregate Stock Tt for 1% Decrease in k1 3-11 Evolution of Network Knowledge Stock K t for 1% Decrease in k1 3-12 Evolution of Integrated Productivity stock At for 1% Decrease In k1 for 1% Decrease in k1 viii 3-13 wts Evolution of Wage Gap u for 1% Decrease in k1 wt 3-14 Evolution of GDP for 1% Decrease in k1 3-15 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Decrease in k1 3-16 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Decrease in k1 3-17 Evolution of Total Unskilled Labor Income for 1% Decrease in k1 3-18 Evolution of Total Skilled Labor Income for 1% Decrease in k1 3-19 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Decrease in k1 3-20 Evolution of Common Aggregate Stock Tt for 1% Decrease in k 2 3-21 Evolution of Ratio of Network Knowledge Stock to Aggregate Stock Kt for Tt 1% Decrease in k 2 3-22 Evolution Of Ratio of Integrated Productivity Stock to Aggregate Stock At Tt for 1% Decrease in k 2 3-23 Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease in k 2 wts for 1% Increase in k 2 wtu 3-24 Evolution of Wage Gap 3-25 Evolution of GDP for 1% Decrease in k 2 3-26 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Decrease in k 2 ix 3-27 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Decrease in k 2 3-28 Evolution of Total Unskilled Labor Income for 1% Decrease in k 2 3-29 Evolution of Total Skilled Labor Income for 1% Decrease in k 2 3-30 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Decrease in k 2 3-31 Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Increase in H 3-32 wts Evolution of Wage Gap u for 1% Increase in H wt 3-33 Evolution of GDP for 1% Increase in H 3-34 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Increase in H 3-35 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Increase in H 3-36 Evolution of Total Unskilled Labor Income for 1% Increase in H 3-37 Evolution of Total Skilled Labor Income for Increase in H 3-38 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Increase in H 3-39 Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Increase in h wts for 1% Increase in h wtu 3-40 Evolution of Wage Gap 3-41 Evolution of GDP for 1% Increase in h 3-42 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Increase in h x 3-43 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Increase in h 3-44 Evolution of Total Unskilled Labor Income for 1% Increase in h 3-45 Evolution of Total Skilled Labor Income for Increase in h 3-46 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Increase in h 3-47 Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease in α wts for 1% Decrease in α wtu 3-48 Evolution of Wage Gap 3-49 Evolution of GDP for 1% Decrease in α 3-50 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Decrease in α 3-51 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Decrease in α 3-52 Evolution of Total Unskilled Labor Income for 1% Decrease in α 3-53 Evolution of Total Skilled Labor Income for 1% Decrease in α 3-54 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Decrease in α 3-55 Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease in γ wts for 1% Decrease in γ wtu 3-56 Evolution of Wage Gap 3-57 Evolution of GDP for 1% Decrease in γ 3-58 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Decrease in γ xi 3-59 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Decrease in γ 3-60 Evolution of Total Unskilled Labor Income for 1% Decrease in γ 3-61 Evolution of Total Skilled Labor Income for 1% Decrease in γ 3-62 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Decrease in γ 3-63 Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease in b 3-64 wts Evolution of Wage Gap u for 1% Decrease in b wt 3-65 Evolution of GDP for 1% Decrease in b 3-66 Evolution of Total Profits of All Firms Undertaking Integrated Mode of Production for 1% Decrease in b 3-67 Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of Production for 1% Decrease in b 3-68 Evolution of Total Unskilled Labor Income for 1% Decrease in b 3-69 Evolution of Total Skilled Labor Income for 1% Decrease in b 3-70 Evolution of Ratio of Total Skilled Labor Income to Total Unskilled Labor Income for 1% Decrease in b xii LIST OF SYMBOLS α β γ δ ρ χ a b d h v Entrepreneurial overload in training unskilled labor Diminishing rate of unskilled workers Entrepreneurial overload in training skilled labor Diminishing rate of effective labor hired in integrated production Cost before quality adjustment Diminishing rate of manual component Inefficiency of network knowledge contributing to present period output Inverse of matching between domestic firms and overseas supplier Diminishing rate of effective labor hired in outsourcing Human capital in foreign labor market Decrease in efficiency of foreign labor producing low-skilled intensive components HLSO t Effective workers LUt Unskilled workers S L U L H n1 n2 C1 C2 k1 k2 ε1 ε2 Vf Skilled labor supply Unskilled labor supply Human capital in local labor market Inefficiency of last period aggregate stock contributing to current network knowledge Inefficiency of last period aggregate stock contributing to current network knowledge Aggregate productivity in evolution of network knowledge stock Aggregate productivity in evolution of integrated productivity stock Rate at which previous network knowledge depreciates. Rate at which previous integrated productivity stock depreciates. Rate at which previous network knowledge depreciates. Rate at which previous integrated productivity stock depreciates. Manual component 1 1. Introduction By splitting up the production process into various components, international outsourcing has transformed the behavior of firms such that they no longer have to constrain production within the domestic country as they can now take advantage of the lower costs overseas. This is especially so when the host country for fragmented production components is a developing country. At the same time, the role of entrepreneurship has become increasingly important to not only utilize the cost advantage but also to manage production (Acemoglu et al., 2002b). In this paper, a simple dynamic model for a small, open and developed economy is constructed to examine the impact of the formation of network knowledge due to international outsourcing on the three key types of players in the domestic economy, which are namely the entrepreneurs, skilled and unskilled workers. We seek to investigate 1) the welfare between entrepreneurs and domestic workers and 2) the wage inequality between skilled and unskilled workers. The model is able to trace the evolution of GDP, profits, and wage incomes over time given various shocks to the economy. Greiner, Rubart and Semmler (2004) have observed that wage inequality had been increasing in the United States (U.S) and the United Kingdom (U.K) from early 1960s to late 1990s1. However, the pattern of wage inequality for West Germany is unclear. Using OECD data, they observed that wage inequality in West Germany has been decreasing over time from 1984 to 1996. In contrast, using disaggregated data from the Federal Office of Statistics, they observed that there is an upward trend in wage inequality. Most studies have attributed the upward trend due to the evolution of technology. Some of the most commonly cited reasons for the evolution of technology over time are skilled-biased technological change (Galor and Moav, 2000) and the 1 For the U.S, U.K and West Germany, cross-country data of wage differentials are taken from OECD Employment Outlook (1993,1996) whereby wage inequality is measured using the ratios of the 10th and 50th percentile to the 90th percentile wage earners. 2 development of skill-complementary technology due to the rapid increase in the supply of skilled labor (Acemoglu et al., 2002a). DeGroot (2001) also proposed that an increase in the efficiency of R&D labor via the accumulation of own past knowledge can achieve technical progress. Moreover, under the assumption that capital and unskilled labor are complements, Greiner, Rubart and Semmler (2004) postulated that technical progress is embodied within new capital goods since the amount of new capital goods affects the efficiency of both skilled and unskilled labor. According to Gao (2005)’s paper, he also postulated that the world’s growth rate increases when more resources are concentrated on R&D in the North2, given a reduction in trade costs due to globalization. Egger and Grossmann (2005) further postulated that the provision of firm-specific on-the-job training by high-skilled, non-production labor leads to accumulation of human capital. We break away from these usual conventions by postulating that the change in wage inequality over time is mainly due to the interaction effects of network stocks formed by entrepreneurs involved in integrated and outsourcing modes of production. One major motivation for the incorporation of network knowledge is that international outsourcing can be hindered by informal trade barriers, such as weak enforcement of international contracts (Anderson and Marcouiller, 2002) and inadequate information about international trading opportunities (Portes and Rey, 1999). Thus, we adopt Rauch (2001)’s approach whereby the development of business and social networks operating across national borders not only alleviate these problems, but also help in facilitating the transfer of technology to the recipient country. These networks also enable foreign agents to be connected to domestic networks via intermediaries. This is consistent with the increasing role of intra trade between parent firms and their affiliates as observed in reality. In Figure 1-1, although there are some fluctuations 2 A North-South endogenous growth model is used, whereby the North is abundant in skilled-labor. It is also assumed to be the only innovator in the world. In the model, there is relocation of production of unskilled components to the South. 3 in the ratio of volume of imports and exports between U.S parent companies and their foreign affiliates to the total volume of U.S imports and exports from 1982 to 1988, there is an upward trend in the percentage ratio from 1989 to 1994. Hence, over the period of 12 years, intra trade between U.S parent companies and their foreign affiliates has been steadily increasing from 18.8% in 1982 to 21.6% in 1994. FIGURE 1-1: PERCENTAGE RATIO OF VOLUME OF EXPORTS AND IMPORTS BETWEEN U.S PARENT COMPANIES AND THEIR FOREIGN AFFILIATES TO TOTAL VOLUME OF U.S EXPORTS AND IMPORTS 22.0% 21.5% 21.0% 20.5% 20.0% 19.5% 19.0% 18.5% 18.0% 17.5% 17.0% 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 Source: Our computations are based on U.S data from the Bureau of Economic Analysis3 In addition, using input-output data from six OECD countries and German timeseries data, Kleinert (2003) has also found strong empirical evidence of growing trade in intermediate goods due to the increasing importance of Multinational Enterprises (MNE) networks. The development and enhancement of such networks can lead to the accumulation of knowledge due to learning activities from abroad through the overseas intermediaries. As a result, technical progress takes place. For instance, through establishing intermediaries in Singapore, Multinational Corporations (MNCs) have gained knowledge such as better labor and capital management, and more efficient management of 3 We obtain the ratio by dividing the volume of exports and imports in terms of millions of US dollars between U.S parent companies and their foreign affiliates by the total volume of U.S exports and imports in terms of millions of US dollars. This is in turn multiplied by 100% in order to obtain the percentage ratio. 4 processing activities. They can therefore apply the knowledge gained to their parent companies, hence increasing their efficiency and output over time. We therefore adopt a simple framework that captures the evolution of technology due to the formation of networks. Using a simple dynamic model, we assume that there are two organizational forms of production in the domestic economy producing similar final products, namely vertically integrated production and outsourcing. We further assume that firms in the developed country are homogeneous and unconstrained by contracts. Firms adopting the vertically integrated mode of production are defined to produce both manual and skilled components, thereafter combining them to form a final product. In contrast, firms engaged in the outsourcing mode concentrate on producing skilled components and purchase manual components from an overseas supplier in a foreign, developing country, which is abundant in unskilled labor. The final product is produced through assembling them by the domestic firms. We hence investigate the impact of domestic firms forming networks within the two modes of production respectively, on the domestic economy. To introduce dynamics to the model in a simple manner, we let both types of networking affect the growth of integrated productivity stock and entrepreneurial network stock over time, which will in turn affect the aggregate stock of knowledge in the economy. The aggregate stock of knowledge will also influence the accumulation of the stocks of integrated productivity and entrepreneurial network in the next period. In this manner, we examine the dynamic linkage between the three stock variables – integrated productivity stock, entrepreneurial network stock, and aggregate stock of knowledge in the economy. We examine the above model via the incorporation of entrepreneurial ability to determine the threshold level above which international outsourcing will occur, which is often neglected by previous literature. This is crucial since entrepreneurs are required to train workers and coordinate outsourcing activities. In the outsourcing mode of 5 production, entrepreneurial ability is required to find the appropriate suppliers in the foreign, developing country. At the same time, entrepreneurs are required to train skilled labor to produce skilled components. Hence, the higher the ability to match firms to supplier, the higher the profit earned by the domestic firms. In the other mode of production, there is no need for entrepreneurial ability in matching since the integrated form of production is done in-house. However, entrepreneurial time is required to train both skilled and unskilled labor to produce skilled and unskilled components respectively. Another key assumption to note is that both home and foreign countries are assumed to have totally different production structures. Thus, human capital is assumed to be exogenous and different across the two countries. This idea is similar to the manager in Acemoglu et al. (2000b)’s model who have to spend time on both production and innovation activities, where skills are more important for the latter. However, in their paper, there exists only corner solution in the economy which is namely imitation-based or innovation-based equilibrium. This is mainly due to their assumption that the skill level of the manager takes on only two values to indicate that he is either high or low-skilled. We differ from their paper by assuming that the ability is uniformly distributed among entrepreneurs so as to allow for a mixed equilibrium, which is more consistent with reality. This implies that the higher the threshold level of entrepreneurial ability, the lower the fraction of firms outsourcing the manual part of the production activities. The idea of the threshold level of entrepreneurial ability is reminiscent of managerial incentives in Grossman and Helpman (2003). Using a threshold level of revenue that acts as the main determinant in choosing the organizational form and the location of their subsidiaries or suppliers, managerial incentives of heterogeneous firms in an industry were examined in the short run. This is under the assumption that the principals of a firm are constrained in the nature of contracts with suppliers and 6 employees. These principals can elect to outsource the production of components by choosing a supplier either in the North or in the South. Input costs and skills required to head a production unit are assumed to be lower in the South. They mainly investigated how firms with different productivity levels are sorted into different organizational forms. They suggested that the least and most productive firms will choose to obtain components from external suppliers from the South and the North respectively. Moreover, firms that operate foreign subsidiaries will be less productive than those that manufacture their own components in a plant nearer to their headquarters. Even though we adopt a different approach from theirs, our model in this paper however provides a richer picture since we investigate the transition of the threshold level of entrepreneurial ability over time. Our results reveal that there exists a mixed equilibrium in the long run whereby at a unique threshold level of entrepreneurial ability, slightly more than half of the firms in the economy will prefer vertical integration to international outsourcing. This is consistent with the trend in Figure 1 whereby the share of intra trade between U.S parent companies and foreign affiliates accounted for less than 50% of U.S total trade in the time period between 1982 and 1994. We also show that although the static model (without the evolution of the stock variables) is inadequate in explaining the impact of networking on the domestic economy, it is able to explain the impact of other exogenous parameters. We find that a reduction in the inefficiency of matching domestic firms to overseas supplier and a decline in the cost of manual components obtained from the overseas supplier will result in a lower threshold level of managerial ability. At the same time, wage inequality falls. Going one step further, we also compare our findings with previous literature’s results and find that most studies have only examined the impact on wage inequality or the decision to outsource, but not both at the same time. Hence, we are able to provide a richer model on the interdependence between entrepreneurs, skilled and unskilled workers. 7 Our model also reveals that as outsourcing activities increase, the welfare of workers decreases, while entrepreneurs’ welfare increases. Hence there is a trade off between the welfare of workers and entrepreneurs. Ethier (2005) has postulated that given the degree of complementarity between skilled labor and equipment, an increase in fragmentation will worsen the policy trade off of limiting the skill premium while maximizing employment. Our model is richer than Ethier’s as he has failed to take into account the role of entrepreneurs, hence neglecting to compare welfare between entrepreneurs and domestic workers. The remainder of our paper is organized as follows. Section 2 presents the static model and static optimization. Section 3 outlines the dynamic model and its steady state outcome, followed by a detailed discussion on the comparative statics for both static and dynamic models. A general discussion on the implications of the results is provided in Section 4. Section 5 concludes this paper. 2. The Model In this section, we first examine a simple static model set up before looking at the dynamic model in the latter section, whereby the evolution of network knowledge and integrated productivity stocks is introduced. 2.1 A Simple Static model In our model setup, we adopt some features similar to Acemoglu et al. (2002b). The economy consists of a continuum of non-overlapping generations of one-period lived agents. In each generation, there constitutes a mass 1 of entrepreneurs, which are the owners of the intermediate firms in the economy. They are profit maximizers and have the option to either engage in vertical integration within the economy, or to outsource the manual aspect of the production process to a foreign, developing country with abundant 8 unskilled labor, depending on the level of their entrepreneurial ability. Thus, there are two organizational forms of production in the economy. Firms produce according to an aggregate production function, which varies according to the form chosen. Hence, firms undertaking either mode of production produce a single, all-encompassing final good of unitary price, and operate within a perfectly competitive environment. 2.2 The Production Process Firms require either a combination of technology, unskilled labor and human capital augmented skilled labor or previous period network knowledge and human capital augmented skilled labor, depending on the organizational form of production chosen. All firms adhere to an aggregate Cobb-Douglas production function which satisfies the usual Inada conditions. We further assume that all firms experience decreasing returns to scale. To simplify the analysis, we assume that there is a fixed exogenous supply of high-skilled and low-skilled labor in the economy. Hence, we assume that skilled labor is mobile between firms undertaking the two different forms of production: L S = LSI + LSO (1) and total labor supply in the economy is equivalent to: L = LU + L S 2.2.1 (2) Firms Choosing To Adopt Vertical Integration The Cobb-Douglas production function is: B I = f (t tu , Lt )g (t ts , HLSIt ) = t tu Lut At t ts ( HLSIt ) δ α β γ (3) where α , β , γ , δ ∈ (0,1) . Firms hire unskilled labor Lut and human capital augmented skilled labor or effective labor HLSIt , and therefore incur wage costs from hiring skilled and unskilled labor, which are denoted by wtu and wts respectively. In addition, 9 entrepreneurs are required to split their time in training unskilled labor, t tu and skilled labor, t ts , such that: t tu + t ts = 1 (4) According to Acemoglu et al. (2002b), managerial overload is modeled by introducing a convex cost of effort into the cost function, whereby the higher the managerial effort, the higher the marginal cost of such effort. Since our model does not have a cost function for the coordination of activities for firms involved in integrated production, we model entrepreneurial overload in the training of unskilled and skilled labor through the parameters α and γ respectively, as t tu and t ts lies between zero and one. Similarly, as Lut and LSI t are less than one, β and δ imply that unskilled workers and effective workers increase at a diminishing rate respectively. 2.2.2 Firms Choosing To Engage In Outsourcing Activities Firms follow an aggregate production structure similar to that adopted in the vertical integration mode of production for easy comparison: c d B O = V fχ [ K t −1 mt t tSO ( HLSO t ) ] a b (5) where a, b, c, d ∈ (0,1) . The firm outsources the manual component to the foreign, developing country and purchases the manual component V f from the supplier at a unit cost of ρ hν , where ρ andν ∈ (0,1) . It can also be interpreted as the effective cost incurred after adjusting for the productivity of the supplier. ρ is seen as an indexing parameter and represents the cost before quality or productivity adjustment i.e. service link costs such as telecommunication, transport and coordination costs. A higher ρ would indicate that cost has increased, leading to an increase in the effective cost of purchasing the manual component. 10 The cost decreases with an increase in the foreign economy’s human capital h , h ∈ (0,1) . We assume that better-trained foreign workers are more efficient in producing the labor-intensive product but such efficiency diminishes with additional increase in human capital via the parameterν . In addition, it is assumed that the foreign UN economy follows a production structure such that V f = λLUN denotes the total t where Lt number of unskilled labor in the developing country and λ is an indexation productivity parameter for overall production in the foreign country. Since the two countries have different production structures, V f is assumed to be exogenous and experiences diminishing returns such that χ ∈ (0,1) . To simplify, V f can be also known as the marginal product of manual component. mt denotes entrepreneurial ability and is uniformly distributed between zero and one. Thus, the parameter b is the inverse of the matching of domestic firms with the overseas supplier. Since mt p 1 , the ability of a successful match decreases with an increase in b . It is to be noted that b is exogenous and may be influenced by government policies that facilitate success matching. K t −1 refers to previous period network knowledge and lies between zero and one in the static model. Thus, a refers to the inefficiency of network knowledge contributing to present period output. Since unskilled components have been outsourced to the foreign country, entrepreneurs are no longer required to hire and train unskilled workers and can fully concentrate on training skilled workers. Thus t tu = 0 and t tSO = 1 whereby ttSO denotes the time spent on training skilled workers in the outsourcing mode of production. Therefore, c denotes the share of time spent in training skilled labor. Similarly, as HLSO t is less than one, the total amount of effective workers increases at a diminishing rate through the parameter d . 11 2.3 Profit Functions Assuming that the price of the final product P takes on the unitary value of 1, firms adopting vertical integration face the aggregate profit function, which is denoted by π tI : π tI = B I − wtu Lut − wts LSIt (6) On the other hand, the portion of the firms that engages in international outsourcing activities faces the aggregate profit function, π tO , which is given by: ρ  V v  f h  π tO = B O − wts LSO − t 2.4 (7) Optimization Behavior Across The Economy. Firms maximize their profits subject to the time constraint: α Vertical integration: u max s u t t , t t , L t , L SI t β γ π tI = t tu L ut A t t ts ( HL SIt ) δ − w tu L ut − w ts L SIt (8) subject to equation (4).  ρ a b SO c χ I SO d s SO  = − − V [ K m t ( HL ) ] w L π Outsourcing: smax t f t − 1 t t t t t  hν t t , LSO t ,V f   V f   (9) subject to t tSO = 1 , since t tu = 0 . The Langrangian for each profit function can be written as follows: α β γ u s Vertical integration: l I = t tu Lut At t ts ( HLSIt ) δ − wtu Lut − wts LSI t + λ1 (1 − t t − t t ) (10) ρ a c b d s SO Outsourcing: l O = V fχ [ K t −1 mt t tSO ( HLSO − ν t ) ] − wt Lt h  (11)  V f + λ 2 (1 − t tSO )   where λ1 and λ 2 are the co-state variables for l 1 and l 2 respectively. 2.4.1 Firms Engaging In Vertical Iintegration The solutions obtained from the first order conditions are as follows: 12 α t tu α −1 α β α β −1 α β L ut β γ A t t ts ( HL γ t tu L ut A t t ts β t tu Lut γ −1 ( HL SI t )δ = λ1 (12) )δ = λ1 SI t (13) γ A t t ts ( HL SIt ) δ = w tu (14) γ δ t tu L ut A t t ts ( HL SIt ) δ −1 H = w ts (15) t tu + t ts = 1 (16) Equation (12) is seen as the marginal benefit of training unskilled labor to its marginal cost. Similarly, equation (13) is the marginal benefit of training skilled labor to its marginal cost. The left hand sides of equations (14)-(15) show the marginal products of the respective types of labor, whereas the right-hand sides are the marginal costs. Solving equations (12) to (16), we obtain the following optimal solutions: t ts = t tu = γ (17) α +γ α (18) α +γ    Lut =   1  α  Atδ δ H   α + γ L SI t   =    H δ β βδ  δ    α δ w ts  γ  α +γ    γ δ  β + δ −1    1− δ δ −1  β δ wtu δ   (19) 1 w ts 1− β (1− β ) w tu β  α  A t   α + γ  α  γ    α + γ  δ  β + δ −1      (20) From equations (19) and (20), we observe that the demand functions for unskilled and skilled labor supply are constrained by wage costs, integrated productivity and human capital in the economy. 13 Proposition 1: Profit for integrated production is positive if and only if the condition β + δ p 1 exists. Proof: See Appendix A. Hence, proposition 1 shows that both effective and unskilled labor must increase at a diminishing rate such that profit for integrated production is positive. Otherwise, firms will have to hire a large amount of effective and unskilled workers, resulting in negative profit as wage costs increase. Substituting equations (17) to (20) back into equation (6), we can re-express the profit function for the intermediate firm that engages in vertical integration as:   δ β  wts wtu I πt =  α γ   δ α   γ  At H  α + γ   α + γ       1  β +δ −1     1   δ δ β β        1 β +δ −1  1 −  δ 1−δ δ β  − − +  = π tI  wts , wtu , At       1 β +δ −1  1  −  1−β β  δ β  1 β +δ −1     (21) It can be seen that π tI has a positive relationship with integrated productivity whereas skilled and unskilled wages are inversely related with it. 2.4.2 Firms Engaging in Outsourcing Activities This time, the solutions under first order conditions are: χ a χ a b cV f K t −1 mt t ts c −1 d ( HLSO t ) = λ2 c d −1 dV f K t −1 mt t ts ( HLSO H = wts t ) b c d χV f χ −1 K t −1a mt b t ts ( HLSO t ) = t ts = 1 ρ hν (22) (23) (24) (25) 14 Equation (22) shows that the marginal benefit of training skilled labor is equaled to its marginal cost while equation (23) shows the marginal benefit of hiring skilled labor equaled to its marginal cost. Equation (24) indicates the marginal benefit of manual component to the marginal cost of acquiring it. Similarly, solving equations (22) to (25), the optimal solutions are:  ρ  V f =  ν  h χ d −1 1−d − χ  K ad d m b H d t  t −1 d s  wt  1  1−d −χ    1 LSO t  1−d − χ  s 1+ dχ −1− dχ  ρ  − χ a b d  wt 1− d − χ d 1− d − χ =  ν  K t −1 mt H     h χ   (26) 1  d −1    (27) From equations (26) and (27), it can be seen that the marginal product of manual component and demand for skilled labor are constrained by the cost of the manual component, previous period network knowledge stock, entrepreneurial ability, human capital and skilled wages. Proposition 2: Profit for outsourcing mode of production is positive if and only if the condition d + χ p 1 exists. Proof: See Appendix A. Thus, proposition 2 indicates that effective labor and marginal product of manual component must be increasing at a diminishing rate in order for entrepreneurs engaging in outsourcing activities to earn positive profits. If both increase at an increasing rate, entrepreneurs will earn negative profit as they have to incur higher costs in hiring more effective labor and purchasing manual components. Similarly, substituting equations (26) and (27) back into equation (7): 15 π O t   a b K m Hd =  t −1 χt   ρ  sd   ν  wt   h        1 1− d − χ   χ d χ d   ( ) 1 1− d − χ  χ d −1( d+ −χ1−)dχ −χ d   1  1− d − χ  − χ 1− d d d   (  − + +  = π tO  wts , K t −1 , mt    ) 1 1− d − χ      (28) From equation (28), it can be seen that previous period network knowledge, entrepreneurial ability and human capital are positively related to π tO while skilled wages and marginal product of manual component are inversely related to it. 2.5 Equilibrium In this section, we analyze firms’ decision to engage in international outsourcing or integration, depending on entrepreneurial ability. Firms will only decide to adopt the former when the profit from engaging in it is greater than that from vertical integration, i.e. π tO > π tI . 2.5.1 Threshold Level of Managerial Ability Setting π tI = π tO from equations (21) and (28) and rearranging the terms, we obtain the critical threshold level of managerial ability: w * mt =  H  s t where     δ (1− d − χ )+ d ( β +δ −1) b ( β +δ −1) χ  wu β  t  At  (1−d − χ )   ρ   ( β +δ −1)b   hν      K t −1a    1 b  1− d − χ  W    b  S   (29) 16    1 W = α  α   γ   α + γ   α + γ     and S =  χ χ d d    ( ) 1 1− d − χ    γ        1 β +δ −1   1  δ δ β β   − χ χd   d −1 + χ − d χ ( d −1 ) 1  β +δ −1    1 −  δ 1−δ δ β 1  β +δ −1    1 −  1− β β δ β )      1  1− d − χ  − χ 1− d d d   ( 1 1− d − χ 1   β +δ −1   (30)    (31) Proposition 3: Given the 3 conditions: 1) β + δ p 1 in Proposition 1, 2) d + χ p 1 in Proposition 2 and  ρ   ν  s u δ (1− χ )− d (1− β )   h  3) wt p wt  K t −1 a   χ β ( χ + d −1)       − b ( β +δ −1 ) b W    S  b ( d + χ −1 )( β +δ −1) b H δ (1− d − χ )+ d (β +δ −1) At (1− d − χ ) , an interior solution exists for mt* . Proof: See Appendix A. Proposition 3 indicates that if skilled wages are too large, all entrepreneurs will switch to vertically integrated production such that mt* = 1 as the cost of hiring skilled labor is too high for firms involved in outsourcing activities to earn positive profit. Hence, these three conditions must hold for 0 p mt* p 1 to exist. From equation (29), several things can be noted. There exists a unique m* whereby entrepreneurs with mt p m * will find it more profitable to undertake vertical integration, whereas those with mt f m * will choose to outsource manual component of the production process to the developing country. Secondly, we assumed that entrepreneurial ability is uniformly distributed in the interval [0, 1], thus m* is 17 constrained by the value 1. When m* = 1 , this implies that all managers find it profitmaximizing to engage in vertical integration. On the contrary, all firms prefer to choose the outsourcing mode of production when m* = 0 . Thus, a mixed equilibrium exists when 0 p m * p 1 , whereby managers decide to undertake vertical integration or outsource, depending on managerial ability. 2.5.2 Labor Market Equilibrium From equations (19), (20) and (27), we can derive the demands for unskilled and skilled workers in the domestic economy: m* Demand for unskilled labor= ∫ L dm u t ( = m t*φ1 w ts , w tu , At t ) (32) 0    where φ1 wts , wtu , At =   1  α  At δ δH  α + γ  ( ) δ wts    α δ  γ  α +γ    γ δ  β +δ −1   ,  1−δ δ −1  β δ wtu δ   (33) whereas m demand for skilled labor= * ∫ 1 L SI t dm t 0 = m t*φ 2 ( w ts , w tu , A t ) + ∫ + m L SO dm t t * (1 − 1+ b − d − χ  d − χ) φ 3 ( m t* , w ts , K t −1 )  1 − m * 1 − d − χ 1+ b − d − χ    s u where φ 2 ( w t , w t , A t ) =    H δ β βδ     (34) 1 w ts 1− β (1− β ) w tu β  α   A t  α + γ  1 α  γ    α + γ   1− d − χ  s 1+ dχ −1− dχ  ρ  − χ a s d  wt 1− d − χ d 1− d − χ and φ3 ( wt , K t −1 ) =  ν  K t −1 H   χ h     δ  β + δ −1      (35) 1  d −1    (36) 18 Since the supply of unskilled and skilled labor, which are denoted by L U and S L respectively, are assumed to be exogenous, we can solve for equilibrium wages in the U S labor market by equating equation (32) to L and equation (34) to L . After rearranging the terms, we obtain:  LU s wt =  *  mt      β + δ −1 δ  α Atδ δH  α + γ 1 α δ  γ    α + γ γ δ  β  1−δ δ wtu δ −1 δ (37)  δ −1  1 − d − χ + d χ   δ  (1 − d − χ )( d −1 ) 1 w tu δ φ 4 ( m t* , A t ) + φ 5 ( m t* , K t −1 )φ 6 ( m t* , At ) w tu    U 1− β β + δ −1  L m t* 1 * whereby φ 4 ( m t , At ) =  α H  α   γ  β At  α + γ   α + γ     φ5 (mt* , K t −1 ) = (1 − d − χ )  1 − m 1 + b − d − χ   U  L * and φ6 (mt , At ) =  *   mt      β +δ −1 δ S (38) 1 ( ) 1+ b − d − χ * 1− d − χ t =L    γ δ    ,     1  ρ    ν   H  h χ  −χ (39)  a K t −1   1 1−d − χ  −1−1−ddχ− χ d   1  d −1  (40)   1− d − χ + dχ  α At δ  α + γ 1 δ    α δ  γ  α + γ    γ δ  (1− d − χ )( d −1) 1−δ  β δ    (41) It can be seen from the two labor equations that the terms are too complicated to be solved simply. Together with equation (29), assuming that the two state variables At and K t −1 are exogenous, there are three endogenous variables in this system of equations, namely mt* , wts and wtu . Therefore, we shall use numerical simulation to solve for the three equations (29), (37) and (38) and study the properties of the system. Since the two labor equations are functions of mt* , we vary mt* to solve for the equilibrium values of wts and wtu . Thereafter, we substitute all the equilibrium values back into the two profit functions to obtain Figure 2-1. Hence, the figure shows the two 19 profit functions corresponding to the two different modes of production, which are denoted by π tI and π tO respectively, with respect to the level of entrepreneurial ability m . π tI shows a downward sloping convex curve, whereas π tO is an upward sloping concave curve. The intersection of the two curves will give a unique m* . From the figure, it is obvious that entrepreneurs with entrepreneurial ability less than m* will opt to undertake vertical integration in order to maximize profit. On the contrary, those with entrepreneurial ability greater than m* will choose to outsource the manual aspect of the production process to the foreign country. This is because profit earned from outsourcing activities is higher than that from vertical integration. Besides indicating firms’ decision to outsource or do vertical integration, the unique threshold level shows the share of firms that undertakes vertical integration as m* . In contrast, 1 − m* indicates the amount of firms engaging in outsourcing activities. Hence m* have two properties: 1) the ability of entrepreneurs to match firms to foreign supplier and 2) a measure of the fraction of firms choosing to adopt vertical integration. FIGURE 2-1: PROFITS OF INTEGRATION AND OUTSOURCING FIRMS π πO 0.25 0.2 0.15 πI 0.1 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m 20 3. Dynamic Model In this section, we introduce simple evolution mechanism of the entrepreneurial network stock and integrated productivity stock and proceed to investigate how the evolutions of the two stock variables, At and K t , may affect the organizational form of production and factor prices over time. 3.1 The Model We assume that interaction between firms involved in vertical integration and outsourcing activities in the domestic economy has spillover effects on next period’s common aggregate stock, Tt . This is modeled in the following equation: Tt = mt*−1 At −1 + (1 − mt*−1 ) K t −1 (42) Thus, present period’s common aggregate stock is influenced by spillover effects from previous period’s entrepreneurial ability mt*−1 , integrated productivity stock At −1 and network knowledge stock K t −1 . Such spillover effects will indirectly affect both the evolutions of present period’s At and K t . For the evolution of network knowledge stock, we use the following equation: K t = C1Tt −1 1 (1 − mt*−1 ) k1 + (1 − ε 1 ) K t −1 n (43) where C1 , n1 , k1 , ε 1 ∈ (0,1) . Since Tt −1 is less than 1, n1 refers to the inefficiency of last period’s common aggregate stock contributing to current network knowledge stock while k1 refers to the inverse of networking efficiency among firms engaging in outsourcing activities. C1 acts as an indexing parameter to the first term in the equation and can be treated as aggregate productivity. In the second term of the equation, ε 1 refers to the rate at which previous period’s network knowledge depreciates. Hence, the second term on 21 the right hand side of the equation indicates the portion of past period’s network knowledge that contributes to future network knowledge stock. The equation for the evolution of integrated productivity stock follows a similar framework and is given as: k At = C 2Tt −1 2 mt*−1 2 + (1 − ε 2 ) At −1 n (44) where C 2 , n2 , k 2 , ε 2 ∈ (0,1) . Similarly, n2 indicates the inefficiency of last period’s common aggregate stock contributing to integrated productivity stock while k 2 refers to the inverse of networking inefficiency among firms choosing to undertake vertical integration. Similarly, C 2 is treated as an aggregate productivity to At and ε 2 determines the rate at which integrated productivity depreciates. Hence, we observe that the common aggregate stock Tt is eventually made up of lagged effects of Tt and mt* since Tt is a function of K t −1 and At −1 . 3.2 Baseline Steady- state System Setting Tt = Tt −1 , mt* = mt*−1 , At = At −1 and K t = K t −1 , we can obtain: Tt = mt* At + (1 − mt* )K t (45) C1Tt 1 (1 − mt* ) k1 − ε 1 K t = 0 (46) n k C 2Tt 2 mt* 2 − ε 2 At = 0 n (47) 1 χ b (1−d − χ )   ρ   δ (1− d − χ )+ d ( β +δ −1) 1− d − χ s  u β  ( β +δ −1)b   ν   b ( β +δ −1)   w w W h        b  t  mt* =  t  H   Ka  S  At       t    where (48) 22    W =  α   α + γ    S =  χ χd d   (  LU s wt =  *  mt      1    α  γ  α +γ ) 1 1− d − χ β + δ −1 δ    γ        1 β +δ −1  − χ χd     1  δ δ β β  d −1 + χ − d χ ( d −1 )  1 −  δ 1−δ δ β δ  γ    α + γ ( γ δ  β  1−δ δ wtu ) 1  β +δ −1  1  −  1− β β  δ β 1  1− d − χ  − χ 1− d d d   α  α Atδ δH  α + γ 1 1  β +δ −1   1 1− d − χ      (50) δ −1 δ (51)  δ − 1  1− d − χ + d χ   δ  (1 − d − χ )( d −1 ) 1 w tu δ φ 4 ( m t* , A t ) + φ 5 ( m t* , K t )φ 6 ( m t* , At ) w tu    U 1− β β + δ −1  L m t* 1 * whereby φ 4 ( m t , At ) =  α H  α   γ  β At  α + γ   α + γ     =L S    γ δ    ,    (53) 1 φ5 (mt* , K t ) = (1 − d − χ )  1 − m 1 + b − d − χ   U  L * and φ6 (mt , At ) =  *   mt      β +δ −1 δ (52) 1 ( ) 1+ b − d − χ * 1− d − χ t 1   β +δ −1   (49)    −χ  1−d − χ  −1− dχ  1  ρ  a  d 1− d − χ   ν  K t    H  h χ    1  d −1    (54) 1− d − χ + dχ  α At δ  α + γ 1 δ    α δ  γ  α + γ    γ δ  (1− d − χ )( d −1) 1−δ  β δ    (55) Substituting equations (43) and (44) into equations (46) and (47) respectively, we can further obtain: [ ] C mt* At + (1 − mt* )K t (1 − mt* ) k − ε 1 K t = 0 n [ ( ) ] n k and C mt* At + 1 − mt* K t mt* − ε 2 At = 0 (56) (57) Using equations (48), (51), (52), (56) and (57) to solve for the baseline steady state values, it can be seen that the equations are too complex to simply obtain an analytical solution 23 for the five endogenous variables mt* , K t , At , wts and wtu . Subsequently, we use numerical simulation4 to obtain the baseline values and the corresponding comparative statics of the system of equations. 3.3 Parameterization The parameter values for the baseline simulation of both static and dynamic models are presented in Table 1 and 2 respectively. We have adopted the same parameter values for the numerical simulation of the dynamic model, so that we can easily analyze the changes in the endogenous variables in both short and long runs. The appropriate parameters are being set at values so as to satisfy Propositions 1, 2 and 3, which have held the guidelines 1) profits for both modes of production are positive, 2) the wage gap wts is greater than one and 3) there exists an interior solution wtu for mt* . Since our focus is on a mixed equilibrium in the economy, corner solutions are ignored. The supply of skilled labor L S is also assumed to be 0.7, in order to reflect the fact that the domestic developed country has a larger pool of skilled labor. The human capital of foreign labor market h is set to be 0.2, which is lower than the domestic country’s human capital of 0.3 so as to reflect the lower level of human capital in the foreign, developing country. Moreover, we assume α 1 p α 2 because setting α 1 = α 2 and α 1 f α 2 do not yield any interior solution in the dynamic model. We further assume that ε 1 p ε 2 in the dynamic model, whereby integrated productivity stock depreciates faster than network knowledge stock, otherwise no interior solution can be achieved as all firms will move towards integrated production when ε 1 f ε 2 or ε 1 = ε 2 . Intuitively, 4 All numerical simulations are run using MATLAB 6.1. 24 entrepreneurs who are involved in international outsourcing are more capable than those choosing to adopt vertical integration since they have higher entrepreneurial ability. Therefore, the network knowledge stock created is more durable than integrated productivity stock. This results in the former stock depreciating slower than the latter stock. Given these parameters, we are able to obtain a unique and stable steady state solution for each of the endogenous variables, where no multiple equilibriums exist. To check the stability of these steady state values, we have done some calibrations and observe that any slight (1%) changes in the values will always evolve back to the original steady state values. The existence of a unique and stable steady state for the threshold level of entrepreneurial ability tallies with reality, whereby firms choose either to outsource or undertake vertical integration. TABLE 1: PARAMETER VALUES USED FOR BASELINE STATIC MODEL Parameter Entrepreneurial overload in training unskilled labor Diminishing rate of unskilled workers Entrepreneurial overload in training skilled labor Diminishing rate of effective labor hired in integrated production Cost before quality adjustment Diminishing rate of manual component Inefficiency of network knowledge contributing to present period output Inverse of matching between domestic firms and overseas supplier Diminishing rate of effective labor hired in outsourcing Human capital in foreign labor market Decrease in efficiency of foreign labor producing low-skilled intensive components Skilled labor supply Unskilled labor supply Human capital in local labor market Integrated productivity stock Network knowledge stock α β γ δ ρ χ Value 0.15 0.1 0.3 0.3 0.79 0.25 a b d h 0.1 0.6 0.1 0.2 v 0.2 S L U L H At Kt 0.7 1 0.3 0.5457 0.6556 25 TABLE 2: PARAMETER VALUES USED FOR BASELINE SIMULATION Parameter Entrepreneurial overload in training unskilled labor α β γ δ ρ χ Diminishing rate of unskilled workers Entrepreneurial overload in training skilled labor Diminishing rate of effective labor hired in integrated production Cost before quality adjustment Diminishing rate of manual component Inefficiency of network knowledge contributing to present period output Inverse of matching between domestic firms and overseas supplier Diminishing rate of effective labor hired in outsourcing Human capital in foreign labor market Decrease in efficiency of foreign labor producing low-skilled intensive components Unskilled labor supply Human capital in local labor market Inefficiency of last period aggregate stock contributing to current network knowledge Inefficiency of last period aggregate stock contributing to current network knowledge Aggregate productivity in evolution of network knowledge stock Aggregate productivity in evolution of integrated productivity stock Inverse of networking efficiency in outsourcing mode Inverse of networking efficiency in integrated production mode Rate at which previous integrated productivity stock depreciates. 3.4. 0.1 0.6 0.1 0.2 v 0.2 L U L H 0.7 n1 0.3 n2 C1 0.3 C2 k1 k2 0.3 ε1 ε2 Rate at which previous network knowledge depreciates. 0.15 0.1 0.3 0.3 0.79 0.25 a b d h S Skilled labor supply Value 1 0.3 0.3 0.3 0.3 0.3 0.4 Simulation Results The baseline steady state values are presented in Table 3 below. TABLE 3: BASELINE STEADY STATE VALUES Threshold level of * SS entrepreneurial ability, m Integrated productivity stock, A SS Network knowledge stock, K SS SS 0.5860 Skilled wage, w s 0.5457 Unskilled wage, w u 0.6556 Common aggregate stock, T SS 0.0952 SS 0.0173 0.5912 Note: The above values are all corrected to 4 significant figures. It can be seen from the above table that there exists a unique and stable mixed equilibrium in the long run. Slightly more than half of the total number of entrepreneurs in the economy will choose to adopt vertical integration whereas the remaining portion will engage in outsourcing activities. The baseline wage gap is observed to be 5.5029. 26 Since the common aggregate stock T SS is a function of m * SS , A SS and K SS , it is SS sufficient to look at the changes in the five endogenous variables, which are namely m * , SS SS w s , w u , A SS and K SS . We also note that it is impossible to show a phase diagram for these endogenous variables. Hence, in the following section, individual phase diagram will be generated for each of them. We observe that K t and At will evolve smoothly to the steady state values since they are state variables. They do not jump upon any changes even though a 1% variation is made one at a time for each exogenous variable, and therefore undergo a smooth transition to the new steady state values. 3.5 Welfare Of The Domestic country Using the baseline steady state values, we can easily obtain the GDP of the domestic country at each time period by summing up the total profits of all firms undertaking vertical integration, total profits of all firms doing outsourcing activities, skilled and unskilled labor income. This can be expressed in the following equation: GDPt = ∫ m* 0 1 * U S * π tI dm + ∫ π tO dm +w tu L + w tS L m * 1  β +δ −1    1 1 1   sδ u β β +δ −1  β +δ −1  β +δ −1   1 1 1 w w     * t t    δ β  −  δ 1−δ  −  1−β β  = mt  α γ    δ β δ β δ β        A H δ  α   γ      t       α + γ   α +γ    1  1−d − χ     a d  b +1−d − χ   1 − d − χ   χ d * 1−d − χ  Kt −1 H  1 − mt  + χ χ d  ρ  sd  b + 1 − d − χ    ν  wt    h      ( * U * + wtu L + wtS L ) 1 1−d − χ 1 1−d − χ d −1+ χ −dχ   −  χ χ d (d −1)        1  (58) − χ1−d d d 1−d − χ     ( ) S Thus, we can obtain the baseline values for the various components of GDP, which is presented in Table 4 below: 27 TABLE 4: BASELINE VALUES FOR VARIOUS COMPONENTS OF GDP 0.2841 Labor income of skilled workers 0.0667 GDP Profit of all firms undertaking Labor income of unskilled 0.1036 0.0173 integrated mode of production workers Profit of all firms undertaking 0.0967 outsourcing mode of production Note: The above values are all corrected to 4 significant figures. Therefore, in the long run, it can be seen that the total profits of all firms undertaking integrated mode of production is greater than that for all firms undertaking outsourcing mode of production as more than half of the all entrepreneurs in the economy will choose to engage in the integrated mode of production. 3.6 Comparative Statics Analysis In this section, we examine the effects of various exogenous changes, one at a time, on the five endogenous values. Before proceeding to do so, we first present a summary of the comparative statics for the static model in Table 5. As K t and At are chosen at steady state values in the static model, it thus shows the short run effects on the economy. Thereafter, Table 6 shows a summary of the comparative statics for the dynamic model. Thus, we analyze short run and long run changes based on these two tables. Moreover, we analyze the transition of GDP and its various components over time. A detailed discussion of the results is made in the following sub-sections. 28 TABLE 5: SUMMARY OF COMPARATIVE STATICS RESULTS FOR BASELINE STATIC MODEL A 1% increase in variable α β γ δ ρ χ a b d h v L S U L H At Kt m* %change in entrepreneurial ability, m* ws wu ws/wu % change in wage gap, ws/wu 0.58499 -0.17065 0.09504 0.01721 5.52287 0.11572 0.58547 0.58524 0.58167 0.58803 0.59157 0.58634 0.58854 0.58773 0.58559 0.58665 -0.08874 -0.12799 -0.73721 0.34813 0.95223 0.05973 0.43516 0.29693 -0.06826 0.11263 0.09524 0.09509 0.09580 0.09526 0.09541 0.09523 0.09532 0.09544 0.09521 0.09524 0.01743 0.01722 0.01709 0.01731 0.01739 0.01727 0.01732 0.01729 0.01725 0.01728 5.46292 5.52125 5.60666 5.50373 5.48766 5.51439 5.50398 5.52030 5.51890 5.51224 -0.97104 0.08751 1.63470 -0.23123 -0.52242 -0.03793 -0.22656 0.06926 0.04376 -0.07687 0.58701 0.17406 0.09458 0.01734 5.45544 -1.10650 0.58660 0.58701 0.10410 0.17406 0.09533 0.09553 0.01712 0.01734 5.56790 5.51001 0.93206 -0.11737 0.59212 1.04609 0.09631 0.01758 5.47858 -0.68703 0.58518 -0.13823 0.09520 0.01724 5.52158 0.09232 0.58599 0.09522 0.01726 5.51648 Baseline Note: Since c has no impact on the static model, we do not investigate its effect. All values are corrected to 5 significant figures in order to reflect changes accurately. 29 TABLE 6: SUMMARY OF COMPARATIVE STATICS RESULTS FOR DYNAMIC MODEL A 1% increase in parameter %change in entrepreneurial ability, m* %change in A %change in K* ws/wu %change in wage gap, ws/wu Entrepreneurial overload in training unskilled labor Diminishing rate of unskilled workers Entrepreneurial overload in training skilled labor Diminishing rate of effective labor hired in integrated production Cost before quality adjustment Diminishing rate of manual component Inefficiency of network knowledge contributing to present period output Inverse of matching between domestic firms and overseas supplier Diminishing rate of effective labor hired in outsourcing Human capital in foreign labor market Decrease in efficiency of foreign labor producing lowskilled intensive components α -0.2526 -0.0531 0.1266 5.5233 0.1191 β -0.1331 -0.0348 0.0656 5.4713 -0.8233 γ -0.1843 -0.0531 0.0961 5.5233 0.1191 δ -0.9523 -0.2364 0.4622 5.6000 1.5102 ρ 0.5154 0.1301 -0.2395 5.4828 -0.6150 χ 1.4028 0.3317 -0.6818 5.4743 -0.7686 a 0.0887 0.0202 -0.0412 5.5087 -0.1453 b 0.6348 0.1484 -0.3005 5.4885 -0.5108 d 0.4300 0.1118 -0.2090 5.5260 0.1690 h -0.0990 -0.0165 0.0503 5.5349 0.3299 v 0.1741 0.0385 -0.0717 5.5087 -0.1453 Skilled labor supply L 0.2594 0.0568 -0.1175 5.4368 -1.4484 0.1570 0.0385 -0.0717 5.5789 1.1286 H 0.2594 0.0568 -0.1175 5.4943 -0.4066 n1 -0.0137 -0.0348 -0.1785 5.5029 -0.2501 n2 -0.2867 -0.2547 0.1114 5.5174 0.0137 C1 1.9147 1.8894 0.4927 5.4358 -1.4670 C2 1.8635 1.6878 -0.6666 5.4551 -1.1172 Unskilled labor supply Human capital in local labor market Inefficiency of last period aggregate stock contributing to current network knowledge Inefficiency of last period aggregate stock contributing to current network knowledge Aggregate productivity in evolution of network knowledge stock Aggregate productivity in evolution of integrated productivity stock baseline ws/wu L S U 5.5167 30 A 1% increase in parameter %change in entrepreneurial ability, m* %change in A %change in K* ws/wu %change in wage gap, ws/wu Inverse of networking -0.0137 -0.0531 -0.3005 5.5192 0.0449 efficiency in outsourcing k1 mode Inverse of networking efficiency in integrated -0.3038 -0.2730 0.1114 5.5174 0.0137 k2 production mode Rate at which previous -0.0478 -0.1997 -1.1547 5.5233 0.1191 network knowledge ε1 depreciates. Rate at which previous -1.8055 -1.6475 0.6452 5.5928 1.3800 integrated productivity stock ε2 depreciates. baseline ws/wu 5.5167 Note: Since c has no impact on the static model, we do not investigate its effect. The values are corrected to 4 significant figures 3.6.1 Cost Before Quality Adjustment, ρ We now consider how the economy evolves to its new steady state when there is a decrease in ρ , which is the cost before quality or productivity adjustment. As mentioned earlier, such cost can also be seen as service link cost which is related to transportation, communication and coordination cost and the degree of openness of the developing country. In the short run, the portion of firms involved in vertical integration decreases. Intuitively, as the service link cost decreases, the cost of purchasing low quality final components subsequently decreases. Thus, firms are encouraged to purchase more manual components instead of producing them in-house. This is consistent with Grossman and Helpman (2003) whereby a decrease in trading costs will encourage * outsourcing. Similarly, m SS evolves to a lower steady state in the long run. 31 FIGURE 3-1: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% DECREASE IN ρ 0.586 0.5855 0.585 m* 0.5845 0.584 0.5835 0.583 0.5825 0 20 40 60 80 t 100 120 140 160 In both short and long runs, a decrease in ρ causes wage inequality to increase. This is because firms demand more skilled labor as the demand for outsourcing mode rises. Subsequently, the wage gap increases and converges to a higher new steady state as seen in Figure 3-2. It is to be noted that we have presented the figures with time periods till 160 so as to provide a clear picture that each endogenous variables will converge to a new steady state in the long run. In contrast, the figures for GDP and its various components are presented with time periods till 40 for the benefit of readers to clearly observe the changes that occur within the first few time periods. FIGURE 3-2: EVOLUTION OF WAGE GAP wts FOR 1% DECREASE IN ρ wtu 5 .5 36 5 .5 34 5 .5 32 5 .53 ws/wu 5 .5 28 5 .5 26 5 .5 24 5 .5 22 5 .52 5 .5 18 5 .5 16 0 20 40 60 80 t 100 120 140 160 32 It can be seen from Figure 3-3 that GDP will initially overshoot in the short run as the total profits for all firms in outsourcing increase more than the fall in labor income. However, it will eventually diminish as the fall in both skilled and unskilled labor income outweighs the increase in total profits even though the labor income gap has increased. Hence, it can be seen that the welfare of entrepreneurs increases although that for both types of labor declines over time. We also observe that the pattern of labor income inequality is similar to that of wage inequality, mainly because the supply stocks of skilled and unskilled labor are constant over time. FIGURE 3-3: EVOLUTION OF GDP FOR 1% DECREASE IN ρ 0.2845 GDP 0.2844 0.2843 0.2842 0.2841 0 5 10 15 20 t 25 30 35 40 FIGURE 3-4: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN ρ 0.1037 0.1036 totalpieI 0.1035 0.1034 0.1033 0.1032 0.1031 0.103 0 5 10 15 20 t 25 30 35 40 33 FIGURE 3-5: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN ρ 0.098 0.0978 totalpieO 0.0976 0.0974 0.0972 0.097 0.0968 0.0966 0 5 10 15 20 t 25 30 35 40 FIGURE 3-6: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN ρ 0.0173 0.0173 total wu income 0.0172 0.0172 0.0172 0.0172 0.0172 0 5 10 15 20 t 25 30 35 40 FIGURE 3-7: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% DECREASE IN ρ 0.0667 0.0667 total ws income 0.0666 0.0666 0.0666 0.0666 0.0666 0.0665 0.0665 0 5 10 15 20 t 25 30 35 40 34 FIGURE 3-8: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN ρ 3.876 3.874 ws income/wu income 3.872 3.87 3.868 3.866 3.864 3.862 3.86 0 5 10 15 20 t 25 30 35 40 3.6.2 Changes In Parameters Affecting Networking Of Both Types Of Entrepreneurs 3.6.2.1 A Decrease In Inverse Of Networking Efficiency In Outsourcing Mode, k1 To examine the impact of networking in outsourcing or integrated activities by entrepreneurs on the mode of production chosen, we first isolate the change in parameters to that in k1 . In the short run, it is observed that a decrease in inverse of networking efficiency in outsourcing initially causes mt* to jump up in the first period. The reason behind the jump is unknown to us. However, in the next period, the decline in mt* is intuitive as entrepreneurs prefer to do more outsourcing due to the increase in networking efficiency in outsourcing. However, in the long run, as Tt −1 increases further with no further decrease in k1 , both At and K t increase, causing profits for both integrated and outsourcing mode to increase. Differentiating profit equations (21) and (28) with respect to the two different types of stocks, we obtain the following equations: ∂ ln π tI 1 = ∂At β + δ −1 (59) ∂ ln π tO a = ∂K t −1 1− d − χ (60) 35 Substituting the parameter values from Table 3 into the above equations, we can obtain the magnitude for each of the elasticity of the two profit equations to be ∂ ln π tI ∂ ln π tO = 1.66667 and = 0.230769 respectively. Since the elasticity of integrated ∂At ∂K t −1 profit is greater than that of outsourcing, the positive impact on integrated profit is larger when the percentage increase in At is similar to that in K t , holding other things constant. However, it can be seen that other factors do not remain constant. Hence in the short run, the direct effect of a fall in k1 dominates whereas integrated productivity stock dominates in the long run due to the elasticity effect. Correspondingly, wage gap initially decreases and then increases in the short run. In the long run, wage inequality converges to a lower steady state as the integrated mode of production gains dominance in the economy. FIGURE 3-9: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% DECREASE IN k1 0.5861 0.5861 0.586 0.586 m* 0.586 0.586 0.586 0.5859 0.5859 0.5859 0.5859 0 20 40 60 80 t 100 120 140 160 36 FIGURE 3-10: EVOLUTION OF COMMON AGGREGATE STOCK Tt FOR 1% DECREASE IN k1 0.5922 0.592 T 0.5918 0.5916 0.5914 0.5912 0.591 0 20 40 60 80 t 100 120 140 160 FIGURE 3-11: EVOLUTION OF NETWORK KNOWLEDGE STOCK K t FOR 1% DECREASE IN k1 0.658 0.6575 K 0.657 0.6565 0.656 0.6555 0 20 40 60 80 t 100 120 140 160 FIGURE 3-12: EVOLUTION OF INTEGRATED PRODUCTIVITY STOCK At FOR 1% DECREASE IN k1 0.546 0.5459 0.5459 A 0.5458 0.5458 0.5457 0.5457 0.5456 0 20 40 60 80 t 100 120 140 160 37 wts FIGURE 3-13: EVOLUTION OF WAGE GAP u FOR 1% DECREASE IN k1 wt 5.5174 5.5172 5.517 ws/wu 5.5168 5.5166 5.5164 5.5162 5.516 5.5158 0 20 40 60 80 t 100 120 140 160 We further observe that an increase in networking efficiency among firms engaging in outsourcing activities will increase GDP over time as seen in Figure 3-14 below. The majority of the increase in GDP is contributed by the increase in total profits of all firms undertaking the integrated mode of production. Both skilled and unskilled workers gain too as the integrated mode of production dominates in the long run. At the same time, income inequality falls. In this case, the overall welfare of entrepreneurs has decreased. FIGURE 3-14: EVOLUTION OF GDP FOR 1% DECREASE IN k1 0.2843 0.2843 0.2843 0.2843 GDP 0.2842 0.2842 0.2842 0.2842 0.2842 0.2841 0.2841 0 5 10 15 20 t 25 30 35 40 38 FIGURE 3-15: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN k1 0.1036 totalpieI 0.1036 0.1036 0.1036 0.1036 0 5 10 15 20 t 25 30 35 40 FIGURE 3-16: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN k1 0.0967 0.0967 totalpieO 0.0967 0.0967 0.0967 0.0967 0.0967 0.0967 0 5 10 15 20 t 25 30 35 40 FIGURE 3-17: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN k1 0.0173 0.0173 total wu income 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0 5 10 15 20 t 25 30 35 40 39 FIGURE 3-18: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% DECREASE IN k1 0.0667 0.0667 0.0667 total ws income 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0 5 10 15 20 t 25 30 35 40 FIGURE 3-19: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN k1 3.8621 3.862 ws income/wu income 3.8619 3.8618 3.8617 3.8616 3.8615 3.8614 3.8613 3.8612 3.8611 0 5 10 15 20 t 25 30 35 40 3.6.2.2 A Decrease In Inverse Of Networking Efficiency In Vertically Integrated Mode, k2 Next, isolating the change to that in k 2 , a decrease in the inverse of networking efficiency in networking among firms undertaking vertical integration implies that the demand for outsourcing activities falls. Hence, there is an increase in demand for integrated production, as shown by a decrease in mt* . The increase in the accumulation of integrated productivity stocks over time causes At to rise over time. In contrast, the Tt decline in network knowledge stocks due to the fall in demand for outsourcing activities 40 Kt over time. Hence, integrated production dominates in both short Tt leads to a decline in and long runs. Subsequently, this results in a narrowing of wage gap. Similarly, an increase in the networking efficiency among firms undertaking integrated mode of production will cause GDP to increase over time as seen in Figure 325. This increase is due to the dominance of the increase in total profits of all firms undertaking the integrated mode of production and labor income over the decrease in total profits of all firms undertaking outsourcing mode of production. Hence, workers in the domestic economy gain from the increase in k 2 . FIGURE 3-20: EVOLUTION OF COMMON AGGREGATE STOCK Tt FOR 1% DECREASE IN k 2 0.5916 0.5916 0.5915 0.5915 T 0.5914 0.5914 0.5913 0.5913 0.5912 0.5912 0.5911 0 20 40 60 80 t 100 120 140 160 FIGURE 3-21: EVOLUTION OF RATIO OF NETWORK KNOWLEDGE STOCK TO COMMON AGGREGATE STOCK Kt FOR 1% DECREASE IN k 2 Tt 1.1095 1.109 K/T 1.1085 1.108 1.1075 1.107 0 20 40 60 80 t 100 120 140 160 41 FIGURE 3-22: EVOLUTION OF RATIO OF INTEGRATED PRODUCTIVITY STOCK TO AGGREGATE STOCK At FOR 1% DECREASE IN k 2 Tt 0.9255 0.925 A/T 0.9245 0.924 0.9235 0.923 0 20 40 60 80 t 100 120 140 160 FIGURE 3-23: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% DECREASE IN k 2 0.588 0.5875 m* 0.587 0.5865 0.586 0.5855 0 20 40 60 80 t 100 FIGURE 3-24: EVOLUTION OF WAGE GAP 120 140 160 wts FOR 1% DECREASE IN k 2 wtu 5.52 5.518 5.516 ws/wu 5.514 5.512 5.51 5.508 5.506 5.504 0 20 40 60 80 t 100 120 140 160 42 FIGURE 3-25: EVOLUTION OF GDP FOR 1% DECREASE IN k 2 0.2846 0.2845 GDP 0.2844 0.2843 0.2842 0.2841 0.284 0 5 10 15 20 t 25 30 35 40 FIGURE 3-26: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN k 2 0.1042 0.1041 totalpieI 0.104 0.1039 0.1038 0.1037 0.1036 0.1035 0 5 10 15 20 t 25 30 35 40 FIGURE 3-27: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN k 2 0.0967 totalpieO 0.0966 0.0965 0.0964 0.0963 0 5 10 15 20 t 25 30 35 40 43 FIGURE 3-28: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN k 2 0.0173 0.0173 0.0173 total wu income 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0 5 10 15 20 t 25 30 35 40 FIGURE 3-29: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% DECREASE IN k 2 0.0669 0.0669 total ws income 0.0668 0.0668 0.0668 0.0667 0.0667 0 5 10 15 20 t 25 30 35 40 FIGURE 3-30: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN k 2 3.863 3.862 ws income/wu income 3.861 3.86 3.859 3.858 3.857 3.856 3.855 3.854 0 5 10 15 20 t 25 30 35 40 44 3.6.3 Changes In Parameters Affecting Both Local And Foreign Labor Markets 3.6.3.1 An Increase In Human Capital In The Local Labor Market, H As the skill profile of the domestic economy is enhanced through an exogenous increase in human capital H , vertical integration mode gains a greater share in the economy in the short run. This is because the supply of skilled labor has increased, hence raising the profit for integrated production more than that for outsourcing. This is mainly due to the parameter values whereby δ > d such that the increase in human capital given a fixed value of δ in firms adopting vertical integration will contribute to a higher increase in profit than that for firms engaged in international outsourcing, while holding d fixed. In the long run, entrepreneurial ability similarly converges to a higher steady state. FIGURE 3-31: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% INCREASE IN H 0.5875 m* 0.587 0.5865 0.586 0 20 40 60 80 t 100 120 140 160 Hence, wage inequality decreases in both short and long runs since the fall in demand for outsourcing will lead to an overall decline in demand for all skilled labor. Conversely, demand for unskilled labor increases, thus increasing wages for such workers. Figure 3-32 shows the transition of wage gap over time. 45 wts FIGURE 3-32: EVOLUTION OF WAGE GAP u FOR 1% INCREASE IN H wt 5.517 5.516 5.515 5.514 ws/wu 5.513 5.512 5.511 5.51 5.509 5.508 5.507 0 20 40 60 80 t 100 120 140 160 An increase in the human capital of the local labor market will also result in an increasing GDP over time. The increase in total profits of all entrepreneurs undertaking the integrated mode of production and total labor income has not only offset the fall in total profits of all entrepreneurs engaging in outsourcing activities, but also dominates it. FIGURE 3-33: EVOLUTION OF GDP FOR 1% INCREASE IN H 0.285 0.2849 0.2848 GDP 0.2847 0.2846 0.2845 0.2844 0.2843 0.2842 0.2841 0 5 10 15 20 t 25 30 35 40 46 FIGURE 3-34: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% INCREASE IN H 0.1043 0.1042 0.1041 totalpieI 0.104 0.1039 0.1038 0.1037 0.1036 0.1035 0 5 10 15 20 t 25 30 35 40 FIGURE 3-35: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% INCREASE IN H 0.0967 0.0967 totalpieO 0.0966 0.0966 0.0965 0.0965 0.0964 0 5 10 15 20 t 25 30 35 40 FIGURE 3-36: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% INCREASE IN H 0.0174 0.0173 0.0173 total wu income 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0 5 10 15 20 t 25 30 35 40 47 FIGURE 3-37: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% INCREASE IN H 0.0669 0.0669 total ws income 0.0668 0.0668 0.0668 0.0667 0.0667 0 5 10 15 20 t 25 30 35 40 FIGURE 3-38: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% INCREASE IN H 3.863 3.862 ws income/wu income 3.861 3.86 3.859 3.858 3.857 3.856 3.855 0 5 10 15 20 t 25 30 35 40 3.6.3.2 An Increase In Human Capital In The Foreign Labor Market, h Turning our attention to the foreign economy, a one percent increase in the human capital in the foreign labor market h leads to an increase in outsourcing activities in both short and long term periods. Entrepreneurs in the domestic economy will want to take advantage of the higher foreign human capital since the quality of outsourced manual components have improved, resulting in a lower effective cost. Hence, domestic firms prefer to purchase more manual components from the overseas supplier. This results in outsourcing gaining a greater share. Wage inequality therefore increases as the demand for skilled workers increases. In the long run, based on the same explanations, 48 mt* converges to a lower, new steady state while wage gap converges to a higher, new steady state. FIGURE 3-39: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% INCREASE IN h 0.5861 0.586 0.5859 m* 0.5858 0.5857 0.5856 0.5855 0.5854 0.5853 0 20 40 60 80 t 100 FIGURE 3-40: EVOLUTION OF WAGE GAP 120 140 160 wts FOR 1% INCREASE IN h wtu 5.5205 5.52 5.5195 ws/wu 5.519 5.5185 5.518 5.5175 5.517 5.5165 0 20 40 60 80 t 100 120 140 160 An increase in foreign human capital will benefit entrepreneurs engaging in outsourcing activities and foreign labor, as seen from the increase in total profits of all firms undertaking outsourcing mode of production and the decrease in skilled and unskilled labor income. Hence, although GDP initially overshoots in the short run, it is dampened by the combined fall in total profits of all firms involved in integrated production and labor income in the long run. 49 FIGURE 3-41: EVOLUTION OF GDP FOR 1% INCREASE IN h 0.2842 0.2842 0.2842 0.2842 GDP 0.2842 0.2842 0.2842 0.2842 0.2841 0.2841 0 5 10 15 20 t 25 30 35 40 FIGURE 3-42: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% INCREASE IN h 0.1036 0.1036 totalpieI 0.1035 0.1035 0.1035 0.1035 0.1035 0.1034 0 5 10 15 20 t 25 30 35 40 FIGURE 3-43: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% INCREASE IN h 0.0969 0.0968 totalpieO 0.0968 0.0967 0.0967 0.0966 0 5 10 15 20 t 25 30 35 40 50 FIGURE 3-44: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% INCREASE IN h 0.0173 total wu income 0.0173 0.0173 0.0172 0.0172 0.0172 0 5 10 15 20 t 25 30 35 40 FIGURE 3-45: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% INCREASE IN h 0.0667 0.0667 total ws income 0.0666 0.0666 0.0666 0.0666 0.0666 0.0666 0 5 10 15 20 t 25 30 35 40 FIGURE 3-46: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% INCREASE IN h 3.865 3.8645 ws income/wu income 3.864 3.8635 3.863 3.8625 3.862 3.8615 0 5 10 15 20 t 25 30 35 40 51 3.6.4 Change In Parameters Related To Efficiency Of Training 3.6.4.1 A Decrease In Entrepreneurial Overload In Training Unskilled Labor, α In the integrated mode of production, a decrease in entrepreneurial overload in training unskilled labor α , will lead to an increase in the efficiency of training such workers, hence reducing the training cost. As a result, profit for integrated production increases and firms prefer to do production in-house in both short and long runs. FIGURE 3-47: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% DECREASE IN α 0.5875 m* 0.587 0.5865 0.586 0 20 40 60 80 t 100 120 140 160 Therefore, entrepreneurs demand more unskilled workers relative to skilled workers, hence depressing the wage gap. Figure 3-48 shows the transition of wage gap over time. It can be seen that wage gap decreases in both short and long runs. FIGURE 3-48: EVOLUTION OF WAGE GAP wts FOR 1% DECREASE IN α wtu 5.517 5.516 5.515 5.514 ws/wu 5.513 5.512 5.511 5.51 5.509 5.508 5.507 0 20 40 60 80 t 100 120 140 160 52 Similar to previous cases, the decrease in entrepreneurial overload in training unskilled workers results in the dominance of increase in total profits of all entrepreneurs involved in integrated mode of production and labor income over decrease in total profits of all entrepreneurs involved in outsourcing mode of production. Hence, GDP increases over time. FIGURE 3-49: EVOLUTION OF GDP FOR 1% DECREASE IN α 0.2845 GDP 0.2844 0.2843 0.2842 0.2841 0 5 10 15 20 t 25 30 35 40 FIGURE 3-50: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN α 0.1041 0.104 totalpieI 0.1039 0.1038 0.1037 0.1036 0.1035 0 5 10 15 20 t 25 30 35 40 FIGURE 3-51: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN α 0.0967 0.0967 0.0966 totalpieO 0.0965 0.0965 0.0964 0.0964 0.0963 0.0963 0 5 10 15 20 t 25 30 35 40 53 FIGURE 3-52: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN α 0.0173 0.0173 0.0173 total wu income 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0 5 10 15 20 t 25 30 35 40 FIGURE 3-53: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% DECREASE IN α 0.0668 total ws income 0.0668 0.0667 0.0667 0.0666 0.0666 0 5 10 15 20 t 25 30 35 40 FIGURE 3-54: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN α 3.863 3.862 ws income/wu income 3.861 3.86 3.859 3.858 3.857 3.856 3.855 0 5 10 15 20 t 25 30 35 40 54 3.6.4.2 A Decrease In Entrepreneurial Overload In Training Skilled Labor, γ In the short run, as the entrepreneurial overload in training skilled labor γ decreases, the training of skilled labor becomes more efficient such that the cost of training them is now lower. This leads to an increase in profit for integration and entrepreneurs prefer not to outsource manual components. Hence in both short and long term periods, outsourcing gains a lower share. Firms demand less skilled workers and instead demand more unskilled workers as more firms switch to integrated production mode. Subsequently, the wage gap decreases. In the long run, the wage gap continues to fall and converges to a lower steady state. Figures 3-55 and 3-56 show the transition of mt* and wage gap over time. In addition, the impact on GDP is similar to the impact due to a decrease in entrepreneurial overload in training unskilled labor. FIGURE 3-55: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% DECREASE IN γ 0.5872 0.587 0.5868 m* 0.5866 0.5864 0.5862 0.586 0.5858 0 20 40 60 80 t 100 120 140 160 wts FIGURE 3-56: EVOLUTION OF WAGE GAP u FOR 1% DECREASE IN γ wt 5.518 5.517 5.516 ws/wu 5.515 5.514 5.513 5.512 5.511 5.51 5.509 0 20 40 60 80 t 100 120 140 160 55 FIGURE 3-57: EVOLUTION OF GDP FOR 1% DECREASE IN γ 0.2845 0.2844 0.2844 GDP 0.2843 0.2843 0.2842 0.2842 0.2841 0.2841 0 5 10 15 20 t 25 30 35 40 FIGURE 3-58: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN γ 0.1039 0.1039 0.1038 totalpieI 0.1038 0.1037 0.1037 0.1036 0.1036 0.1035 0 5 10 15 20 t 25 30 35 40 FIGURE 3-59: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN γ 0.0967 0.0966 totalpieO 0.0966 0.0965 0.0965 0.0964 0.0964 0 5 10 15 20 t 25 30 35 40 56 FIGURE 3-60: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN γ 0.0173 0.0173 total wu income 0.0173 0.0173 0.0173 0.0173 0.0173 0.0173 0 5 10 15 20 t 25 30 35 40 FIGURE 3-61: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% DECREASE IN γ 0.0668 total ws income 0.0668 0.0667 0.0667 0 5 10 15 20 t 25 30 35 40 FIGURE 3-62: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN γ 3.862 ws income/wu income 3.861 3.86 3.859 3.858 3.857 3.856 0 5 10 15 20 t 25 30 35 40 57 3.6.5 A Change In Parameter Relating To Matching Ability, b It is interesting to observe how a decrease in the inverse of matching between domestic firms and overseas supplier b will affect the mode of production and wage inequality. Allowing a 1% decrease in b results in a higher entrepreneurial ability to find a suitable match. Subsequently, outsourcing profit rises, hence increasing outsourcing activities in both short and long runs. Similarly, as more entrepreneurs switch to outsourcing mode of production, they demand more skilled labor relative to unskilled labor, resulting in an upward pressure on wage inequality. Thus, the wage gap increases in the short run and converges to a higher steady state in the long run as shown by Figure 3-64 below. FIGURE 3-63: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY mt* FOR 1% DECREASE IN b 0.5865 0.586 0.5855 0.585 m* 0.5845 0.584 0.5835 0.583 0.5825 0.582 0 20 40 60 80 t 100 FIGURE 3-64: EVOLUTION OF WAGE GAP 120 140 160 wts FOR 1% DECREASE IN b wtu 5.545 5.54 ws/wu 5.535 5.53 5.525 5.52 5.515 0 20 40 60 80 t 100 120 140 160 58 It is striking to observe that an increase in matching ability will initially result in a sharp increase in GDP, followed by a decline in GDP over time. The increase in profits of total entrepreneurs engaged in outsourcing activities has contributed to the initial increase in GDP. However, in the long run, the fall in total integrated profits and labor income overwhelms the increase in outsourcing profit, causing GDP to be lower than the baseline value in the long run. This shows that an increase in outsourcing activities is not necessary beneficial to the welfare of the economy all the time. In this case, GDP has worsened in the long run. FIGURE 3-65: EVOLUTION OF GDP FOR 1% DECREASE IN b 0.2843 0.2843 GDP 0.2842 0.2842 0.2841 0.2841 0 5 10 15 20 t 25 30 35 40 FIGURE 3-66: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN b 0.1036 0.1035 0.1034 totalpieI 0.1033 0.1032 0.1031 0.103 0.1029 0.1028 0 5 10 15 20 t 25 30 35 40 59 FIGURE 3-67: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN b 0.098 0.0978 totalpieO 0.0976 0.0974 0.0972 0.097 0.0968 0.0966 0 5 10 15 20 t 25 30 35 40 FIGURE 3-68: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN b 0.0173 0.0173 total wu income 0.0172 0.0172 0.0172 0.0172 0.0172 0.0171 0 5 10 15 20 t 25 30 35 40 FIGURE 3-69: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1% DECREASE IN b 0.0667 0.0667 total ws income 0.0666 0.0666 0.0665 0.0665 0.0664 0 5 10 15 20 t 25 30 35 40 60 FIGURE 3-70: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN b 3.878 3.876 ws income/wu income 3.874 3.872 3.87 3.868 3.866 3.864 3.862 3.86 0 5 10 15 20 t 25 30 35 40 Table 7 thus summarizes the relations between a 1% increase in each of the selected exogenous parameters and the five endogenous variables. The outcomes in the table below are different from what we have discussed in the main text above. For easy interpretation and comparison, we have assumed an increase in all the selected exogenous parameters. In contrast, in the main text, we have considered increases in domestic and foreign human capital whereas other exogenous parameters each experience a decrease so as to be consistent with world developments. TABLE 7: SUMMARY OF OUTCOMES OF COMPARATIVE STATICS EXERCISE FOR AN INCREASE IN EACH SELECTED PARAMETERS Parameter Cost before quality adjustment Inverse of networking efficiency in outsourcing mode Inverse of networking efficiency in integrated production mode Human capital in local labor market Human capital in foreign labor market Entrepreneurial overload in training unskilled labor Entrepreneurial overload in training skilled labor Inverse of matching between domestic firms and overseas supplier Threshold entrepreneurial ability ρ k1 mt* Wage gap wts wtu At Kt + - + + - - k2 - + - + H h α + - + + + - + + γ - + - + b + - + - Similarly, Table 8 shows all the relationships between the 1% increase in each exogenous parameters and the welfare of the three major types of players in the economy: 1) 61 entrepreneurs, 2) skilled workers and 3) unskilled workers. From the table, we observe that there exists a trade off between the welfare of domestic workers and entrepreneurs. TABLE 8: SUMMARY OF GDP OUTCOMES OF COMPARATIVE STATICS EXERCISE FOR AN INCREASE IN SELECTED PARAMETERS Parameter Cost before quality adjustment Inverse of networking efficiency in outsourcing mode Inverse of networking efficiency in integrated production mode Human capital in local labor market Human capital in foreign labor market Entrepreneurial overload in training unskilled labor Entrepreneurial overload in training skilled labor Inverse of matching between domestic firms and overseas supplier 3.7 GDP ρ + Profit of entrepreneurs involved in integrated production + k1 - - + - - k2 - - + - - H + + - + + h + - + - - α - - + - - γ - - + - - b + + - + + Profit of entrepreneurs involved in outsourcing activities - Skilled labor income Unskilled labor income + + Comparison With Previous Literature Results We compare our results with previous literature and present the summaries of the differences in Tables 9 and 10. We find that Egger and Grossmann (2005) only examined the effects of outsourcing on wage inequality in the short and long runs, whereas Grenier, Rubart, Semmler (2004) and DeGroot (2001) have only examined the decision to outsource or adopt integrated production in the long run. Hence our model provides a richer model by exploring the interdependence between entrepreneurs, skilled and unskilled workers. Moreover, previous literature has failed to take into account other factors affecting outsourcing and integrated production, such as entrepreneurial overload in training unskilled and skilled labor. 62 In our results, a change in skilled (unskilled) labor supply will lead to a decrease (increase) in wage inequality respectively. In contrast, Egger and Grossmann (2005) postulated that wage inequality remains constant regardless of an increase in high-skilled or low-skilled workers. This is because in their model setup the reduction in relative wages is offset by the increase in relative wages. For instance, an increase in high-skilled labor leads to a decrease in wage gap due to an increase in the skill intensity of production labor. However, supporting low-skilled labor becomes more attractive since the marginal cost of supporting low-skilled labor is now lower relative to non-supported low skilled labor. Thus, as more high-skilled labor is allocated towards non-production activities, the skill-intensity of production labor decreases. This results in a narrowing of wage gap. From Table 9, it can be seen that the decision to adopt integrated production is inversely related with unskilled labor supply in DeGroot (2001)’s results. According to his paper, he postulated that an increase in the scale of economy, whereby labor supply is the sum of skilled and unskilled labor supply, will result in an increase in outsourcing. This is mainly because the fixed cost of superior technology can now easily be distributed over a larger output (the size of the market will restrict the degree of specialization). In contrast, in our model, the decision to do integrated production is positively related to unskilled labor supply. In Table 10, Grenier, Rubart, Semmler (2004) postulated that an increase in the number of skilled workers will lead to an increase in the profitability of technology which are complementary to skilled labor. Hence, skilled wages increase, resulting in an increase in wage inequality. However, our model shows that wage inequality should fall. Comparing our model with a model that performs foreign direct investment (FDI) instead of international outsourcing, Davies (2005) has developed a static model of FDI whereby the skilled workers of different countries are imperfect substitutes for one 63 another. In addition, the production of HQ services by skilled labor takes place in both countries. Thereafter a Multinational Enterprise (MNE) combines the services using unskilled labor. Hence, FDI can occur without trade costs or factor-price differences. Davies postulated that the increase in the hiring of host country’s skilled labor increases home country’s unskilled wages. At the same time, there is an ambiguous effect on home country’s skilled wages. Furthermore, an increase in the host production of the multinational’s good will result in an increase in wage inequality in the home country. However, depending on the degree of imperfect substitution of skilled labor, FDI will lead to additional wage effects. For instance, if the skilled labor of both home and host country are perfect substitutes, home skilled wage will fall as the role of FDI increases. In contrast, as the degree of substitutability falls, wage inequality in the home country increases as domestic skilled wages increase. In contrast, we show that an increase in network knowledge stock in the static model will lead to an unambiguous increase in wage inequality. Since Davies has only examined these changes in the short run, our model is more realistic as we examine the transition of wage inequality over time. According to Grossman and Helpman (2003), they postulated that heterogeneous firms in an industry will choose their mode of organization and location of their subsidiaries or suppliers, depending on their level of productivity. A fall in trade cost will lead to firms with low level of productivity to increase outsourcing to the South. Firms with intermediate level of productivity will prefer to perform more FDI while the fraction of components in the market produced by vertically integrated firms in the North declines. Although we have adopted a different approach from their paper, our model is richer as we have examined the endogenous relationship between entrepreneurs’ decisions to outsource and wage inequality. To summarize, most literature has focused the impact of international outsourcing on wage inequality and failed to endogenize the influential role of entrepreneurship 64 together with wage inequality. Furthermore, they have neglected to compare the welfare of entrepreneurs versus domestic workers over time. In contrast, we have not only examined the transition of GDP over time, but also compare the welfare of the three major types of players in the domestic economy. 65 TABLE 9: COMPARISON WITH PREVIOUS LITERATURE RESULTS (1) DeGroot (2001) Model Parameters SR Entrepreneurial overload in training unskilled labor Diminishing rate of unskilled workers Entrepreneurial overload in training skilled labor Diminishing rate of effective labor hired in integrated production Cost before quality adjustment Diminishing rate of manual component Inefficiency of network knowledge contributing to present period output Inverse of matching between domestic firms and overseas supplier Diminishing rate of effective labor hired in outsourcing Human capital in foreign labor market Decrease in efficiency of foreign labor producing low-skilled intensive components Skilled labor supply Unskilled labor supply Human capital in local labor market Integrated productivity stock Network knowledge stock Inefficiency of last period aggregate stock contributing to current network knowledge Inefficiency of last period aggregate stock contributing to current network knowledge Aggregate productivity in evolution of network knowledge stock Aggregate productivity in evolution of integrated productivity stock Inverse of networking efficiency in outsourcing mode wts wtu LR LR mt* wts wtu mt* + - + - - - - - + - + - + - + - - + + - + + - + - + - + - + + + + + + - + - - + - + + - + + + + - + + + + + - - + - - + - - + - wts wtu mt* Grossman and Helpman (2003) SR wts wtu mt* Egger and Grossmann (2005) SR wts wtu LR mt* wts wtu + + + + - 0 0 0 0 - - - + * + mt* 66 DeGroot (2001) Model Parameters SR LR LR s t u t s t u t s t u t w w Inverse of networking efficiency in integrated production mode Rate at which previous network knowledge depreciates. Rate at which previous integrated productivity stock depreciates. Note: * stands for ambiguous mt* w w mt* + - + - + - w w mt* Grossman and Helpman (2003) SR s t u t w w mt* Egger and Grossmann (2005) SR s t u t w w LR mt* wts wtu mt* 67 TABLE 10: COMPARISON WITH PREVIOUS LITERATURE RESULTS (2) Grenier, Rubart, Semmler (2004) LR Model Parameters SR Entrepreneurial overload in training unskilled labor Diminishing rate of unskilled workers Entrepreneurial overload in training skilled labor Diminishing rate of effective labor hired in integrated production Cost before quality adjustment Diminishing rate of manual component Inefficiency of network knowledge contributing to present period output Inverse of matching between domestic firms and overseas supplier Diminishing rate of effective labor hired in outsourcing Human capital in foreign labor market Decrease in efficiency of foreign labor producing low-skilled intensive components Skilled labor supply Unskilled labor supply Human capital in local labor market Integrated productivity stock Network knowledge stock Inefficiency of last period aggregate stock contributing to current network knowledge Inefficiency of last period aggregate stock contributing to current network knowledge Aggregate productivity in evolution of network knowledge stock Aggregate productivity in evolution of integrated productivity stock Inverse of networking efficiency in outsourcing mode Inverse of networking efficiency in integrated production mode Rate at which previous network knowledge depreciates. Rate at which previous integrated productivity stock depreciates. FDI Note: * stands for ambiguous LR w w mt* - + - - - - - + - + - + - + - - + + - + + - + - + - + - + + + + + + - + - - + - + + + + + + + - + - + + + - - + - - + - - + - + - + - + not considered - s t u t w w m + * t s t u t s t u t w w mt* Davies (2005) SR s t u t w w + + + - * mt* 68 4. General Discussion After obtaining interesting relationships from the comparative statics analysis, we hereby attempt to provide a general discussion on the implications of the selected relationships, which tally with world developments, on the domestic economy with respect to entrepreneurs’ decision to perform outsourcing and factor prices. In the model, we found that the reduction in the cost before quality adjustment of the manual components can lead to an increase in the prevalence of outsourcing activities. With the advancement of technology over time, service link costs have been rapidly reduced. Such advances have included the advancement in management, human resource, information and engineering technology. These technological changes have unambiguously led to higher wage inequality which is consistent with Egger and Grossmann (2005). Although the welfare of entrepreneurs has been raised, the welfare of domestic workers has fallen. A reduction in the inverse of matching between domestic firms and overseas supplier can lead to an increase in outsourcing activities. This is reinforced by the implementation of policies which include the liberalization of the telecommunication sector in developing countries such as China and India and the formulation of Free Trade Agreements (FTAs) between nations, which can encourage more outsourcing activities. However, the prevalence of outsourcing activities will lead to a fall in GDP as the fall in welfare of domestic workers dominates the overall increase in that of entrepreneurs. Thirdly, entrepreneurs undertaking the integrated mode of production have been enhancing their efficiency in training skilled and unskilled workers. Such an increase in efficiency will lead to the dominance of integrated production over time. In addition, the welfare of the economy is raised, as skilled and unskilled labor earn higher income. Since there is a trade off between the welfare of domestic workers and entrepreneurs, the overall welfare of entrepreneurs decline. 69 The recent trend of an increase in the human capital of developing countries such as China and India has resulted in more outsourcing activities. This is consistent with reality as developed countries such as Japan and the U.S have increasingly outsourced manual components to these developing countries. Furthermore, to raise the welfare of domestic workers, the developed country should seek to actively raise the skill level of the economically active through providing skills upgrading courses and providing higher education opportunities for the population. 5. Conclusion This paper takes a fresh approach in developing a simple dynamic model for a small, developed and open economy, which captures the transition of the two state variables, namely integrated productivity and entrepreneurial network knowledge stocks. Our motivation arises from the fact that firms are increasingly outsourcing manual components to foreign, developing countries, thus establishing networks with affiliates in the process. Through the evolution of the two stock variables, previous periods’ stocks have contributed to a common aggregate stock which has spillover effects on all firms in the domestic economy in the present period. Moreover, we have endogenized the entrepreneurial ability threshold together with skilled and unskilled wages. This paper has thus examined the impact of evolution of networking on 1) wage inequality between skilled and unskilled labor 2) the decision to outsource by entrepreneurs and 3) the welfare of entrepreneurs versus domestic workers. In the long run, both wage inequality and the threshold level of entrepreneurial ability undergo a gradual transition to a unique and stable mixed equilibrium, which differs from Acemoglu et al. (2002b) whereby only corner solutions exist. This is more consistent with the observation made in the real world. In addition, through examining the 70 transition of the threshold level of entrepreneurial ability and wage inequality over time, the short-run and long-run impacts on endogenous variables are different in magnitude. In comparing the comparative statics for both static and dynamic models, we find that the static model is inadequate in explaining the impact of networking on the economy since it fails to take into account the transition of the state variables over time. However, it is adequate in explaining other exogenous parameters such as human capital in local and foreign labor markets and service link cost. We find that the decrease in service link cost and increase in human capital of foreign country will increase outsourcing activities while increasing wage inequality. In particular, the increase in human capital of the domestic economy and decrease in entrepreneurial overload in training both types of labor reduce wage inequality, which differ from conventional results. Interestingly, an increase in networking efficiency in the outsourcing mode leads to different impacts on the endogenous variables in the short and long runs: outsourcing activities will dominate in the short run whereas integrated production dominates in the long run. Given the exogenous changes in all the parameters, we also observe that there exists a positive correlation between outsourcing activities (which is defined in terms of threshold level of entrepreneurial ability) and wage inequality. Thus, they co-move in the same direction. In addition, we examine the impact of the exogenous parameters on the GDP of the domestic economy, as well as the welfare of the three major types of players in the economy. Interestingly, we observe that there exists a trade off between the welfare of domestic workers and entrepreneurs. This implies that an increase in outsourcing activities will reduce the welfare of domestic workers while increasing the overall welfare of entrepreneurs. The converse is true when entrepreneurs prefer to undertake integrated production. Another striking result is that an increase in outsourcing activities is not necessary beneficial to the overall welfare of the domestic economy. An increase in 71 outsourcing activities due to an increase in matching ability of the entrepreneurs actually worsens GDP. This is mainly due to the dominance of the decrease in total integrated profits and labor income over the increase in total outsourcing profits. From these interesting findings, we are able to shed light on world developments, which are namely the reduction in transaction and telecommunication costs, increase in training efficiency and increase in human capital of developing countries. Finally, we also compare our model’s results with previous studies’ and find that most papers have focused on wage inequality. Our model is thus richer as we explore the endogenous relationships between entrepreneurs, skilled and unskilled workers in both short and long runs. Hence, the above results add a challenge to many of the prevailing views on wage inequality and the structure of the economy. Future research could incorporate FDI and endogenous human capital accumulation of skilled workers and the subsequent impact on wage inequality, GDP, welfare of entrepreneurs and domestic workers and hence growth of the economy. It also remains to test the hypothesis empirically, whether the formation of the two different types of networking stocks truly affects wage inequality and the decision to outsource. 72 Bibliography 1. Acemoglu, Daron (2002a). “Technical Change, Inequality, and the Labor.” Journal of Economic Literature, Vol.40, no.1, p.7-72 2. Acemoglu, Daron, Aghion, Philippe and Zilibotti, Fabrizio (2002b). “Vertical Integration and Distance to Frontier.” National Bureau of Economic Research Working Paper 9191. 3. Anderson, James E. and Marcouiller, Douglas (2002). “Insecurity and the Pattern of Trade: An Empirical Investigation.” Review of Economics and Statistics, Vol.84, no.2, p.342-52 4. BEA, 1997. Survey of Current Business, the United States. 5. Davies, Ronald B. (2005). “Fragmentation of Headquarter Services and FDI.” North American Journal of Economics and Finance, Vol.16, p.61-79 6. DeGroot, Henri L.F De (2001). “Macroeconomic Consequences of Outsourcing: An Analysis of Growth, Welfare, and Product Variety”, De Economist, Vol.149, no.1, p.53-79 7. Egger, Hartmut and Grossmann, Volker (2005). “The Double Role Of Skilled Labor, New Technologies and Wage Inequality.” Metroeconomica, Vol.56, no.1, p.37-57 8. Ethier, Wilfred J. (2005). “Globalization, globalization: Trade, technology and wages.” International Review of Economics and Finance, Vol.14, p.237-258 9. Galor, Oded, Moav, Omer, (2000). “Ability-biased technological transition, wage inequality, and economic growth.” Quarterly Journal of Economics, Vol.115, p.469-497. 10. Gao, Ting (2005). “Foreign Direct Investment and Growth under Economic Integration.” Journal of International Economics, Vol.67, issue 1, p.157-74 73 11. Greiner, Alfred, Rubart, Jens and Willi, Semmler. (2004). “Economic growth, skilled-biased technical change and wage inequality: A model and estimations for the US and Europe.” Journal of Macroeconomics, Vol.26, p.597-621. 12. Grossman, Gene M. and Helpman, Elhanan. (2003). “Managerial incentives and the international organization of production.” Journal of International Economics, Vol.63, p.237-262 13. Kleinert, Jörn (2003). “Growing Trade in Intermediate Goods: Outsourcing, Global Sourcing, or Increasing Importance of MNE Networks?” Review of International Economics, Vol.11, Issue 3, p.464-482 14. Portes, Richard and Hélène, Rey. (1999). “The Determinants of Cross-Border Equity Flows.” Working Paper 7336, NBER, Cambridge, MA. 15. Rauch, James E. (2001). “Business and Social Networks in International Trade.” Journal of Economic Literature, Vol. XXXIX (December 2001), p.1177-1203. 74 APPENDIX A i) Proof of Proposition 1 We substitute equations (17) to (20) into equation (6), and re-express the profit function for the intermediate firm that engages in vertical integration as:     δ β s u   w w t t πtI =  α γ      α γ   δ  At H α +γ  α +γ         1 β +δ −1 1 1 1   β + δ − 1 β + δ − 1 β + δ −1       1 1  1   − δ 1−δ  − 1−β β   δ δ β β   (A1) δ β  δ β      For the above profit function to be positive, we set π tI f 0 . It can be seen that the first term in equation (A1) is positive regardless of positive or negative values for β and δ . Hence, we will be focusing on the second term in the equation: 1  1  δ β δ β  β +δ −1    1 −  δ 1−δ δ β  1  δ β δ β  β +δ −1  1  f  δ 1−δ  δ β 1  1 Dividing  δ β δ β 1  β +δ −1   1 1  1 −  1−β β δ β  β +δ −1  1  +  1− β β δ β   β +δ −1  f0  (A2) 1  β +δ −1   (A3) 1  β +δ −1 throughout equation (A3) and rearranging the terms, we   obtain β + δ p 1, hence proving the sufficient condition for Lemma 1. It can easily be seen that the necessary condition is satisfied too. ii) Proof of Proposition 2 Similarly, we substitute equations (26) and (27) back into equation (7): π tO   a b K t −1 mt H d  =   ρ χ sd   ν  wt   h  1  1− d − χ  d −1+ χ − dχ   χ d 1−d1− χ  χ  ( χ d ) − χ d ( d −1)         1  1  1− d − χ  1 − d d  − (χ d )1− d − χ      (A4) 75 For outsourcing profit to be positive, we set π tO f 0 . It can be seen too that the first term in equation (A1) is positive regardless of positive or negative values for d and χ . Hence, focusing on the second term in the equation: (χ χ d  −χ χd   ) 1 d 1− d − χ d −1+ χ − dχ ( d −1)     1 1− d − χ ( ) 1 1− d − χ − χ 1− d d d f0 (A5) 1 (χ χ d ) 1 d 1−d − χ Dividing  χ d −1(d+−χ1−)dχ 1−d −χ  f χ d + χ 1−d d d     (χ ( χ dd ) 1 1−d − χ ) 1 1−d − χ (A6) throughout equation (A6) and rearranging the terms, we obtain d +χp1, thus proving the sufficient condition for Proposition 2. Similarly, it can easily be seen that the necessary condition is satisfied too. iii) Proof of Proposition 3 To prove that the conditions must be given so that an interior solution 0 p mt* p 1 exists, we use equation (29):  ws * mt =  t  H     t   At    χ 1  b 1− d − χ   W h        b   K t −1a   S      (1−d − χ )   ρ δ (1− d − χ )+ d ( β +δ −1) β ( β +δ −1)b   ν u b 1 β + δ − ( ) w   (A7) where    W =  α   α + γ    S =  χ χd d   ( 1 1    ) α  γ  α + γ 1 1− d − χ    γ  β +δ −1     1   δ δ β β      − χ χd   d −1 + χ − d χ ( d −1 ) 1  β +δ −1    1 −  δ 1−δ δ β 1  1− d − χ  − χ 1− d d d   ( ) 1  β +δ −1  1  −  1− β β  δ β 1 1− d − χ      1   β +δ −1   (A8)    (A9) 76 Assumptions in Proposition 1 and Proposition 2 prove that m t* f 0 . This is mainly because under both the assumptions whereby β + δ p 1 and d +χp1 , W and S are ensured to be positive and greater than zero. In addition, since wts , w tu , H , At , K t −1 and  ρ   ν  are between zero and one, it can be easily seen that the right hand side of h  equation (A7) is greater than zero, hence proving m t* f 0 . To prove that condition 3 must be given so that m t* p 1 : χ (1− d − χ )   ρ  δ (1− d − χ )+ d ( β + δ −1) b ( β + δ −1 )  w u β  (β +δ −1)b   hν   wts    t    H   At   K t −1 a       δ (1− d − χ )+ d ( β + δ −1 ) s b ( β + δ −1) wt β (1− d − χ ) u ( β + δ −1)b wt  ρ χ  ν  h p   a  K t −1         − 1 b 1− d − χ  W      b p1  S    (A10) 1 b W    S  d + χ −1 b H δ (1− d − χ )+ d ( β + δ −1) b ( β + δ −1) (1− d − χ ) At (β +δ −1)b (A11) Rearranging the terms, we can rewrite equation (A11) as:  ρ   ν  s u δ (1− χ )− d (1− β )   h  wt p wt  K t −1 a   χ β ( χ + d −1)       − b ( β + δ −1 ) b W    S  b ( d + χ −1 )( β + δ −1 ) b H δ (1− d − χ )+ d ( β +δ −1) At (1− d − χ ) (A12) At this point, given that wages are not yet endogenized, it can be seen that equation (A12) must hold in order for m t* p 1 . To illustrate this, if wtu increases, wts must increase too. However, the magnitude of increase in wts cannot be too large until it exceeds the left hand side of equation (A12), hence violating the third condition. Intuitively, when equation (A12) is violated, no entrepreneurs will choose to undertake outsourcing mode 77 of production when wts is too large, which implies that skilled workers are too expansive to be hired. [...]... evolution of GDP, profits, and wage incomes over time given various shocks to the economy Greiner, Rubart and Semmler (2004) have observed that wage inequality had been increasing in the United States (U.S) and the United Kingdom (U.K) from early 1960s to late 1990s1 However, the pattern of wage inequality for West Germany is unclear Using OECD data, they observed that wage inequality in West Germany... in wage inequality over time is mainly due to the interaction effects of network stocks formed by entrepreneurs involved in integrated and outsourcing modes of production One major motivation for the incorporation of network knowledge is that international outsourcing can be hindered by informal trade barriers, such as weak enforcement of international contracts (Anderson and Marcouiller, 2002) and. .. small, open and developed economy is constructed to examine the impact of the formation of network knowledge due to international outsourcing on the three key types of players in the domestic economy, which are namely the entrepreneurs, skilled and unskilled workers We seek to investigate 1) the welfare between entrepreneurs and domestic workers and 2) the wage inequality between skilled and unskilled... integrated production, we model entrepreneurial overload in the training of unskilled and skilled labor through the parameters α and γ respectively, as t tu and t ts lies between zero and one Similarly, as Lut and LSI t are less than one, β and δ imply that unskilled workers and effective workers increase at a diminishing rate respectively 2.2.2 Firms Choosing To Engage In Outsourcing Activities Firms... and aggregate stock of knowledge in the economy We examine the above model via the incorporation of entrepreneurial ability to determine the threshold level above which international outsourcing will occur, which is often neglected by previous literature This is crucial since entrepreneurs are required to train workers and coordinate outsourcing activities In the outsourcing mode of 5 production, entrepreneurial. .. trend in wage inequality Most studies have attributed the upward trend due to the evolution of technology Some of the most commonly cited reasons for the evolution of technology over time are skilled-biased technological change (Galor and Moav, 2000) and the 1 For the U.S, U.K and West Germany, cross-country data of wage differentials are taken from OECD Employment Outlook (1993,1996) whereby wage inequality. .. 1  d −1    (27) From equations (26) and (27), it can be seen that the marginal product of manual component and demand for skilled labor are constrained by the cost of the manual component, previous period network knowledge stock, entrepreneurial ability, human capital and skilled wages Proposition 2: Profit for outsourcing mode of production is positive if and only if the condition d + χ p 1 exists... (20) From equations (19) and (20), we observe that the demand functions for unskilled and skilled labor supply are constrained by wage costs, integrated productivity and human capital in the economy 13 Proposition 1: Profit for integrated production is positive if and only if the condition β + δ p 1 exists Proof: See Appendix A Hence, proposition 1 shows that both effective and unskilled labor must... it can be seen that previous period network knowledge, entrepreneurial ability and human capital are positively related to π tO while skilled wages and marginal product of manual component are inversely related to it 2.5 Equilibrium In this section, we analyze firms’ decision to engage in international outsourcing or integration, depending on entrepreneurial ability Firms will only decide to adopt... introduce simple evolution mechanism of the entrepreneurial network stock and integrated productivity stock and proceed to investigate how the evolutions of the two stock variables, At and K t , may affect the organizational form of production and factor prices over time 3.1 The Model We assume that interaction between firms involved in vertical integration and outsourcing activities in the domestic economy ... technology either due to international outsourcing or skilled-biased technical change In this paper, we investigate the impact of international outsourcing on both wage inequality and entrepreneurs’... that international outsourcing can be hindered by informal trade barriers, such as weak enforcement of international contracts (Anderson and Marcouiller, 2002) and inadequate information about international. .. both short and long runs, a decrease in ρ causes wage inequality to increase This is because firms demand more skilled labor as the demand for outsourcing mode rises Subsequently, the wage gap