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论文作者签名: 日期: 年 月 日 1 ContentsEssay One: Endogenizing “Endogenous Technical Change”: A Model of the Optimal Research Behavior with Endogenous Time PreferenceAbstract………………………………………………………………………………31. Introduction……………………………………………………………………...42. General Framework of the Model……………………………………………….63. An Example with Specific Functional Forms…………………………………...9 3.1 Assumptions………………………………………………………………….9 3.2 Steady State Analysis………………………………………………………..10 3.3 Dynamics of the Innovation Achievement and Research Behavior…………13 3.4 Short-run Analysis on Cooperation in Research Activities………………….184. Concluding Remarks……………………………………………………………23References…………………………………………………………………………...24Figures……………………………………………………………………………….26Essay Two: Endogenous Coalition Economic Growth and Income DistributionAbstract………………………………………………………………………………291. Introduction……………………………………………………………………... 302. Literature Review………………………………………………………………...313. Growth Model of the Three-player Recursive Game…………………………….35 3.1 Full Coalition………………………………………………………………...36 3.2 No Coalition………………………………………………………………….38 3.3 Partial Coalition……………………………………………………………...39 3.4 Endogenous Coalition………………………………………………………..404. Strategic Behavior Under Partially Protected Property Right……………………44 4.1 Full Depreciation of Inventory……………………………………………….46 4.2 Not Full Depreciation of Inventory…………………………………………..48 4.2.1 Steady State…………………………………………………………..50 4.2.2 Existence of BGP and Properties…………………………………….515. Concluding Remarks……………………………………………………………..60Mathematical Appendix……………………………………………………………...63References……………………………………………………………………………66Acknowledgement…………………………………………………………………...71 2 Endogenizing “Endogenous Technical Change”: A Model of the Optimal Research Behavior With Endogenous Time Preference Yong Wang English Discussion Paper E2003003CCER Peking University First Draft: December 2001 Second Draft: October 2002 This Version: April 2003 Abstract Most of the existent literature on RampD-based endogenous growth theory only implicitlyassumes that RampD and other innovation activities take place automatically within a profit-seekingfirm or within a black box called “scientific sector” so long as labor and physical or human capitalare optimally input into the innovation generator. With an aim to provide a more primitivebehavioral micro-foundation both for the endogenous technical progress and the technicalfluctuations assumed in RBC theory we explore the dynamic research behavior of a representativeresearcher with endogenous time preference. We find that the researcher’s optimal effort level andthe innovation achievement obey a saddle path or show tremendous fluctuations even withoutintroducing uncertainty in the innovative activity. Following Judd’s method we also make theshort-run analyses on the effect of cooperation in the innovation process.Key Words: research behavior technical change economic growthJEL Classification Codes: E0 O3 O4The author’s current correspondence address: China Center for Economic Research CCER at Peking University.Fax 86-10-62751474 Tel 86-10-62762839 email: yongwangpku.edu.cn The author thanks Richard NelsonColumbia Univ. Paul Romer Stanford Univ. Liutang Gong Justin Yifu Lin Guoqing SongPekingUniv. Danyang XieIMF Heng-fu ZouWB Cheng Wang Iowa State Univ. Tianshu Chu East-West CenterZeng Song UCL and Huanxing Yang U Penn for helpful comments. The feedbacks from the participants at theTheoretical Macroeconomic Workshop at CCER and the Macroeconomics Session of the Second China EconomicsAnnual Conference are also gratefully acknowledged. The usual disclaimer applies. 3Endogenizing “Endogenous Technical Change”: A Model of theOptimal Research Behavior With Endogenous Time PreferenceI.IntroductionThe modern growth theory has pointed out that the genuine engine for a nation’ssustainable economic growth is the continuous increase of productivity due totechnological progress or human capital accumulation Solow 1956 Romer 19861990 Lucas 1988 Aghion and Howitt 1992 Grossman and Helpman 1991. Thenwho are the main contributors to this technical advance In the pre-modern societythe technology advanced slowly mainly through non-professional’s workingexperience accumulation and daily observations which might be best characterizedby Arrow’s “learning by doing” model Arrow 1962 thus the aggregate scientificlevel of an economy is largely determined by the nation’s population size and the spanof its history. However with the advent of industrial revolution in the eighteenthcentury the technology progress has become more and more heavily dependent on thepurposeful research behaviors conducted by well-educated professional scientistsengineers and other technicians by means of sophisticated instruments and otherscientific methods within research institutions Lin 1995. This is particularly true fortoday’s knowledge-based economy. The total population size eventually loses therelevance for the technological advance replaced by the suitable proportion of ableresearchers with high human capital the various input in the research and theefficiency of the revolved research institutions including the RampD sectors of firms. In the human-capital induced endogenous growth literature human capital can beaccumulated through formal education on-the-job training Lucas 1993 which isessentially only the spreading rather than the expansion of existent stock ofknowledge. For instance Lucas 1988 implicitly assumes that the infinite knowledgestock is already there with no explicit research sector and all the workers areconducting physical production as well as knowledge assimilation simultaneously. Inhis model human capital itself is automatically accumulating in a constant-returnway. Therefore we argue that the advance of new technological frontier hence thelong-run technical change is mainly accomplished by the researchers in variousresearch institutions such as research universities and the research sector of privatefirms. It is theoretically very helpful to see how a representative researcher behaves inthe research institution. What determines their effort decisions and their innovationachievements How is knowledge per se produced If we have a thoroughunderstanding in these questions then we will be more confident to provide somesuggestions as to how to enhance a representative researcher’s innovationachievement and ultimately boost the technical progress of the whole nation. 4 Moreover we believe that the analysis of a researcher’s behavior can also makesubstantial contribution to the endogenous growth literature. Although the existentliterature is quite successful in explaining the technical change through variouschannels such as the spill-over effect of knowledge due to its externality Romer1986 1990 Griliches 1992 the increase of human capital or in the global contexttechnological innovation and imitation Krugman 1979 Segerstrom 1991 Grossmanand Helpman 1991. However most of the above papers treat the innovation within arelatively macro context while little effort has been by far devoted to the analysis ofan individual researcher’s research behavior1. Actually in most cases the RampD andother innovation activities are just implicitly assumed to take place automatically solong as labor human capital and physical capital are optimally input into the“innovation generator”. Therefore the micro-foundation of the endogenous growththeory is still not solid enough. There is an abundant literature analyzing the demand side of invention andinnovation in the market economy especially within a specific industrial structureSee Nelson 1959 Dusgupta and Stiglitz 1980 Lee and Wilde 1980 Loury 1979Helpman 1993. Pretty much research has also been focused on the supply side aswell. For example Phelps 1966 derives a golden rule of research which determinesthe optimal labor allocation in the research sector in an economy. Aghion and Howitt1992 point out that the input to RampD activity sometimes could be too high to beefficient. There are also many empirical studies focusing on the investment problemin the RampD sector Lach and Schankerman 1989 Jones 1995 Adam 1990. But allthese papers barely provide many insights for the individual research behavior. The task of this paper is therefore to make an analysis on a utility-maximizingrepresentative researcher’s behavior2by developing a new model compatible with thedynamic general equilibrium setting which aims to provide a more primitivebehavioral micro-foundation for the endogenous technical change. We will see laterthat this model might also provide a micro-foundation for the technical fluctuationassumption assumed universally in RBC models. The remainder of this paper is arranged as follows: Section II develops a generaldynamic model where an infinitely-lived representative researcher has an endogenoustime preference similar to Uzawa’s model Uzawa 1968 Section III examines amore specific example with concrete functional forms where we find that theresearcher’s optimal effort level adjusts dynamically in a diversifying way and theresearch achievement also undergoes variation accordingly. In some circumstancesthe achieved innovation follows a saddle-point stable equilibrium path while in othersit demonstates a cyclical change. The frequency of the fluctuation is determined bythe nature of the research process and the researcher’s characteristics such as herinter-temporal elasticity of substitution or innovative ability. In section IV with the1 Some models of the costly innovation and/or imitation are built on the base of profit-seeking firms’ optimizingstrategy. For example even when the innovation sector producing designs is explictly brought into the modelRomer 1990 assumes that the new designs can be automatically generated by exogenously determined humancapital and the existing designs.2 In this paper we do not take the trouble to differentiate the innovation invention RampD and imitation all ofwhich are referred to as the research behavior or for some abuse of terminology innovation. 5method initially estabilshed by Judd 1985b we make the short-run analysis of theeffect of the cooperation in the innovation activity. This is very indespensible for ourunderstanding of scientific research because cooperation becomes more and moreimportant among the researchers in today’s highly specialized research. Theconcluding remarks are in the last section.II The General Framework of The Model Surprisingly however this important issue of research behavior has by farreceived inadequate formal treatment. There are at least two reasons. First it seemsquite difficult to make the analysis beyond the frameworks such as game-theoreticteamwork theory or principle-agent theory etc. Admittedly these frameworks couldbe important in dealing with this problem under asymmetric information but they arestill not proper in some essential aspects. For instance the analysis of researchbehavior should be compatible in a dynamic general equilibrium setting hence thehorizon should be the same with other economic agents such as a consumer or a firmand the researcher’s time preference can be endogenously determined as we arguebelow. Morevoer there may be intrinsically dynamic adjustments in the researcher’sbehavior even without any shock from outside and we have to examine whether theoptimal path of effort supply is stable or not. All of the above could be hardlyanalyzed simultaneously in principal-agent models. Another reason is possibly that people tend to treat innovation process in essentiallythe same way as physical production which has a mature body of theory. Howeverthese two processes are fundamentally different in many aspects. One is that theknowledge and innovation are partially non-excludable and non-competitive Nelson1952 Romer 1986 therefore the accumulation of knowledge is essentially differentfrom accumulation of physical capital. Today’s innovation relies heavily onyesterday’s achievement see Dosi 1988. Nelson 1982 even differentiates the rolesof various forms of knowledge in the RampD efficiency Secondly the innovationprocess is intrinsically more independent harder to monitor more risky andvulnerable to failure Thirdly the remuneration system for the researchers is greatlydifferent from that for the traditional workers the former is based on the non-marketpriority right or the market-oriented patent system and it is more likely thatknowledge can be undersupplied due to externality. That’s why the patent system hasbeen tremendously studied see Judd 1985a Pakes 1985etc. Fourthly these twokinds of processes also take place in the different institutions. Nelson 1986 analyzesthe various organizational forms of research institutions and their contributions topushing forward the technology frontier. He strongly emphasized the important role ofthe universities which has been almost completely ignored in endogenous growthliterature. The RampD innovation and invention activities in the less developedcountries are also distinct from those in the advanced countries Eckaus 1966. Allthese researches support that the innovation behavior should be examined in a newframework. At the individual level we know that the utility of the representative researcher 6can be influenced by many factors such as the general respect from the colleagues theacademic awards the monetary return for a specific innovation or invention etc. andof course the effort level. Actually the utility function can best be characterizedaccording to the entire remuneration system. Here for simplicity we only select thetwo most fundamental factors namely the achieved innovation I t and the effortmt where t represents the time. The utility function u I t mt is assumed to u 2u ube twice differentiable and satisfies that gt0 lt 0 lt0. I I 2 m The researcher’s time preference factor β is not constant in this paper.