薪資軌跡之年齡、時代與世代效果之實徵研究－以華人家庭動態資料庫為例

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(1)國立臺灣師範大學管理學院全球經營與策略研究所碩士論文 Graduate Institute of Global Business and Strategy College of Management National Taiwan Normal University Master Thesis. 薪資軌跡之年齡、時代與世代效果之實徵研究—以華人家庭動態資料庫為例 Effects of age, period and cohort effects on wage trajectory: An application of Panel Study of Family Dynamics (PSFD). 曾欣蕾 Hsin-Lei, Tseng 指導教授：邱皓政博士 Advisor：Hawjeng, Chiou, Ph.D. 中華民國一○七年八月 August 2018.

(2) 中文摘要本研究旨在透過縱貫資料與多層次模型的整合，檢驗年齡、時代及世代變數的效果，以及性別、教育程度與工時等薪資溢酬變數對薪資軌跡的影響。過去這類型的研究多半是由橫斷面資料及相對應的統計方法來完成，因此年齡、時代與世代變數兩兩之間會有完全線性相依的問題；然而，透過兩階層的多層次模型，即可將這三個變數分成兩個層次來處理，亦即時代效果在組內、世代效果在組間，而年齡效果則可以同時作用在組內和組間層次，如此一來，三個變數便可以一起納入模型，解決年齡、時代與世代變數所存在的共線性問題。本研究運用「華人家庭動態資料庫」自 1999 年至 2016 年長達 18 年共 16 波的追縱調查資料，以多層次模型分析 5,800 位受訪者的薪資軌跡與其他變數的變動關係。研究結果顯示，年齡效果的薪資軌跡不論是組內或組間，都是顯著的二次曲線模型，且在 50 歲左右的時候會有最高點；其次，發生在組內的時代效果也同樣對薪資軌跡有顯著影響，然而隨著其他共變數(控制變數)的加入，該二次曲線的最低點會從原本的 2009 年遞延到 2014 年。再來，世代效果對薪資軌跡的二次曲線則說明了，1966 年到 1970 年出生的人的薪資水準最高，可是一旦把年齡、時代和其他溢酬變數控制住之後，世代效果就會變成不顯著。最後，性別、教育年數和工時的溢酬效果則再一次證明，隨著人力資本的累積，薪資水準會跟著增加。本研究運用高階統計方法進行年齡、時代與世代效果分析，除了具備學術意涵，也提供人力資源管理實務的決策性參考。關鍵字：薪資軌跡、年齡-時代-世代分析、人力資本理論、縱貫資料、多層次模型. i.

(3) Abstract This study is aimed to combine longitudinal data analysis with multilevel models to examine effects of age, cohort and periods on wage trajectory. With an extension of those, premium effects of human capital factors on wage, such as gender, education and working hours, are also included. In the past, examination of such effects had relied on crosssectional data and methodology, thus confounding any two of the three variables—age, period and cohort. However, by adapting a two-leveled multilevel modeling, relationships among these three variables are able to be decomposed into within- and between-effects, where period is counted as within-variable in level one, cohort is a between-variable in level two, and age is viewed as both within- and between-variable in level one and level two, so that all three variables are simultaneously analyzed. In this study, a longitudinal data with 16 waves spanning 18 years of over 5,800 individuals in a Panel Study of Family Dynamics (PSFD) database was used to conduct wage trajectory research, and a series of multilevel models were proposed. It is found that age effect is a curvilinear trajectory across life span, with the highest level around 50s, and it is steadily significant both within an individual and among individuals. Period effects also bring about significant variations in one’s wage trajectory; moreover, the lowest points of this effect defer from the year 2009 to the year 2014, when other covariates are controlled. Lastly, cohort effect reveals that people born in 1966 to 1970 earn most in each month; however, this effect becomes insignificant as the other two temporal effects are simultaneously included. Three premium effects (i.e. gender, years of education and working hours) are also examined and thus verify the fact that the accumulation of human capital can result in an increase in wage. In all, this study not only successfully demonstrates effects of age, period and cohort with improved methodology, but also generate useful implications and empirical solutions to classical human resource practices. Keywords: wage trajectory, age-period-cohort analysis, human capital theory, panel data, multilevel modeling. ii.

(4) TABLE OF CONTENTS 中文摘要 .................................................................................................................................. I ABSTRACT ....................................................................................................................... II CHAPTER I. INTRODUCTION ............................................................................................. 1 1.1 RESEARCH BACKGROUND AND MOTIVATION ............................................................. 1 1.1.1 CURRENT SALARY ISSUES IN TAIWAN ..........................................................................1 1.1.2 PAST AND CURRENT RESEARCH ON SALARY ISSUES ...................................................1 1.1.3 RELEVANT ISSUES ON AGE, PERIOD, AND COHORT (APC) ANALYSIS ..........................2 1.1.4 THE IMPORTANCE, THE MAIN PROBLEMS AND SOLUTIONS OF APC ANALYSIS..........3 1.1.5 APPLYING AN APPROPRIATE DATABASE TO TRAJECTORY RESEARCH ..........................4 1.1.6 HOW TO INCORPORATE THE HUMAN CAPITAL THEORY .............................................5 1.2 RESEARCH PROBLEMS AND PURPOSES ...................................................................... 6 CHAPTER II. LITERATURE REVIEW .................................................................................... 7 2.1 SALARY ISSUES .......................................................................................................... 7 2.2 CRITICAL FACTORS OF HUMAN CAPITAL THEORY ON WAGE ISSUES ............................ 9 2.2.1 FORMAL EDUCATION ...................................................................................................9 2.2.2 TENURE ........................................................................................................................9 2.2.3 JOB INVOLVEMENT ....................................................................................................10 2.3 OTHER FACTORS OF WAGE ISSUES ........................................................................... 11 2.3.1 DEMOGRAPHIC FACTORS...........................................................................................11 2.3.2 ACCIDENTAL IMPACTS ................................................................................................11 2.4 EARNING FUNCTION WITH TEMPORAL PERSPECTIVE ............................................... 13 2.5 STATISTICAL ISSUES WITH AGE, PERIOD AND COHORTS ............................................ 15 2.5.1 AGE EFFECT ................................................................................................................15 2.5.2 PERIOD EFFECT ..........................................................................................................15 2.5.3 COHORT EFFECT.........................................................................................................16 2.5.4 DATA STRUCTURE IN APC MODELS ............................................................................16 2.5.5 RECENT ANALYTICAL TECHNIQUES FOR APC ISSUES .................................................18 2.6 INFERENCE ABOUT RESEARCH HYPOTHESIS ............................................................. 20 CHAPTER III. METHODS ................................................................................................. 22 3.1 DATABASE AND RESEARCH SAMPLE ......................................................................... 22 iii.

(5) 3.2 RESEARCH VARIABLES .............................................................................................. 25 3.2.1 WAGE VARIABLES .......................................................................................................25 3.2.2 AGE, PERIOD AND COHORT VARIABLES.....................................................................25 3.2.3 HUMAN CAPITAL VARIABLES .....................................................................................26 3.3 RESEARCH PROCEDURE ........................................................................................... 27 3.4 ANALYTICAL METHODS ............................................................................................ 28 3.4.1 MULTILEVEL MODELING (MLM) ................................................................................28 3.4.2 MLM OF APC VARIABLES IN THE PANEL DATA ...........................................................31 3.4.2.1 APC/MLM MODEL WITHOUT COVARIATES ............................................................31 3.4.2.2 APC/MLM MODEL WITH COVARIATES....................................................................32 3.4.3 OVERALL RESEARCH MODELS APPLIED .....................................................................33 CHAPTER IV. RESULTS .................................................................................................... 34 4.1 SAMPLE STRUCTURE ................................................................................................ 34 4.2 AGE EFFECTS ON THE TRAJECTORY OF WAGE ........................................................... 40 4.2.1 NULL MODEL ..............................................................................................................40 4.2.2 AGE EFFECTS ON THE TRAJECTORY OF WAGE WITHOUT COVARIATES .....................40 4.2.3 AGE EFFECTS ON THE TRAJECTORY OF WAGE WITH COVARIATES ............................42 4.3 PERIOD EFFECT ON THE TRAJECTORY OF WAGE ....................................................... 44 4.3.1 PERIOD EFFECT ON THE TRAJECTORY OF WAGE WITHOUT COVARIATES .................44 4.3.2 PERIOD EFFECT ON THE TRAJECTORY OF WAGE WITH COVARIATES ........................45 4.4 COHORT EFFECT ON THE TRAJECTORY OF WAGE ...................................................... 47 4.4.1 COHORT EFFECT ON THE TRAJECTORY OF WAGE WITHOUT COVARIATES ...............47 4.4.2 COHORT EFFECT ON THE TRAJECTORY OF WAGE WITH COVARIATES ......................48 4.5 RESULTS OF APC EFFECTS ON WAGE ......................................................................... 49 4.5.1 THE RESULTS OF APC ON WAGE WITHOUT COVARIATES ..........................................49 4.5.2 THE RESULTS OF APC ON WAGE WITH COVARIATES .................................................50 CHAPTER V. DISCUSSIONS AND CONCLUSION ................................................................ 51 5.1 AN OVERALL DISCUSSIONS ON AGE, PERIOD AND COHORT EFFECTS ........................ 51 5.1.1 AGE EFFECTS ..............................................................................................................51 5.1.2 PERIOD EFFECTS ........................................................................................................54 5.1.3 COHORT EFFECTS .......................................................................................................56 5.2 AN OVERALL DISCUSSIONS ON THE PREMIUM EFFECTS ........................................... 58 iv.

(6) 5.3 METHODOLOGICAL DISCUSSIONS ............................................................................ 59 5.4 CONCLUSION ........................................................................................................... 61 5.5 MANAGERIAL IMPLICATIONS ................................................................................... 61 5.6 LIMITATIONS AND SUGGESTIONS ............................................................................. 62 REFERENCE.................................................................................................................... 63 APPENDIX I. SYNTAX OF MPLUS OF MA6 ....................................................................... 67 APPENDIX II. SYNTAX OF MPLUS OF MA7 ...................................................................... 68 APPENDIX III. SYNTAX OF MPLUS OF MAPC ................................................................... 69 APPENDIX IV. SYNTAX OF MPLUS OF MM ...................................................................... 70. v.

(7) LISTS OF TABLES Table 1 17 Table 2 ................................................................................................................................................ 19 Table 3 ................................................................................................................................................ 33 Table 4 ................................................................................................................................................ 34 Table 5 ................................................................................................................................................ 35 Table 6 ................................................................................................................................................ 37 Table 7 ................................................................................................................................................ 41 Table 8 ................................................................................................................................................ 43 Table 9 ................................................................................................................................................ 44 Table 10 .............................................................................................................................................. 46 Table 11 .............................................................................................................................................. 47 Table 12 .............................................................................................................................................. 48 Table 13 .............................................................................................................................................. 50 Table 14 .............................................................................................................................................. 58. vi.

(8) LISTS OF FIGURES Figure 1 Changes in Taiwan’s GDP and Consumer Price Index in the past 15 years ....................... 12 Figure 2 Changes of salary and working hours of Taiwan industrial and service industry in the past 15 years ...................................................................................................................................... 12 Figure 3 Data structure of survey years ............................................................................................. 23 Figure 4 Wage by age ........................................................................................................................ 38 Figure 5 Wage by period .................................................................................................................... 38 Figure 6 Wage by cohort .................................................................................................................... 39 Figure 7 Wage by years of education ................................................................................................. 39 Figure 8 Anchor points of quadratic function of wage by ages ......................................................... 53 Figure 9 Anchor points of quadratic function of wage by periods .................................................... 55 Figure 10 Anchor points of quadratic function of wage by cohorts .................................................. 57. vii.

(9) Chapter I. INTRODUCTION 1.1 Research Background and Motivation 1.1.1 Current Salary issues in Taiwan Salary issues had been widely discussed in management and social sciences fields throughout the years, because it could draw dramatic impacts on micro and macro levels. One of the popular research fields in micro perspectives, such as organizational behavior, deals with organizational performance, job satisfaction, quit intention of employees, and other issues. Salary is a very popular factor for discussing the causal effects among these issues, thus identifying mechanism behind. On the other hand, salary in a macro scale influences every individual from a broader perspective. For example, new entrants to the workplace in Taiwan have been troubled with 22k (Taiwanese legal minimum wage) for many years. Additionally, people nowadays have been arguing about the amendment of the law of minimum wage, which not only associates with labor rights but also draws implications on the competitiveness of a country. Overall, salary issues are so complicated but crucial to many fields that corporate leaders, policy makers, employees, and household members tend to bring them up from time to time, urging researchers to incessantly conduct analysis on various topics.. 1.1.2 Past and current research on salary issues When coping with issues about impacts of salary, lots of research compare the amount of salary among different people based on several demographic variables, such as job categories, gender, educational levels, and other sociodemographic. For instance, human capital theory talks a lot about the impacts of several variables—formal education years, experiences, working hours, on the level of salary. Human capital is a term popularized by Gary Becker (1964) and Jacob Mincer (1958) which refers to the stock of knowledge, habits, social and personality attributes embodied in labors so as to produce economic value. A series of human capital variables, such as formal education, working hours, seniority, marital status, were taken into the examination of wage premium and/or wage penalty (e.g. Gupta & Shaw, 2014; Blaug, 1972; Becker, 1993; Card, 1995). In addition, issues about salary changes as a result of changes in marital status in terms of women and men, termed as “wage penalty” and “wage premium”, respectively, have been popular research topics 1.

(10) these years (Hsu & Chiou, 2015). Consequently, research on salary comparisons among people has been developed for many years, and mostly has been done by cross-sectional analytical techniques. Nevertheless, discussions about salary nowadays are not only limited to betweensubject analysis, but are expanded to areas which are suitable for using temporal variables, such as age, period and cohort variables (Hsu & Chiou, 2015; Fienberg & Mason, 1985). This kind of research requires more advanced statistical tools; therefore, traditional analytical models, such as cross-sectional models, are still inadequate. Nowadays, more advanced models driven by more comprehensive data—data obtained from individuals of a representative sample being measured across numbers of years— enable researchers to observe individual’s wage profile throughout his/her life span, and compare wage levels among different cohort groups at the same time. Compared to traditional techniques, it is more likely for modern advanced analytical tools to complete wage trajectory research from more perspectives.. 1.1.3 Relevant Issues on Age, Period, and Cohort (APC) Analysis One of the systematic studies of temporal issues is called age-period-cohort (APC) analysis, which deals with the influence of age, period and cohort variables on certain dependent variable (Jaspers & Peters, 2016; Chernyavskiy, Little, & Rosenberg, 2017; Sun & Chen, 2017). In following sections, in order to make it more clearer, some past research as well as modern applications on age, period and cohort variables are introduced. Age effects are variations associated with age groups chronologically. They can result from physiological changes, accumulation of social experience, social role changes, or a combination of these. Age effects therefore represent biological and social processes of aging to individuals and also reflect developmental changes across the life span. This can be seen in considerable variations across time and space in many outcomes, such as fertility, schooling, employment, marriage, disease prevalence, mortality, and other socioeconomic issues. Due to the limitation of statistical tools and database, past researchers had difficulties tracking down and analyzing the wage profile across one’s lifespan. Most research collected cross-sectional data and compared and drew conclusions on the relationship between salary and age. For example, a prior research confirmed that there is a quadratic relationship between age and salary, indicating a downward concave of the relationship (Hsu & Chiou, 2.

(11) 2015). Nonetheless, due to the nature of age, we should focus more on the changing trajectory within subjects as they get older when doing research on salary trajectory. Period effects are variations over time periods or calendar years that influence all age groups simultaneously. Shifts in social, cultural, economic, or physical environments may in turn induce similar changes in the lives of all individuals at a point in time. Period effects subsume a complex set of historical events and environmental factors, such as world wars, economic expansions and contractions, famine and pandemics of infectious diseases, public health interventions, and technology breakthroughs. For example, the financial crisis occurred in 2007-2008 or even Taiwan's reform to labor policy and annuity implemented in 2017 are such variations that influence people of all age groups at the same time. Cohort effects are changes across groups of individuals who experience an initial event such as birth or marriage in the same year or years. A birth cohort moves through life together and encounters the same historical and social events at the same ages. Birth cohorts that experience different historical and social conditions at various stages of their life course therefore have diverse exposures to socioeconomic, behavioral and environmental risk factors. For instance, in the 1940s, it was the starting point of economic development in Taiwan, so people born before 1940s experienced those years of low wage level. In the 1950s, Taiwanese people encountered the painful Post-Martial Law Period together. Whereas in 1960s and 1970s, they went through the prosperous periods of economic takeoff, and the wage level had peaked in those 20 years. However, in the 1980s, Taiwan saw an economic downturn again, with people experiencing the falling wage level (Directorate General of Budget, Accounting and Statistics, Executive Yuan, R.O.C, 2013). That is to say, cohort effect means that people of different birth cohorts went through different social or economic events as a whole.. 1.1.4 The importance, the main problems and solutions of APC analysis APC analysis has the extraordinary ability to depict the whole complex of social, historical and environmental factors that affect individuals and populations of individuals in the meantime. Many research topics emphasize trajectory, such as the studies of social change, etiology of diseases, aging, and population processes and dynamics, often show that age, period and cohort effects exist in both longitudinal and cross-sectional data. That is to say, age, period and cohort effects exist in the lifespan of different people simultaneously. Researchers from all kinds of fields are interested in separating them to find out the 3.

(12) mechanism behind those time-related issues. However, the challenges posed by APC analysis are also well-known because the three variables are completely collinear. Whether time-related changes can be sorted out and separated into age effect, period effect, and cohort effect is viewed as conceptually important but practically difficult. If we know the age of an individual and what year he/she is measured, we can also know his/her cohort, that is, the year he/she was born, which making it impossible to separate linear age, period and cohort effects from one another. It also means that if we get one of these trends wrong, we will get the others wrong as well. Data produced by just a linear period effect would look identical to data produced by a combination of age and cohort effects of the same size, but telling them apart is impossible. And this is the identification problem that lies in solving the APC issues:. Age = Period – Cohort, or Period = Age + Cohort. There have been many attempts to figure out solutions to identification problem. Thanks to the evolution of advanced statistical tools, research on APC issues has gradually increased over the last few years. Compared to cross-sectional data which mostly applied in prior studies on APC issues, when longitudinal data is adapted, we have to not only focus on the theoretical and practical implications of the issue itself, but also apply rigorous methodological design with more complex statistical models. Therefore, the rise of highlevel statistical models, such as hierarchical linear modeling (HLM), structural equation model (SEM), and latent growth model (LGM) can provide better analytical solutions for processing temporal variables.. 1.1.5 Applying an appropriate database to trajectory research When dealing with broad topics like salary issues, both between-person differences in development and the development of individuals as they age are concerned. As mentioned in the previous section, age-period-cohort analysis can be used to deal with such differences across genders, races, socioeconomic classes and other characteristics, where birth cohort to which an individual belongs and period events (i.e. economic downturn) play important roles in shaping development. And this is one kind of so called “trajectory research”. 4.

(13) Trajectory methods have emerged over the last several decades as important tools for investigating life course dynamics, including between-person differences in development (George, 2009). Trajectories are simply patterns of variable values over time. For example, one may be interested in trajectories of unemployment rates, stock market closing values, or other macro-level phenomena; on the other hand, one may have interests in trajectories of income or health at an individual level. In addition, trajectories can also be referred as the ordered timing of life events, such as school completion, employment, marriage, childbearing, retirement, and death (Lynch & Taylor, 2016). In this study, models of such trajectory issues would be restricted to repeated measures (i.e. levels) of the same phenomenon, not the timing of multiple qualitative events. For the purpose of illustrating trajectory methods, we rely on a subset data from Panel Study of Family Dynamics (PSFD), a panel study of adults in Chinese families. It not only contains demographic information and human capital variables but also a long-term collection of household dynamics and income information. Therefore, this study combines the use of this database with high-end statistical methods (i.e. multilevel modeling) to make salary comparisons in both between- and within-perspectives. When measuring variables within subjects, it is more difficult but at the same time more meaningful because such research is able to detect internal variations which couldn’t be achieved in most prior research. For example, when processing age and period variables in this study, it is crucial to note that they are synchronized along the trajectory. Namely, variations along a trajectory can sometimes be counted as the aging process of individuals but other times be referred to as the shifting of time. To deal with such confusing concepts and inseparable relationships between variables in trajectory research, research on age-period-cohort analysis therefore thrives and becomes more and more important.. 1.1.6 How to incorporate the Human Capital Theory Results reveal that human capital is the primary factor that explains wage differences between and within subjects. One of the most popular theories credited to it is human capital theory (Mincer, 1958; Becker, 1964; Blaug, 1976). Economist Mincer constructs an earning function that describes individuals’ wage trajectory across lifespan, and Becker (1964) proposed the word “human capital” to explain that labors’ techniques and abilities can have positive impacts on their level of production and wage. They both talked about some basic 5.

(14) human capital factors, such as job experiences, personal techniques, and abilities, and their contribution to the enhancement of personal production value and wage premium. Blaug (1976) later elaborated that the enhancement of human capital can be seen as a kind of personal investment, including accumulating years of formal education and work experiences, finding a better job, as well as looking for better medical and health supports, and the overall purpose is to exchange for monetary and non-monetary compensation. Of all the above discussions about human capital theory, we will select some critical factors that benefit our study the most on wage trajectory.. 1.2 Research Problems and Purposes The purpose of this study is to investigate APC issues by applying an evidence-based database with an incorporation of human capital factors, age, period and cohort variables as well as the wage variable. We hope to conduct a longitudinal research by expanding our discussions about salary issues to the influences of age, period and cohort effects on wage trajectory. Accordingly, we will incorporate A, P and C respectively, or simultaneously in our study, and our research purposes are listed as follows: 1. The relationship between age effects and wage trajectory 2. The relationship between period effects and wage trajectory 3. The relationship between cohort effects and wage trajectory 4. Discussions about an incorporation of the combination of age, period and cohort effects to wage trajectory 5. Examination on the relationship between human capital factors and wage premium. 6.

(15) Chapter II. Literature Review 2.1 Salary Issues From personal aspects to industrial aspects, from microeconomic discussions to macroeconomic discussions, and from within-subjects’ analysis to between-subjects’ analysis, salary issues are just so critical and relevant to our lives that we can see them leading various discussions everywhere. Some people care about the organizational design of salary structure in a micro-level, while some people put more emphasis on the national wage structure in a macro perspective. Many terms like wage or earnings are the alternatives to salary; therefore, it is important to define in this paper the terms that would be used to describe such concept. And it is their different managerial implications that needs to be clarified before being further interpreted in this paper. Normally, "wages" are accumulated on the basis of working hours, and paid by employers every day or every week, while "salary" typically defines a fixed amount paid by employers, not necessarily for specific hours worked but for completing the duties of job. On the other hand, "earnings" can indicate a variety of income. It can include wages and salary, but it also describes funds received from nonworking income, such as interests and dividends (Gupta & Shaw, 2014; Merriman, 2014; Hsu & Chen, 2011; Carliner, G., 1980; Mincer, 1974). By definition, salary and wage issues are both parts of studies of earnings, or we can say, compensation. In order to make the terms we use in our study as consistent as possible, we will use “wage” as we address our main discussions in this research, for it fits our research objectives the best and it is the most suitable term to conduct analysis on the wage trajectory across lifespan. Different from what we expected, in 2014, there was an article published in Human Resource Management Review pointing out that employee compensation had been a neglected area of HRM research. Therefore, Gupta and Shaw offered a plea for more research on compensation. Among many reasons mentioned in the article for the neglect of compensation research, we think the most important one is that compensation can arguably make critical influences on the quality and effectiveness of human capital (Gupta & Shaw, 2014). It implies that the variation and accumulation of one’s salary are highly associated with the organizational design. Unless the compensation system is done appropriately, other organizational policies and procedure cannot have their desired effects (Gupta & Shaw, 2014). Downes and Choi (2014) quoted the taxonomy of Gupta et al (2012) for horizontal 7.

(16) versus vertical pay variation, and they illustrated the positive and negative influence mechanisms of pay dispersion on employees' performance. Therefore, since compensation remains probably the most influential tool for executing successful human capital management and enhancing organizational effectiveness, such questions are in critical need of more comprehensive answers. Recently in Taiwan, there have been lots of conflicts between different parties. In 2017, the implementation of the reform to annuity and the amendment of minimum wage legislation resulted in not only political opposition and disputes but also the changes in operation, especially the wage level and welfare system, of the entire industry in Taiwan. Take the impacts of minimum wage legislation for example: research found out that such legislation influenced mainly the employment of youths, and results showed that a 10 % jump in the minimum wage would increase the youth employment rate and the youth labor participation rate by 0.47% (Chuang, 2006). In a short summary, labor problems recently in Taiwan had not only aroused organizational pay structure and pay distribution issues (which corresponds to the minimum wage issue), but affected some human resource practices and operational costs of corporations; last but not the least, it even influenced the structure of the whole labor industry. Obviously, salary issues have two-sided effects: one with individual and microeconomic impacts, and the other one with labor-sided and macroeconomic impacts. Throughout history the most comprehensive and clearest function view of earnings is Mincer Earnings Function. Mincer, father of modern labor economics, proposed the Mincer Earnings Function in 1974, which was the first empirical formulation of earnings over one’s lifecycle. It is a model that illustrates wage as a function of schooling and experience, with the logarithm of earnings modelled as the sum of years of schooling and a quadratic function of years of labor market experience (Mincer, 1974). Yi (T )  ln( wage) it   0   1 Ti   2 Ti 2   s S i   i. The function construct and the selection of variables above are based on human capital theory, and the t and t square reflect that Mincer believed the accumulation of years of experience make the most critical contributions to organizational performance. S is a collective concept in the function, which is associated with the schooling phase of human capital, such as education and employee trainings. The total investment of schooling is a kind of investment that we define as a fixed element of human capital, while tenure on the other hand, develops and increases as we age. Thanks to Mincer’s pioneering work, 8.

(17) variables such as schooling and work experience are now the most commonly used in human capital research.. 2.2 Critical Factors of Human Capital Theory on Wage Issues Wage level can reflect the outcome of production and the value of human capital. Among factors that cause variations and distinctions of wage levels, the most critical element is the investment and accumulation of human capital factors, namely factors of wage premium. In this study, we are going to incorporate some most widely studied variables in the human capital theory (Mincer, 1958; Becker, 1964) to our statistical models to test their interpretation of variations in wage.. 2.2.1 Formal Education The influence of formal education on rising levels of labor production had been a classical topic discussed since human capitalist like Adam Smith. They assumed that such mechanism is the same as physical capital investments (such as machines or equipment), which have direct impacts on improving the efficiency of labor production. In more recent years, Mincer (1974), Becker (1975) and Blaug (1976) also suggested that accumulation of schooling years can lift up one’s knowledge level and his/her capabilities; subsequently, level of production and returns on jobs increased. Education is the main human capital factors that causes wage premium: if human capitals are invested and level of production and capacity are enhanced, the individual capabilities of employees as well as their investments on themselves define the wage differences accordingly. Comparing to tenure that is beyond one’s control, people can actively invest in their education and get higher returns on job. The wage premium effect of formal education plays an indispensable role in wage differentiation individually.. 2.2.2 Tenure Because of the influence of job supply, accumulation of tenure is impossible to be decided by individuals. Despite of this, tenure is still a crucial wage premium factor in human capital theory. The longer employees stay in the same company, they are more likely to accumulate knowledge in that field and achieve higher proficiency of that job. In the end, 9.

(18) they will contribute to the enhancement of their production levels as well as their wages (Ang et al., 2002; Johnston, 2002; McKnight & Tomkins, 2004). In addition, according to the job match theory, employees’ production levels depend on how they’re matched to their jobs. If they match their jobs well, it means that they are likely to perform higher production on jobs, resulting in higher salary (Topel, 1991). Otherwise, if they match their jobs poorly, they tend to leave their jobs in the end. Therefore, the longer employees stay (higher tenure), the better they fit their jobs—a positive effect on wage premium. However, due to its high collinearity with age variable, eventually tenure variable is not considered as the research variable.. 2.2.3 Job Involvement Another important human capital factor is job involvement. In addition to the vertical competition in an organization, which makes employees actively invest in education and work harder to pursue higher positions and higher salary returns, employees in the same job level or in the same position may create horizontal pay dispersion via pay-for-performance pay structures or seniority pay structures (Gupta et all., 2012; Shaw & Gupta, 2007). Downes and Choi (2014) pointed out that vertical variations can be explained by competitive theory; however, horizontal differences should refer to traditional theories such as social comparative theory and equity theory. When discussing wage premium, working-hour variable is another important explanatory variable. In a recent study, Merriman (2014) examined the relationships among working mode, working hours and wage, and he argued that the increase of working hours not only contributes to objective benefits, but also generates subjectively perceptual differences and cognitive variations. He pointed out that overwork in most cases results in the reduction of productivity instead. Therefore, Merriman (2014) argued that if more working hours generate higher wage premium, it is based on vertical competitiveness. However, when examined in another perspective from the research, benefits of working hours to wage are defined as a quadratic polynomial, with an existence of an optimal level. Whether to adopt a linear premium perspective or an optimal level perspective is to be tested in the future. All in all, different working hours can not only create wage differences between individuals but create wage variations within individuals at different periods of time.. 10.

(19) 2.3 Other Factors of Wage Issues Besides human capital theory, there are many other demographic factors, such as genders, marital status, motherhood penalty, and health conditions, and some accidental factors that might have impacts on earnings. 2.3.1 Demographic factors In terms of industrialized countries in Europe and America, some relevant studies pointed out that the gender wage gap has gradually narrowed, but the shrinking rate has gradually slowed or stagnated (Blau and Kahn 1981; Eurostat 2013; Weichselbaumer and Winter-Ebmer 2005). Other researchers paid attention to the impacts of motherhood on gender wage gap, called “motherhood wage penalty”. Hsu and Chiou (2015), have proved that human capital is the primary factor that explains motherhood wage penalty.. 2.3.2 Accidental impacts Above are some research reviews about impacts on individuals; however, some factors may influence earnings from a broader environmental context: economic cycle, industry structure, and financial crisis. In years 2007-2008, global financial crisis began with a crisis in the subprime mortgage market in the United States, and developed into a full-blown international banking crisis with the collapse of the investment bank Lehman Brothers. Subsequently, Taiwan’s economy was affected most seriously in the year 2009, and it caused several negative impacts of all kinds. As we can see from Figure 1, Taiwanese GDP declined significantly in the year 2009, and it could cause a rise in unemployment rate. Another interesting discovery is in Figure 2 that while there was a drop in monthly salary in 2009, there were decreasing working hours in 2009 as well. We can infer that it was resulted from the “unpaid leave” policy proposed that year in Taiwan, which made people go on holidays without being fired.. 11.

(20) GDP（dollar）. CPI. 25,000. Financial Crisis. 22,500 20,000 17,500 15,000 12,500 10,000 7,500 5,000. 2,500 0. 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81. Figure 1 Changes in Taiwan’s GDP and Consumer Price Index in the past 15 years Source: Directorate-General of Budget, Accounting and Statistics, Executive Yuan, R.O.C. National Income and Monthly Price Statistics 50000. average monthly salary of employees. 48000. 46000. 190 185 180. 44000. 175. 42000 40000. average working hours per week of employees. 38000 36000. 170 165 160. 34000. 155. 32000 30000. 150 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106. Figure 2 Changes of salary and working hours of Taiwan industrial and service industry in the past 15 years Source: Directorate-General of Budget, Accounting and Statistics, Executive Yuan, R.O.C., Salary and Production Statistics. It showed that factors with regard to age which variates individually, such as some human capital factors and working hours, as well as factors concerning period effect which impacts people in the same period as a whole, can both contribute to wage differences among people, or even different wage trajectory across one’s lifespan.. 12.

(21) 2.4 Earning function with temporal perspective Researchers have been paying attention to the relationships between wage differences and organization’s fairness, justice, and performance. In human resource field, when researchers discuss issues of wage differences, they basically take a cross-sectional between-individual dispersion perspective. Nevertheless, if we pay attention to the forming mechanism and process of wages, wage difference is not a static result. It is a longitudinal result of cross-time accumulation. That is to say, wage issues should be discussed not only in an individual differences perspective, but in a within-individual change view, namely conducting analysis in the form of earning profile or wage profile. Basically, wage profile is an essential point of view to human capital theory, and it’s also a fundamental basis for human capitalists to build earning function. The most classical wage profile econometric model is Mincer’s earning function, with quadratic polynomial temporal factors. Different from our previous discussions about this function, we are going to elaborate it in a more temporal way; therefore, we have to demonstrate it once more: 2 (1) Yi (T )  ln( wage) it   0  1 Ti   2 Ti   s Si   i. The outcome variable is the logarithm of wages as a function of time, and the intercept reflects the starting point of wage, while the slope associated with T is a temporal effect with quadratic function. β1 is the first-order term of temporal effect, and β2 is the secondorder term of temporal effect, showing a downward opening when the latter one is negative. Si represents schooling phase of investment. This earning function indicates that as the time goes by, wage profile is a parabolic shifting from positive to negative. Because time usually increases with age, the time term is mostly substituted with age, becoming an invert-Ushaped of concave age-earning profile (Becker, 1993; Ben-Porath, 1967). Literally, Mincer Earning Function only depicts time as one of the explanatory variables of wage; therefore, observations in empirical models are cross-sectional continuous spectrum obtained by different individuals at different points of time or ages. And that’s the reasons that the equation 1 has no time coding in subscript. Late scholars used panel data, which is collected repeatedly across many years on a fixed sample, to conduct wage profile analysis both between- and within- individuals. Taking a motherhood penalty research done by Staff and Mortimer (2012) as an example, its earning function is illustrated as follows: (2) Yit = ln(𝑤𝑎𝑔𝑒)𝑖𝑡 = 𝛽0𝑖 + 𝛽1𝑖 𝑡𝑖𝑡 +𝛽𝑠𝑖 𝑆𝑖𝑡 +𝜀𝑖𝑡 13.

(22) In the equation 2, each variable contains t in subscript, indicating that the same individual would be measured or surveyed t times, while the i in subscript representing different individuals. Such function enables researchers to test premium effects of crosstime and cross-sample simultaneously. In other words, panel data here could be regarded as a two-leveled multilevel modeling (MLM), with t in the first level in subscript representing variation of time, and i in the second level in subscript depicting individual differences. In the first level, wages at different points of time were taken as the outcome variables, and the regression equation is called level-one equation. Additionally, the intercept and the slope in level-one equation can be used as the outcome variables in level-two equation, and explained by the level-two regression equation. It is called the hierarchical linear modeling (HLM).. 14.

(23) 2.5 Statistical Issues with Age, Period and Cohorts Because earning function is associated with time-series issues, time related variables are regarded as the main focus of these studies. Age, period and cohort variables are among them the most representative variables.. 2.5.1 Age Effect Basically, wage increases as we age, and this is called an age effect. In terms of wagerelated research, age variable is the most fundamental explanatory variables that variates with time. Based on human capital theory, productivity increases as we age, hence a wage premium effect of age. According to Hsu & Chiou (2015) and Hsu & Chen (2011), they affirmed that there is a quadratic relationship between age and wage in the wage trajectory study, namely, age is an explanatory variable with downward concave characteristics.. 2.5.2 Period Effect As for people living in a specific period, their wage levels are easily influenced by some specific social and economic events, and we refer this as period effect. For instance, 2008 to 2009 global financial crisis and the adjustments to Taiwanese labor policies and annuity policy have impacted everyone during those periods of time. In a recent research, Jaspers and Pieters (2016) conducted an APC analysis on the development of materialism across the life span of American people. Over 4,200 individuals were examined through 8 waves spanning 9 years, and divided into 13 birth cohorts with 5-year interval. They were measured repeatedly by their thoughts about materialism, monetary values, and health conditions. Additionally, during the measurement period of this study, a global economic downturn took place; therefore, to capture the economic downturn, a period dummy variable (1= years before 2008, and 0= years after 2008) was put into the model in addition to age and cohort variables. The results showed three ways that respondents’ material values and desires are influenced. Acquisition as the pursuit of happiness (the belief that possessions are essential to satisfaction in life) was lower after the economic downturn. Moreover, AgePeriod interaction effects were also significant: younger adults, who were threatened more by the economic downturn, were higher on acquisition centrality (the extent to which one places possessions and acquisition at the center of their lives) and possession-defined success (using possessions as indicators of success) after the economic downturn. Especially when the outcome variable is possession-defined success, the quadratic coefficient is 15.

(24) negative and significant. It indicates that before the economic downturn, the significant and positive quadratic effect on age would slow down, which means that from young to older age, quadratic effect on materialism gradually becomes a linear effect. However, after the economic downturn, age effect on acquisition centrality accelerated instead. Overall, this research emphasizes the importance of period effect on trajectory research.. 2.5.3 Cohort Effect Nevertheless, despite every measurement period, different people with different birth cohorts have distinct life experiences, while people in the same cohort experience life together and encounter similar historical and social events at the same ages. It is called the cohort effect. Hsu and Chen (2011) compared the wage differences between the secondgeneration immigrants from China to Taiwan after 1949 and natives (Hokkien and Hakka) in Taiwan, by using cross-sectional data from Taiwan Social Change Survey for six years 1992, 1993, 1995, 2000, 2003, and 2005. This research found out that there are significant wage differences between different generations in Taiwan, and the major cause of differences in wages among ethnic groups is the difference in productivity. However, the influence of other factors, such as discrimination, is minimal. Furthermore, the difference between ethnic groups gradually shrink as more and more younger generations enter. In other words, if research subjects are across different generations, especially in wage research, cohort variables become the essential focus of such research. Unfortunately, the study of Hsu and Chen is not a panel study but an analysis of cross-sectional data, so it is impossible to investigate the interaction effects between age and cohort variables in this study. As a result, to examine the cohort effects on wage trajectory, accelerated longitudinal data is adopted in our study.. 2.5.4 Data Structure in APC models In social studies, such as social demography, epidemiology, education development and production economy, which focus on vicissitudes, age, period and cohort effects often coexist in those panel data, and because of this, it is called an APC issue (Bell & Jones, 2016; Feinberg & Mason 1985; Yang & Land, 2008, 2013). Because A, P, and C are all related to time, their collectively shared experiences are taken as contextual factors (Robertson, Gandini, & Boyle 1999; Glenn 2003). When A, P, and C are discussed in the form of some 16.

(25) data structures, they are often called an APC model (Feinberg & Mason 1985; Yang & Land, 2008, 2013). When coping with the data structure of APC analysis, we have to pay attention that in terms of individual observations, period variable increases with time, but everyone’s beginning and ending periods of time are the same, thus resulting in the same mean value and variance. Period variable only has within-subject variance, but it does not have between-subject variance. On the contrary, age variable regarding individual observations also changes with time, but the age variable of every respondent varies in beginning, end points and mean values, except for variance remaining the same. Even though both age and period are variables that change with time, they are constrained to a linear equation that period minus age is equal to cohort. Assuming that from 2010 to 2019, we repeatedly measured respondents who were born in 1980 to 1989 for ten times, and developed a 1010 cells of age, as demonstrated in Table 1. In each cell, age equals to period minus cohort. For instances, in the 2010 survey, people born in 1980 aged 30, while people born in 1989 was at the age of 21. By the year 2019, people born in 1980 to 1989, they are going to be 30- to 39-year-old.. Table 1 Data format of age matrix for different cohorts in different periods. Period Cohort 1 2 3 4 5 6 7 8 9 10 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 1. 1980. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 2. 1981. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 3. 1982. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 4. 1983. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 5. 1984. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 6. 1985. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 7. 1986. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 8. 1987. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 9. 1988. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 10 1989. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 17.

(26) Although people of different cohorts are measured in diverse periods, they are simultaneously aging, making the relationships among age, period and cohort become inseparable and completely dependent. Besides, if researchers would like to explore issues of a specific age range, take juvenile years 21-29 for example, only the first measurement period (2010) has the complete samples of 21- to 29-year-old. As time passes, fewer samples are of that age range; therefore, we have to increase our sampling cohorts in order to obtain sufficient samples. In general, social science studies take age variable as the most fundamental demographic variable, so it needs adequate range and sample size. Secondly, we have to compare cohort differences with sufficient numbers of cohorts. As a consequence, when a study involves issues of age, period and cohort variables simultaneously, the key to the design of sampling is how to obtain ample observations of certain ages and cohorts within a limited time of collection. It is referred to as an issue of cohort design.. 2.5.5 Recent Analytical Techniques for APC Issues Thanks to the improvement of statistical analytical techniques, in recent years ageperiod-cohort analysis has gradually increased (for example: Chernyavskiy, Little, & Rosenberg, 2017; Jaspers & Pieters, 2016; Mehrotra & Carter, 2017; Huang, Keyes, & Li, 2018; Sun & Chen, 2017; Schomerus, Auwera, Matschinger, Baumeister, & Angermeyer, 2015). It revealed that in longitudinal research design, besides the practical meanings of the issue itself, the more important thing is the way of dealing with these three critical time variables. Especially for the rise of some advanced statistical models, such as multilevel modeling and structural equation modeling, it provides more ideal analytical tools for APC analysis. The value of conducting research on the issues of age, period and cohort is the existence of an identification problem among these three variables. That is, these three variables are completely linearly dependent, making them impossible to coexist in a statistical model: Period= Age + Cohort, or, Age=Period – Cohort. 18.

(27) Some researchers have approached this problem by cross-classified model in the multilevel modeling (MLM) to analyze APC issues of non-panel study (Jou & Chu, 2008; Yang & Land, 2006, 2008, 2013). In single-cohort longitudinal data, where people of the same initial age are observed over a longer time period, cohort effects fail to be estimated, and age confounds with period. As illustrated in Table 2 (a), if we repeatedly measure people born in a single cohort 1980 from the year 2003 to 2017, for 15 years, and then we are able to analyze their age changes. Nevertheless, if a single cohort from 23 to 37 years old is examined, then the same groups of people need to be repeatedly measured for 15 times, and then the research has to be suspended for 15 years. However, if we repeatedly measure respondents who are born in 1980(23-year-old), 1975(28-year-old), and 1970(33-year-old) simultaneously in 2003, and we are able to obtain a complete age-spectrum data from 23 years old to 37 years old in five years. This kind of repeated longitudinal design targeting at multiple-cohort respondents is called a “multiple cohort design”, as we can see in the Table 2 (b) and (c). Table 2 Longitudinal Data Structure of Different Numbers of Cohorts AGE Cohort. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. P1. P2. P3. P4. P5. P6. P7. P8. P9. P10. P11. P12. P13. P14. P15. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P1. P2. P3. P4. P5. P2. P3. P4. P5. (a)Single Cohort 1980 (b)Three Cohorts 1970 1975 1980. P1 P1. P2. P3. P4. P2. P3. P4. P5. P5. (c)Eleven Cohorts 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980. P1. Note: P stands for measurement period. P1=2003, P2=2004, …, P15=2017. 19.

(28) In the multiple cohort design, age data obtained from different birth cohorts and in different periods, gradually increases in the data structure showing above, thus called “accelerated longitudinal design” (Bell, 1953). This kind of data can not only conduct research on changing trajectory between different cohorts, but also separate age effect from period effect. Most importantly, it can save researchers’ time to keep track of respondents and reduce sample loss. Furthermore, accelerated longitudinal designs combined with multilevel models have been gradually developed to identify age, period and cohort effects (Fienberg, 1985; Yang & Land, 2013), which would be elaborated in the following chapters.. 2.6 Inference about research hypothesis In this research, three human capital factors—gender, years of education and working hours, are selected as wage premium factors. Considering the effect of gender, an inference that men earn more than women is still proposed as our hypothesis. In terms of years of education variable, it does not change with time; therefore, it is supposed to have positive premium effects on between-subject wage levels. Regarding working-hour variable, it differs with time, thus resulting in positive premium effects at both within- and betweensubject levels. In all, the following is a set of hypothesis regarding premium effects of human capital variables. Hypothesis 1: Human capital factors have different effects on wage levels. Hypothesis 1a: Gender difference is positively associated with wage difference. Hypothesis 1b: More years of education are relevant to higher wage levels. Hypothesis 1c: More working hours are associated with higher wage levels. In addition to hypothesis about human capital factors’ impacts on wage premium effects, in this study the most important discussions about wage trajectory are the temporal effects, namely identifying the issue of APC effects. According to our previous discussions, many precedent research had drawn some inferences about relationships between wage and 20.

(29) age, period and cohort variables. Therefore, in this section regarding temporal effects on wage levels, some hypothesis is developed as follows. Hypothesis 2: Age, period and cohort variables have different effects on wage levels. Hypothesis 2a: Age variable influences within- and between-subject wage levels. Hypothesis 2b: Period variable influences within-subject wage levels. Hypothesis 2c: Cohort variable influences between-subject wage levels. It is particularly worth mentioning that these three variables draw impacts on wage at different levels. Both age and period are variables that change with time, which means that they may influence the wage level on the within-individual level (L1). However, the influence of age effect may not only occur across one’s lifespan but among individuals. That is to say, as people age, their own wage level might change (L1 age effect), and levels of wage among people might diverse as well (L2 age effect). Lastly, one’s birth cohort does not. change with time, so this variable only impacts between-individual comparisons (L2). on wage levels. Among the hypothesis made in the previous two sections, some are further investigated to test whether wage premium effects differ when APC factors are incorporated. Based on the hierarchical regression analysis, A, P and C variables belong to demographic variables, and their effects on wage are prior to the human capital variables. To discuss the covariate effects of these variables, because A, P and C provide temporal effects of history context, they would be firstly examined in the models, and after that, the human capital factors are subsequently examined. Namely, the integration effect of APC variables on premium effects is acted as a role of controlling variable which derives the APC controlling effect hypothesis as below. Hypothesis 3: Age, period and cohort effects are significant with human capital premium variables. (Controlling effect hypothesis) 21.

(30) Chapter III. Methods To begin the APC analysis on wage trajectory, in this chapter the longitudinal database— Panel Study of Family Dynamics (PSFD) database as well as the corresponding methodologies would be introduced. To illustrate, firstly detailed information of the PSFD database are presented, and then characteristics and processing of research variables are elaborated. Subsequently, the research procedure would be listed; last but not the least, some methodologies adapted in this study would also be summarized.. 3.1 Database and Research Sample “Panel Study of Family Dynamics” is a long-term fixed-sample panel design initiated in 1999, targeting the adult population in Chinese families. It covers different birth cohorts, and in the Taiwan survey, children of the main respondents have been added into the sample since 2000. It is currently administrated by the Project for the Study of Family in Chinese Societies (PSFCS) under the Research Center for Humanities and Social Sciences (RCHSS). The latest data has been released on 16th, Jan, 2018. The PSFD project aims to undertake a comprehensive research on economic, social, psychological and institutional aspects of Chinese families. It originates from the belief that the types, structures, and patterns of interaction of families in Chinese societies are more complicated than those in Western societies. Correspondently, the theoretical models embodied in the values and practices of Chinese families should be more complex than those set up from Western ones. The PSFD project is therefore intended to examine whether existing western theories of the family can be applied to Chinese society. On the other hand, based on the empirical findings from PSFD, new theoretical frameworks different from Western ones are expected to be abstracted and developed.. 22.

(31) Measurement--Years (Common Era). -. Bi r t h. (Newly Sampled). (N ew ly Sa m ple d). (New ly Samp led). (Survey in 2000 on parents of RI1999 and RI2000) (Survey in 2000 on siblings of RI1999 and RI2000). Figure 3 Data structure of survey years Note: * means that the data has not been publicly released. Birth cohorts are denoted by the Republic Era. Blue area (RR) is the main sample; yellow area (CV) is the child sample; green area (RCI) is the main samples of either newly sampling ones or children who aged over 25 and being tracked for the first time. The same box represents the same questionnaire. RI-2009 questionnaire consists of newly nationally sampling representative and those who aged 25 and being tracked as the main sample for the first time. Source: http://psfd.sinica.edu.tw/web/check.htm 23.

(32) As demonstrated in Figure 3, in 1999, the first face-to-face interview of PSFD was conducted to collect 1,000 randomly sampled individuals born in 1953-1964. Refreshment samples of adult respondents born in 1935 -54, 1964-76, and 1977-83 were first interviewed in 2000, 2003, and 2009, respectively. These follow-up surveys for these four groups of main respondents were conducted annually. The core contents of the follow-up questionnaire (Questionnaire R) include the respondent’s demographic traits, work status and job information, marital status and spousal information, demographic traits of parents and parents-in-law, interaction with family members, housing and living arrangement, income and expenditure, and childbearing and rearing information. The parent-child relationship is one of the most important intra-family relationships. In the questionnaire of the main respondent, there are many question items regarding his or her children. To establish more comprehensive two-generational data, the surveyed sample has been extended to the young children of the main respondents since 2000. When the children were aged between 16 and 24, they were re-interviewed biennially using Questionnaire C. When the children reach the age of 25, they are treated as main respondents and interviewed using the first-wave questionnaire of the main respondents (Questionnaire RCI). After that, the children are traced annually using the same questionnaire as the main respondents (Questionnaire R). To lessen the interviewing burden, since 2012 the follow-up survey of the main respondents (Questionnaire R) is conducted on a biennial basis, in the mean while as Questionnaire C and Questionnaire RCI. Please refer to SRDA website (https://psfd.sinica.edu.tw/web/plan_01en.htm ). In our study, we focus on the discussions about salary issues and corresponding issues of APC; therefore, only some research variables would be extracted from PSFD. We dropped question items regarding parent-child relationship, marital status, spousal information, childbearing and rearing information, and those that are unnecessary to the study, which accounts for a large proportion of PSFD database. Moreover, other great proportion of detailed information of work status and job description: daily commuting hours, reasons for leaving the last job, reasons for not having a job, reasons for not looking for jobs, and so on, are also excluded. Although these items are invaluably important to this database, only some variables based on our research purposes would be used and further elaborated in the following sections. Of the four groups of main respondents born in 1953-64, 1935 -54, 1964-76, and 197783, the numbers of complete interviews of the first-wave survey conducted in 1999, 2000, 24.

(33) 2003, and 2009 were 999, 1,960, 1,152, and 2,182, respectively. In a previous study (Chiou, 2014-2016), the data from 1999 to 2011 were used for analysis (The survey data from 2012 to 2016 were under verification then). In 2012, their corresponding numbers of complete interviews were 545, 1,066, 652, and 1,649. In the same year, the number of complete interviews for the sample of children was 1,836 in total, of which 1,064 cases were interviewed by Questionnaire R, and the rest (752 cases) by Questionnaire C. Our study will be expanded to 2016 (4774 cases) with the latest data released on 25th Jan, 2018. From 1999 to 2016, an average cluster size of 5.598 indicates the average number of years to which participants had given their answers is 5.598, less than half of the overall measuring years.. 3.2 Research Variables This research aims to explore the impacts of human capital premium factors on wage level in different periods and different cohorts. Consequently, we not only extract variables with wage information, but include data about formal education, tenure, and working hours.. 3.2.1 Wage Variables Total amount of wage is derived from monthly returns of jobs that states in the question: “How much do you receive from the total of your job in one month (sources ranging from salary, bonuses, overtime pay, year-end bonuses, executive business income, and self-employment income) ?” Normally the data obtained is nominal and positively skewed; therefore, in order to reduce skewness, eliminate the impact of prices, and align the scale with other variables, wage variable used in this model is the logarithm of actual monthly income, adjusted by Consumer Price Index updated from the website (https://www.dgbas.gov.tw/ct.asp?xItem=760&ctNode=3091 ), and then all multiplied by 100.. 3.2.2 Age, Period and Cohort Variables (1) Age: It is obtained from the interview year minus the year in which subjects were born. Since there might be a diminishing effect of the positive linear relationship between age and wage variables (Waldfogel 1997; Budig and England 2001), we also use the square of age variable as a quadratic form, testing the non-linear effect of age by incorporating both of them into the polynomial regression. 25.

(34) (2) Period: During the measurement period (1999-2016) of our study, a global economic downturn took place. In order to capture the incidence, a period dummy variable indicating whether measurement took place before or after (during) the economic downturn (1 = 1999 to 2009, and 0 = 2010 to 2016) is inserted (Jaspers and Pieters, 2016). (3) Cohort: Eleven birth cohorts were defined based on birth years: 1935-1940, 1941-1945, 19461950, 1951-1955, 1956-1960, 1961-1965, 1966-1970, 1971-1975, 1976-1980, 1981-1985, 1986-1989 (Jaspers and Pieters, 2016; Hsu& Chiou, 2015), all with a 5-year interval except the oldest and the youngest birth cohorts spanning four years and six years respectively because of fewer people in these groups.. 3.2.3 Human Capital Variables In this category, this study focuses on schooling years and working hours: (1) Years of schooling (eduyear): This number is obtained from the question, “What is your highest educational level?”, and it is originally coded as ordinal variable; however, in this study, we recode it into continuous one. Continuous variables, on the other hand, are years of formal education converted by the educational levels, such as 0 year for none-educated or self-study, 6 years for graduation from primary schools, 9 years for graduation from junior high schools (or any degrees that take 9 years to graduate), 12 years for graduation from senior high schools (or any degrees that take 12 years to graduate), 14 years for graduation from institutes of technology (or any degrees that take 14 years to graduate), 15 years for graduation from three-year junior colleges, 16 years for graduation from universities, 18 years for graduation from graduate schools, and 22 years for graduation from doctoral degrees. (2) Working hours (WH): Working hours of every participant is obtained from the question, “On average, how many hours do you work each week?”.. 26.

(35) 3.3 Research Procedure In this section, some critical procedures of data preparation and data analysis are introduced. Firstly, we have to register the member of SRDA website and get the permissions to download the latest data without any restrictions. Secondly, researchers have to thoroughly inspect the dataset, and refer it the code book, which is also provided on SRDA website. Third, we extract some of the research variables that we need from the data, and try to keep them consistent every year. Fourth, data concatenation proceeds. It is essential that we get the logarithm of variables after data concatenation. Fifth, we prepare and create variables forms that are needed for doing analysis, such as continuous schooling variables. Later on, we will keep examining our observations, and filter unqualified observations from our dataset. For example, observations with two-year information, or those who aged above 65, would be filtered.. 27.

(36) 3.4 Analytical methods In this study, we are going to apply MPLUS8 (Chiou, 2017) to conduct a two-level analysis on wage among employed people. To better normalize and standardize the data and the model structure, an MLR (maximum likelihood parameter estimates with standard errors) estimation approach was used in MPLUS 8 (Muthen & Muthen, 1998-2012), as well as a Bayesian measure of model fit (BIC). Models with smaller BIC values are preferred to models with larger values. Wage comparisons among individual differences and the analysis with some related factors belong to the level-two model, and the variations within individuals during periods of study, namely the wage changes within-subjects, belong to level-one model.. 3.4.1 Multilevel Modeling (MLM) In a hierarchical linear modeling, explanatory variables that change with time are separated into level-one variables, such as age (quadratic polynomial), tenure (quadratic polynomial), working hours, and other continuous variables. In order to maintain the same design as a fixed coefficient model, explanatory variables or control variables in level-one function need to enter the equation in the form of group-meaning centering, and then we can get some within-subject information of variables changing with time (Staff and Mortimer 2012; Wen and Chiou 2015). Except that the dependent variable does not need to do the mean deviation process, other features of variables are the same as the fixed effect regression model. Explanatory variables that do not change with time in a hierarchical linear model are some fixed information of individuals, and they are treated as level-two variables. These variables include levels of cohorts, levels of education, and the mean value of level-one variables, namely age (quadratic polynomial), tenure (quadratic polynomial), and working hours (the mean value of repeated measures). In addition, such variables that both applied in level-one and level-two functions: individual numbers applied in level one function representing within-subjects’ variance and mean value applied in level two function reflecting between-subjects’ variance, can be regarded as the contextual effects of individuals; therefore, they are called “contextual variables” (Duncan, Jones and Moon 1996). Explanatory variables in level-two function need to enter the equation in the form of grand-meaning centering, so that we can keep the overall intercept of the entire equation fixed. 28.