Economics of Human Capital, notes, Schemi e mappe concettuali di Economia

Scarica Economics of Human Capital, notes e più Schemi e mappe concettuali in PDF di Economia solo su Docsity! ECONOMICS OF HUMAN CAPITAL Part of our personal human capital: knowledge and health. They are acquired through education on one side and health care (medical care, diet, exercise, etc.) on the other. The term capital: from a humanistic or social, political point of view is more appealing the term human resources. If I’m heathy I can do things if I’m not. Healthy population is connected with development. Investment is the increase in the stock of knowledge and health: economist point of view (intangible resources). In which sense are knowledge and health a ‘capital’ of an individual, a household or society? They are acquired at an actual cost and give a prospective return What are the costs of education? Effort and sacrifice: psychological costs, many different things (for individual, parents, teachers) Expenditures for formal education Foregone incomes during the time of formal educations Does knowledge embed in an individual decay? (and in society?) Individual are liable to forget and the more so the older they get; moreover, our knowledge is subject to obsolescence; when we die, all our knowledge is lost. For society thigs are different: we normally have a safe store of scientific and technical knowledge (ex. Article in a journal). What are the returns to education? A higher prospective income and a better prospective job (the ability of reaching more fitting and better jobs). A better consciousness of the limits and opportunities of life, and of one’s role in society. There are social returns to education: positive externality. About health: health care involves costs, effort and sacrifice, expenditures. It decays through time, it gives prospective returns (a longer life expectancy, more healthy days for work and leisure in every year). Education and health are not independent one another. Correlations: - Better educated people know why some patterns of behaviour improve our damage health conditions. More educated people have a better health - More healthy people learn better (ex. The study of Michael Kremer on the effects of deworming in Kenya; moreover, their returns on education are earned for a longer time) - Education and healthcare are both positively related with some third variables, like income or public expenditure We must see in details decision concerning health and education. Having said that, both education (increase in knowledge) and healthy days (which are the results of investment in healthcare) are enjoyable themselves quite independently of prospective returns. Thus, they are not only and investment; we also buy them as we do for consumption good. We may say that consume them. Three big questions: 1. What limits the individual and public resources devoted to education and medical care? 2. Why there is inequality in the stock of knowledge and health across individuals, households, societies? (what differences are important about people?) 3. What policies are most effective for stimulating investment in human capital? Population, income, life expectancy and education: some stylized facts If we see the recent developments in the main regions of the world concerning human development (against the background of economic performance and social inequality), in a nutshell, we shall see that: - There has been in the past 50 years or so an improvement in many dimensions of human development, in all regions. In parallel, per capita output increased and extreme poverty declined. The world is making progress for some aspects. - Secondly, if we compare macro regions of the world -> a natural question is whether there is catching up. There is some catching up towards education and health indicators of the leading countries, but inequality across the world remains very high. - Yet, there is no evidence of reduced income inequality; to the contrary, there is clear evidence of increasing inequality, since the 1980s. - Labour market participation, employment and earning increase with educational attainments. Schooling, health and per capita output Let us consider the school enrolments by world regions (1970-2015). There is an international standard qualification system-> we can compare data of different countries (ISCED), it includes nine level of schooling (example: primary, secondary and tertiary education, which are also divided in other categories) Enrolment rate = we consider one particular rate and the age range expected for the level. If we consider only the children of enrolment age (how many of them are effectively enrolled?)-> this is called net enrolment rate = enrolled of enrolment – age / population of enrolment – age We can also find the repeaters and we need also to introduce a second measure: total enrolled over the population (gross enrolment rate = total enrolled / population of enrolment – age - In all regions there has been an increase in access to schooling at all levels - There are leaders (among the OECD members) and followers - There is a clear catching up at the primary level, some catching up at secondary level, no catching up at tertiary level Source: Education Statistics - all indicators Net enrolment rate, primary, both sexes Tendence of full access for most regions of the world. At primary level there are catching ups Net enrolment rate, secondary, both sexes If we look at secondary school there is progress in all areas but convergences are much less evident. Distance is not reducing but situation is even worse if we turn in university level, while in the previous we consider the net rate now we consider the gross rate. We find in university people of different ages not only between 19 and 25, that’s the reason why we choose to use gross rate. If inequality of education diminishes, we have to expect that also inequality of income diminishes? This is not the case. We have a sort of paradox. Income increases and also education but paradoxically inequality in income increases. Population is more unequal in respect to income: this has happened in the past 20 years. It’s not easy to explain this paradox, a contribution to an explanation is given by analysis of the labour market outcomes in relation to education. We have to see labour market outcomes and education: generally speaking, education has a strong positive effect on labour market participation and a negative effect on unemployment. Also, it has a strong positive effect on earnings. However, such labour market outcomes should be considered in more detail, in relation to a complex interplay between the supply (by households) and the demand (by firms) of different kinds and levels of tasks and qualifications. Such a relative demand has decreased since the 1990s in developed countries, due the diffusion of the ICTs and artificial intelligence, which has displaced the ‘routine’ tasks in the labour market. This is called ‘job polarization’. This helps explaining the increase in income inequality in spite of a decrease in education inequality (the latter has not been reduced enough!). Another interesting question is what prevents some 18-24 year olds holding an upper secondary education diploma or so and without a job from enrolling in tertiary education. This is the phenomenon of the NEET. A possible hypothesis is that they had a poor performance at school. A framework of analysis The longer you have studied, the higher on average are the earnings than can be in labour market. There is nothing mechanical in this correlation nor is the correlation linear type (not constant). Earnings in relation to skills depend on very complex interplay between supply and demand in the labour market. On one side, people demand to work and on the other side, firms offer working opportunities (for supply of labour we mean supply of labour services by households). Two fundamental constraints (every kind of economic choice) The activities that characterize people’s live are subject to two main economic constraints - We cannot spend more than our revenues (in a sufficiently long-time horizon) – the budget constraint - We cannot span our activities in more than 24 hours a day – the time constraint The budget constraint: is an upper bound to expenditures in relation to revenues, in the course of time (inter temporal constraint) Let Rt and Et denote, respectively, the revenues and the expenditures at time t (time goes by without any break of continuity). Since there is no necessity that Rt = Et at all times, we must first of all have a criterion for aggregating revenues, on one side, and expenditures on the other, referring to different times. People normally do not like equally to have a certain thing today or to have the same thing “tomorrow” (different things according the period of time in which they are related). In the economist’s terminology, people have a “time preference”. The present is normally preferred to the future, because: - There is a pure time preference of the present, due to impatience - A future outcome is uncertain and therefore it is subject to risk (probability to gain or lose with respect to expect values) Different people have different time preferences and a different attitude towards risk. The future is always uncertain, being uncertain does not mean we don’t know nothing about the future (we can calculate expectation about the future) If X1 is a sum of money (or the amount of a commodity) delivered one year hence and X0 is the quality of the same thing delivered today, the excess of the ration X1/X0 over 1 is the annual rate of time preference (r). Negative time preference -> time preference for the future. Thus r = X1/X0 – 1 Or (1 + r) = X1/X0 Or X0 = X1/(1 + r) X0 is called “present value” of X1. The operation of expressing an economic value at time 1 in a corresponding value at time 0 is called “discounting”. If r is greater than 0, X0 is reduced because we have discounted it. In the equation, X1 and r are known, while X0 is the calculated unknow. r can be interpreted either as a subjective rate of time preference, or as a market interest (discount) rate, according to our focus. They tend to be equalized if financial markets are “perfect” (incentive to borrow if time preference exceeds interest; incentive to lend in the opposite case). The present value of R1, E1, will be R1/(1 + r)’ , E1/(1 + r)’ respectively Discounting is dividing (1 + r) How about R2,E2? They should be discounted “twice”: R2/(1 + r) is the value of R2 at time 1 and therefore R0 = (R2/(1 + r)) 1/(1 + r) = R2/(1 + r)2 is the present value of R2 More generally, the present value of Rt is R0 = Rt/(1+r)t’ and the same for Et If the relevant time span is of n years, the budget constraint can therefore be written as R0 + R1/(1 +r ) + … + Rn/(1 + r)n ≥ E0 + E1/(1 + r) + … + En/(1 + r)n You expect returns from investments: future (revenues) and present are different things. Current expenditures are certain while future revenues are subject to risk (only have an expectation) and even a certain thing that happen tomorrow is perceived as different thing as obtained right now. Future revenues and expenditures -> by discounting we make future variables comparable with present variables. The possibility is open to make calculation: education and health care are so important for a good functioning of society that the study of the decision concerning these things has to makes us as precise as we can. R0 (revenues at time 0), R1…Rn E0 (expenditures at time 0), E1…En My future revenues depend on what I’m doing today, what are my choices now. The expenditures are: in consumption or in investing (not financial). The variables should be made comparable: R0 + R1/(1 + r) + … + Rn/(1 + r)n (we obtain an aggregate express in present value, so present value of revenues) Present value of expenditures: E0 + E1/(1 + r) + … + En/(1 + r)n Expenditures cannot exceed revenues: the present value should not exceed the present values of all expected revenues. Problem of scarcity: we must plan to live in our own means. R0……. ≥ E0……. (R0 – E0) -> surplus, savings of families (add to my wealth: accumulated value of the families) S = deltaW (is the variation of W) All savings are in present values (R0 – E0) -> S0 (R1 – E1 / (1 + r)) -> S1 (Rn – En / (1 + r)n) -> Sn S0 + S1 + … + Sn ≥ 0 Every individual term can be either positive or negative, the sum should never be negative -> intertemporal budget constraint (negative wealth is death). Having said that, we must notice that the timing of positive and negative term is important. During a lifetime, there are periods in which S < 0 (typically youth and old age) and periods in which S > 0 (typically adulthood). Negative savings, positive savings, negative savings in a life cycle from childhood to adulthood to old age (- ; + ; -). Some considerations are in order: - The higher is t, the more heavily discounted is S (and of course Sn tends to 0 as n tends to infinitum); it follows that, with n sufficiently high, the precise time limit does not matter a lot - Without any bequest motive, the lifetime present-value saving should be zero; otherwise, the time limit should include the lives of our offspring - The timing of positive and negative terms is important. If, say, S is first positive and then negative, one holds some wealth for the entire life (except at time 0 and n); in the opposite case, one has debts for the entire life (except at time 0 and n) Expenditures consist in goods and services purchased in the market, for consumption and investment. Many expenditures of the parents are for consumption and investment of their children. In particular the investment of human capital can be made by three means: - Using current revenues (and giving up some current consumptions; by the parents? The children?): I have to spend in investment by giving up some consumptions today in order to pay for example my university. Expectation of increasing future consumption -> only this case does the investment in human capital fully contribute to higher future consumption. - Reducing wealth (using previous savings and giving up some future consumptions). Past savings come from previous generation - Making debts (committing to future saving and again giving up some future consumption; by the parents? The children?). Is present consumption sacrificed? There is a liquidity or financial constraint -> presence or absence of organized financial market or intervention of public sector. Education has positive externality: reasonable that the public sector collects taxes in order to provide and cover some expenditures. The time constraint It simply says that all time-absorbing activities are rival in the use of time (a day, a week, a year) and more of one activity necessitates less of some other in the same day or week or year. All activities, all consumptions are time-absorbing (can be classified as follows): - Work in the labour market (work for pay) Historical overview of human capital The investment “in people” meant different things in the course of time (and it means different things for different countries now). Accordingly, also the economic analysis of the various activities affecting human quality changed. Three periods 1. Agricultural as the bigger sector and artisan activities (1776-1870) -> early industrial revolution. In this period, Classical political economy theorized the social and ethical aims of education 2. Factory system (Fordism). In this period Marshallian economics integrated the social, ethical and productive aims of education (1870-1958) 3. The knowledge-based economy. This is the period in which the modern economics of human capital completely reshaped the way of thinking about education and health care (1958-) The early industrial revolution The new factory system of manufacture gradually displaced the artisan shop and was characterized by • a far larger number of workers in each production unit, each specialized in elementary tasks (division of labour, larger scale of operations) • a sharp increase in labour productivity (increasing returns) • the introduction of new mechanic tools (‘machines’) which were themselves produced in factories, at diminishing costs The new system of production involved a ‘deskilling’ of labour: it just necessitated ‘hands’ more than ‘skills. Number of tasks/operations: a job is divided in lots of simple operations in a factory system. In the previous period the person involved did the contrary (artisans), in a factory system you have simple and individual tasks. Do you expect that this revolution required new human capital or not? Education was not important for the working for the new system (Fordism), you only need your hands. The works of the economists of the time (Adam Smith, 1776; T.R. Malthus, 1803 and 1820; D. Ricardo, 1817; J.S. Mill, 1848) did NOT consider education, health care or migrations as investments in human capital: they were reluctant to consider a human being as ‘capital’ or ‘wealth’. Capital was for them a collection of produced means of production, and they insisted that human beings are not wealth or capital, but the purpose for which wealth and capital exist. The main components of physical capital were the necessaries of life (food, shelter and clothing), which were advanced to workers by capitalists. The investment of that capital not only kept the labour force alive and able to reproduce itself: it contributed to its quality in terms of physical strength, health, self-respect, responsible participation to social life. The main concern was with the evil of an excessive population growth in the face of economic progress, which would undermine any improvement in living standards. Education was seen as something that can have families to change their habits concerning fertility. The parents wanted to have better educated sons/daughters and transmit more comfortable life. Negative correlation between fertility and school enrollment: the bigger are the families, the less the children study. The spread of education among adults and children was the fundamental means for the diffusion and intergenerational transmission of prudential habits. The end of that period saw a marked improvement in working-class living conditions and a reduction in fertility, called the ‘Demographic Transition’. It was at that point that the education-productivity nexus gained momentum Fordism Characterized by increase in service tasks (big corporations). As corporations became giant by the success of mass production, the demand for skilled labour assigned to ‘service’ tasks (accounting, coordinating, instructing, supervising...) started to increase, while assembly lines still required unskilled operatives As an effect of better living conditions, the employment share of the service sector (banking, insurance, trade, professions) started to increase faster than that of manufacturing. Skilled workers were therefore on demand and families were able to meet this new demand, by the increase of wages. Education became functional to economic system. Education was stimulated by economic development, which demanded new skills for more workers, and became indispensable to the economy. The knowledge-based economy Towards the middle of the XXth century it was realized that the growth of physical capital per worker (so important for assembly lines and returns to scale in the previous period) explained a relatively small part of the growth in per capita income. Moreover earnings differentials (by task, age, education) and their variations in the course of time were largely unexplained. These new developments were closely connected with the gradual establishment of a knowledge- based economy. They called for a better understanding of the connections between the skills, knowledge, innovations, on one side, and earnings differentials, employment and economic growth, on the other. A series of contributions by Gary Becker, Theodore Schultz, Jacob Mincer dating from 1958 provided the microeconomic foundations and the empirical methodology for a much deeper analysis of household and firm behaviour focused on the resources embedded in people This was called the ‘Economics of human capital’. Productivity and wages Double connection: education to productivity-> more education means more productivity. But higher productivity means higher wages. People educate, go to school until certain age in expectation to have higher wage in adult age. Connection between higher productivity and wages you can obtain in labour market. Investment in human capital is part of a multifaceted and highly integrated economic choice made by people, involving consumption, saving, the allocation of time. Introducing assumptions: in order to reach simple theoretical results, suitable to empirical verification, we need to separate the investment in human capital from other aspects of economic behavior. We make two kinds of simplifications dealing with choice of investment in education: 1. Every choice is subject to time constraint. The time of education is rival with respect to the time of work for pay alone (so we ignore any interaction with housework time, leisure time, consumption patterns, etc.) 2. Budget constraint -> ignoring all possible interaction between education and budget constraint, in the sense that it is paid for by future returns (even though there might be a liquidity or borrowing constraint for some families) A fundamental premise of the analyses presented below is that education enhances productivity. How productivity can me measured? How it can be affected by education/learning? All goods and services are produced using a variety of inputs; they can be listed under two heading: - Produced means of production (physical capital): IT machinery, mechanical machinery, energy, raw materials, intermediate inputs, buildings, vehicles, etc. - Labour: operatives, foremen, engineers, accountant, managers, etc. Main problem of accessing productivity of each input of production: all these inputs are used together. Every worker cooperates with other workers and is assisted by some psychical capital-> the output is the result of the entire organization. How can then we assess the productivity of individual workers (or, for the matter, individual items of physical capital?) An idea might be to divide production by the number of workers or, better, their working hours. This is a good idea if we can aggregate across the various tasks that are performed by the employees of a certain firm, or industry, or the entire economy. Q = level of production L = significant labour aggregate Q/L = labour productivity Investment in information, IT capital, more education by the people in general, innovation due to development-> aggregate level (increasing productivity in the economic system). Accordingly, the labour compensation increases along with productivity. GDP per capital -> increasing as well. These variables are real, evaluated in money, assumed that the change is real. This calculation is particularly useful at a macroeconomic level (entire economic system) and we find a positive correlation between labour productivity, real wages and real GDP per capita. Example: The Tesla factory in Vermont produces nearly 1,000 cars per day, sold at about 50,000 dollars each, by mean of 160 industrial robots and 3,000 workers: operatives, supervisors, accountants, managers, engineers, etc. assume they include 20 cleaners and 20 engineers performing a particular task. Productive capacity: 1,000 cars Connection between productivity and wages: 20+20 cleaners and engineers (list of different tasks performed: writing reports and documentation). There might be some useful ideas for further improving and efficiency. The concept that we are looking for is marginal productivity. What the economist means with marginal: the adjective stands for effect of a small variation. Every marginal variable has to do with variation, possible variation. and more efficiently are the resources used and the cost of production decreases in the course of time. We expect a down trend in the rental price. What are the implications for the labour market? And what if firms cut the humans? An interesting implication is that a falling price of cleaning-robots reduces, ceteris paribus, the wage offered to cleaners. In the example, robots are substitutes for low skilled labour. But other kinds of IT capital goods tend to replace middle skilled routine labour, and some intelligent machines are now able to perform tasks typical of highly skilled labour (like market and financial analysts, medical doctors, engineers, ...) • The number of workers is reduced in that specific task (not overall labour market). Those humans and workers that have the knowledge and education to perform that tasks are less employed, their wage tends to be reduced. How much? That depends on pr and equilibrium wage. Economists use the “technological race” to explain how inequality has increased in the course of time. Some tasks are in excess demand and other excess supply. The value of marginal productivity is not constant and depends on the number of workers in that task relative to all other workers, machinery. Economists generally assume that the higher the number of workers (ceteris paribus) the lower their marginal productivity. The same is true of individual items of physical capital. A model of schooling Let us start from an admittedly over-simplified model [adapted from D. Checchi, Economics of education, 2006, pp. 18-35], which will enable us to formalize schooling choices in a very simple way. Possible realistic variations will be considered against this benchmark. We consider an individual, whose active life can be divided in two periods of equal length: youth (suffix 𝑦) and adulthood (suffix 𝑎). Education is made during youth and gives returns in adulthood. People do not even consider any further in education during adulthood (on-the-job-training is ignored). Compulsory school is done in childhood and we may imagine that youth lasts 16 years (from age 14 to 30). One individual has to choose the share of that time, 𝜎 (sigma), to be devoted to schooling (from 0 to 1). • If 𝜎 = 1, then one has chosen 16 years of full time schooling (after compulsory school); if, say, 𝜎 = 0.5, then one has chosen either 8 years full time or 16 years of part time schooling; if 𝜎 = 0, then one has chosen to work full time in youth (as well as in adulthood) Distinction between educational attainments (related to time of studying) and learning on the other side -> years of schooling, however, do not automatically increase human capital: many other factors affect the outcome of schooling in terms of skills & knowledge. Labour productivity increases with the amount of human capital embedded in a worker. 𝐻 = the amount of human capital and 𝑀𝑃(𝐻) = the marginal productivity of a worker endowed with 𝐻 (assumed to be independent of the quality and number of co-workers etc.). Linear function of marginal productivity (provisional assumption): 𝑀𝑃(𝐻) = 𝛽𝐻, with 𝛽 > 0 But under competition the wage should be equal to marginal productivity: 𝑤(𝐻) = 𝑀𝑃(𝐻) Hence: 𝑤(𝐻) = 𝛽𝐻 Marginal productivity depends on human capital -> MP is a function of a variable (that is H) -> Marginal productivity is a function of human capital. Let the given amount of human capital embedded in our individual in youth be 𝐻#, which is determined by the education received before schooling (presumably by the parents) and in compulsory schools and let 𝐻$ be the amount after schooling, in adulthood. Accordingly, the wage offered by firms in youth and adulthood will be, respectively: 𝑤# = 𝛽𝐻# and 𝑤$ = 𝛽𝐻$ The production of human capital Labour market -> W W = 𝛽H (positive correlation) Beta is a constant positive parametra: 𝛽 = W/H -> constant The higher is beta the higher is the wage at any given of human capital. Beta precisely says the wage per unit. Beta is the ratio between wage and human capital. “All persons have the same 𝛽”: we have to delete this assumption. There are some differences and problems all over the world, such as gender differences. If we consider Sweden, we find gender gap lower than Greece, but still there is a wage gap with same human capital that produces different earnings. We have also to consider racial wage gap (Hispanic, Afro-American) -> difference in wage because of ethnical origins. We must add other aspects and modify the equation with dealing with empirical issues. Everyone arrives at youth with human capital = Hy and then when he/she turns to adulthood the HC is Ha. Educational policy = how long should school be open? How many days a week? In Italy we have a system that university is available for everyone who has attended secondary school. Particular aspect about quality of education: number of pupils in a class (overcrowded is bad for education). Optimal number? Researches can be done on this field (PISA). Private schools VS public schools. Point Ha: we are assuming that HC does not decay. In adulthood can be equal or greater than the HC in youth. Grater if there is some investment in HC. Now we need to clarify the relation between the schooling choice in youth and the expected human capital in adulthood. If I is the increase in human capital ascribed to schooling in youth, we have then: Ha = Hy + I I = investment in HC I = measure of accumulation of HC depends on some variables. The first is time of schooling (𝜎) Investment is a function = F Talent is a natural or an acquired thing? Talent has more to do with family environment, ability to learn is something that goes with time. Symbol of talent is A (either innate or depending on family background) The ability to learn also depends on the level of previous school cycle. The better is the previous school the better is the learning in the next school. The investment in HC depends in how much you learned in childhood. Learning in school is more effective: the more activities you have at home, the better are these activities, the more success is in school. Having electronic tools = important to have a very good internet collection, other expenses that must be considered. E = other expenses (the amount of resources devoted to learning in addition to tuition fees). Hy = initial human capital (depending on the quality of pre-school and compulsory education, as well as on health) This investment is positively related of each variable (hence the skills & knowledge acquired in youth can be expressed as a function of all these variables): I = F (𝝈, A, E, Hy) 𝜎: the more you study, the more you learn. F sigma > 0 -> F𝜎 (𝜎, A, E, Hy) -> F sigma is a function of all these variables. F sigma is what you learn in one more year of schooling. Another assumption: the higher the level you reach, the less is amount of learning of one year of schooling. F sigma sigma = how the learning of 1 year of schooling increase/decrease depending on the level of school where you are. F sigma sigma < 0 One year more in secondary school adds more to your learning than one year more at university for example. Diminishing returns to schooling = you always learn some more but it does not pay to go to school for 34 year. You learn less and less and less. Substitute I in the equation Ha = Hy + I Ha = Hy + F (sigma, A, E, Hy) I = 0 if any on sigma, A, E, Hy is 0 The demand for schooling Optimal sigma: how many years one decides to stay in the school system? Let the tuition feeds for a student who is full time in his entire youth (sigma = 1) be 𝛾 (gamma), and let them be simply sigmagamma when sigma < 1. Let us provisionally take A, E, Hy as a constant and concentrate on the choice concerning sigma. The criterion of choice is the maximum possible lifelong net revenues (i.e. revenues minus costs) accruing from schooling time in youth. The costs of schooling are: - The direct outlays: sigmagamma - Opportunity cost in terms of foregone wages: sigmaWy = sigmabetaHy Wy = BHy Two components of cost: one is sigmagamma, and the other is sigmabetaHy. Hence total costs are 𝐶 = 𝜎>𝛾 + 𝛽𝐻#@ We ignore the psychic costs due to effort and foregone leisure Taking into account, the net revenues in youth are: Vy = (1 – sigma)betaHy – sigmagamma In adulthood, there are no costs, and the revenues are Wa = betaHa Such revenues, however, accrue one period later and must be transformed in present value. Let the discount fact appropriate to bringing adulthood returns “youth” value be (1 + r) Hence the present value of betaHa will be Va = betaHa/(1 + r) But Ha = Hy + F(sigma, A, E, Hy) hence Va = beta Hy+F(sigma, A, E, Hy)/(1 + r) Defining V = Vy + Va’ we finally get 𝑉 = (1 − 𝜎)𝛽𝐻# − 𝜎𝛾 + 𝛽 𝐻# + 𝐹>𝜎𝐴𝐸𝐻#@ (1 + 𝑟) I = investment in human capital (increase in knowledge and skills embedded in a person) The period of time in which we increase our knowledge is youth. I is a function of a series of variables: I = F (sigma; A, E, Hy) -> learning function Hy = amount of knowledge acquired in childhood from parents and primary school expenditures, those families (if unable to borrow from someone to make it possible to children to school level) suffer and decisions are limited by financial or borrowing or liquidity constraint. The demand for schooling would be lower than the optimal (this is a loss for society). A second aspect is family size (and educational gap between genders). A third example is labour market discrimination based on race, gender, religion, such that human capital has different returns for people of different groups. Another candidate is health. Assuming you can demand your desired level of schooling: the cost you pay in financial term is an investment and that money should have a return (that should be measured) -> rate of return to schooling. The returns on schooling The rate of return in our simplified model: how is it worth to invest in education? Position of an investor when decide if continue school, the investor asks himself the returns of percentage rate (rate of return). We must consider a given sigma (given number of years of school, given proportion of younghood in school). Our problem is to measure years of schooling. Recall that, at the chosen sigma*, the wage in adulthood is betaHy + betaF(sigma*, A, E, Hy); thus the wage premium due to education (which we call the returns on education) is betaF(sigma*, A, E, Hy). If sigma* is 0 = situation in which you have studied in childhood but not in youth, you are in labour market with childhood human capital. We have to compare the wage premium with the investment that has been made in order to obtain the premium -> sigma* (y + betaHy). We can make two kinds of calculation when make the comparison: a. Consider the discount rate as given and just simply evaluate the returns in present value and compare it with costs. The wage premium should be expressed in present value using a given discount rate b. Take the wage premium and costs as given but the discount rate as unknown In terms of our model, we have to equate the present value on the right side -> at the numerator the wage premium and divide by discount factor (not a constant, unknown of our equation). Left side-> money measure of the investment, costs that you have done. 𝜎∗>𝛾 + 𝛽𝐻#@ = &'()∗,+, ,-". (012) , or 𝜌 = 𝛽𝐹>𝜎∗, 𝐴, 𝐸, 𝐻#@ 𝜎∗>𝛾 + 𝛽𝐻#@ − 1 p is rate of return on schooling (p is a percentage rate). The rate of return on education more generally: Let us consider a certain school attainment requiring T years after compulsory schools (say T = 3 for upper secondary school; T = 8 for a University Master level). Let n denote the total years in a lifetime after compulsory schools. From the standpoint of the first year of the chosen school, the present value of total costs (direct outlays and forgone earnings) is 𝐶 = 𝐶4 + 𝐶0 (1 + 𝑟) + 𝐶5 (1 + 𝑟)5 +⋯+ 𝐶6 (1 + 𝑟)6 C0 = costs when you have just left compulsory school, first year of voluntary schooling From the same standpoint, the estimated revenues (earnings) from labour, are 𝑅 = 𝑅610 (1 + 𝑟)610 +⋯+ 𝑅7 (1 + 𝑟)7 We can calculate the returns on education in different ways: a. We choose a rate of discount (say 2%) and calculate R, C and their difference (R – C): the latter gives us a pecuniary measure of returns to education relative to no education at all. b. We choose a rate of discount (say 2%) and calculate the present value of the extra costs and the extra earnings from that educational level as compared to the previous one: this gives us a pecuniary measure of the returns to proceeding to the next educational level. We focus on the delta. c. Given discount rate, we can calculate the particular discount rate p which equates costs and revenues, that is the solution in p of the equation 𝐶4 + 𝐶0 (1 + 𝜌) + ⋯+ 𝐶6 (1 + 𝜌)6 = 𝑅610 (1 + 𝜌)610 +⋯+ 𝑅7 (1 + 𝜌)7 Notice that the prospective earnings are weighted more heavily than the costs: they decrease ‘faster’ than costs as 𝜌 increases and there will be a break even point at a critical 𝜌 (the rate of return): the higher the earnings, the higher this 𝜌 will be. The rate of return on education can be calculated either on the basis of the total costs and earnings or on the basis of the extra costs and earnings, as compared to those of the previous educational level. Thus far, we have considered the private returns on education But there are also public costs and benefits from education ü The costs consist in public expenditure (consumption and investment) on education ü The pecuniary benefits consist in the additional tax revenues and social contributions arising from the increase in output due to the enhanced productivity There are also social benefits (positive externalities) from education, because: - The productivity of an individual worker is enhanced by highly educated co-workers - The information technology physical capital is more productive the more sophisticated is the knowledge of managers - In researches and teaching institutes -> knowledge as a public good (non-rival and non- exclusive) - Public opinion is better informed and this may help political stability and a better decision making by the public sector Problem of measuring the returns of education. We have to choose a level of educational attainments and then we need a term of comparison, we have 2 possibilities: obtain a money measure of the return (choose a discount rate, list of costs and lists of benefits or revenues -> both should be discounted), the other measure of the returns is expressed not in money but as a percentage (the calculation is more complicated: the unknown is the rate of discount). Private VS public returns: private of household deciding how long to have schooling for the families, and public for standpoint of society. You might distinguish between returns for the public budget and financial returns on public spending VS wider benefits which depend on what are the positive externality of education (= my interest that you study because if average level increases then productivity is higher and all incomes tend to be higher). The model is unrealistic: the same with little modifications -> further aspects, make it more realistic. - Indivisibilities Education has indivisibilities but in a practical point of view it is not true. Schooling is organized in cycles (levels) and the benefits of each cycle appear only upon completion. There are different levels (international standard in distinguish between levels and codifications) - > OECD statistics distinguishes between 8 levels: primary, lower secondary, upper secondary, post- secondary non-tertiary, bachelor, master, doctoral. University cycles (bachelor, master, doctorate) -> let simga1 = 0.3 be the fraction of time needed to complete a Bachelor, sigma2 = 0.5 that needed to complete a Bachelor and a Master, sigma3 = 1 that needed to complete the full cycle of University studies, including Doctorate. The variable sigma makes jump, that is a consequence of indivisibility. Our function F (sigma, A, E, Hy) should now be written as 𝐹(∙) = 0 𝑖𝑓 0 ≤ 𝜎 < 𝜎0 𝐹(∙) = 𝐹>𝜎0, 𝐴, 𝐸, 𝐻#@ 𝑖𝑓 𝜎0 ≤ 𝜎 < 𝜎5 𝐹(∙) = 𝐹>𝜎5, 𝐴, 𝐸, 𝐻#@ 𝑖𝑓 𝜎5 ≤ 𝜎 < 1 𝐹(∙) = 𝐹>1, 𝐴, 𝐸, 𝐻#@ 𝑖𝑓 𝜎 = 1 This is a step-wise function Notice that it is impossible to calculate 𝐹) and thus the marginal revenues But it is enough to calculate the difference between present value revenues and costs at the end of each cycle, and evaluate which is higher It would not be difficult to see that the qualitative change in 𝜎 when any of the ‘givens’ changes is the same here as it was in the ‘smooth’ model There are some returns in each level, but the maximum return is simga2. Best choice: maximum return = master’s degree. - More periods of time Our benchmark model assumes that youth and adulthood have the same time length and that that length is our unit of time: this is clearly unrealistic. Let us now introduce a finer subdivision of time. Let the unit of time be one year, and let youth and adulthood last 𝑦 and 𝑎 years, respectively (with 𝑎 > 𝑦); youth starts at time 0 Accordingly, Ht refers to human capital at a particular year, which is a year of youth (and potential schooling) when 0 ≤ 𝑡 ≤ 𝑦 and of adulthood (and work) when 𝑦 < 𝑡 ≤ 𝑦 + 𝑎 • We have so far implicitly assumed that the longer one studies in youth the shorter his/her lifetime work, because the time of work in adulthood was assumed constant Tau = number of years of studying/compensate the years of schooling in the period in which you may retire. An advantage of a multi-period model is that we can fix - Either the time of work, thus implying that more educated people retire later - Or the age of retirement, thus implying that more educated workers work less The effect of one more year of schooling (when t < a) is a. To postpone returns (which are more heavily discounted) b. To increase direct costs c. To increase opportunity costs d. To increase the wage in the entire working life - Look at the people who studied in the past (actual adults, finished their cycles of education) and ask what is their position, educational attainment -> attainments of adults of certain age (or age range, normally 25-64 or 25-34), who had made their educational choices in the past. 25-64: big gap between Italy VS USA and Germany -> if the younger generation has more similar composition in Italy than other country, the expectation is that we become more similar to other countries. 25-34: the gap is narrowing and there are some catching ups (rather slow). As times goes on there will definitely be some catching ups. - Look at the people who is studying now (we focus on enrollments, ages of youth and at different age ranges how many people we find enrolled in schools) -> the enrollments of school-age youth of different ages (say 17, 18…14), who are making their choices now. Pupils and students in education by age groups – as % of corresponding age population: low share of the young generation remains in schools after the age of 18 and before the age of 24, lower enrolments rate in Italy compares to Germany. The main practice in the economics of education is to consider attainments of adults aged 25-34, measured in statutory years of schooling. Let np, ns, and nt denote the cumulative years of schooling corresponding to primary, secondary and tertiary-or-more attainments, respectively. Let now P0, Pp, Ps, Pt be the numbers of the population that have reached the various levels as their maximum attainment. Their sum is P (entire population in the age range that we have selected). We must translate the data on shares of population. We note by #(pai) -> these are shares, their sum is necessarily equal to 100%, 1. Needless to say that 𝜋4 + 𝜋8 + 𝜋9 + 𝜋: = 1 If we associate each attainment with its share of the population, we obtain a distribution of education. The average years of schooling (𝑛R) is a weighted average of the cumulative years, corresponding to the various attainments, using the shares of population as weights. We must make a weighted sum. Different ways of measuring years of schooling, educational attainments, test scores in learning assessment surveys. Statutory years of schooling associated to the different maximum attainments possible by the population-> population from 25 to 34-> trend in educational attainment in the course of time. Distribution of attainments: percentages of the population that have different levels of attainments. We can extract from a distribution its mean, in our case the average years of schooling in a certain social group. There are many different ways of having an average number-> i.e. 12 years means something very different with regards to the population; we must attach to the mean of the distribution another number that tells us how unequal the distribution can be. Why do we want to measure inequality with a number? It is useful to compare different countries in respect to the inequality of schooling; if we want to explain inequality, we need to measure it (manipulate and analyze data, assign to each variable a role in determine inequality in order to measure inequality). Example: Half of the population with primary education (8) 0.5, and half with secondary education (13) 0.5-> mean 10.5 (between 8 and 13). The mean of education is not satisfactory because there is no one in university, but inequality is low because people is all grouped around the average and there is nobody at the edges. Inequality in a variable = income is unequal means that individuals do not have the same income for example. A second way is to calculate the distance between the distribution and the average: we calculate differences in respect to the average. Standard deviation-> we calculate the distance between two different variables (i.e. income), for each group we calculate the difference with the average. Differences between the two groups and the average. (calcolare la media e vedere di quando si allontanano dalla media i due termini di paragone). In the second distribution inequality has increased dramatically. We want to build an index of inequality based on individual observation and the mean of inequality. GRAFICO: (n0- n’) (np- n’) (ns-n’) (nt-n’)-> average out the distances between them. There are some negative and positive differences. We want to transform these differences in positive values- > square each difference. Weight the squared differences-> by the shares of the population, we multiply each for the shares of population π0, πp, πs, πt, and then all under square roots. What is the minimum possible value of standard deviation? It’s zero, it happens when all the people have the same education, so no inequality at all. If we have inequality there is a positive value. It is a measure of dispersion, how individual observation are far away of the average (to be specific, it is an absolute measure of dispersion = dimensionally, it is a number of years). The maximum value of the standard deviation is obtained when the population is polarized at the two extremes (maximum average distance we can have). In this case the maximum standard deviation is the mean itself. Calculate the standard deviation of case/distribution 1: 0.5(8-10.5)2+ 0.5(13-10.5)2-> all under square root = 2.5. Standard deviation case/distribution 2: square root of 0.5(0-9)2+ 0.5(18-9)2-> 9 (maximum value that the standard deviation can have). Standard deviation of case/distribution 3: square root of 0.9(-1.8)2+ 0.1(18-1.8)2-> 5.4 Distribution 3 is less unequal than distribution 2 (population is polarized). From a social point of view, in distribution 3 we have higher inequality because the education is given to very few people and that is uneven, 90% of people have no education, and 10 % has all the education. In this case, perhaps standard deviation shall not be used. Gini index It captures the concentration of the education which is given in a certain society. The minimum is 0 -> when all the population has the same attainments, no matter which one; the index is maximum when it is 1-> all people but a very few have zero education, so education is concentrated on a very few people. The Gini index is a pure number, ranging from 0 (maximum equality) to 1 (maximum inequality)-> designed to represent social inequality. The Gini index can be calculated indirectly in terms of the Lorenz curve. Example: Attainments in years π/n 0 8 13 18 Share of population 0.02 0.18 0.5 0.3 Quintile = one fifth of the population Notice that 𝑛R = 0.02 ∗ 0 + 0.18 ∗ 8 + 0.5 ∗ 13 + 0.3 ∗ 18 = 13.34 (average) π/n-> 0–8-13-18 share of population-> 0.02-0.18-0.5-0.3 Divide them in equally numerous groups-> 5 groups, each group has 20% of the population-> quintiles of population. How big or small is the country and its population is not important, so assume that population is 1 (we are interested in proportions and not the absolute number of the population). If population is 1, then 𝑛R will be the total years of schooling by population as a whole. Total years of schooling in a society? P0n0 (no schooling at all) + Ppnp + Psns + Ptnt = total years of schooling (years of each attainments multiplied by the number of people with the attainment) Let’s normalize the numbers assuming population is 1-> we divide everything by the number of the population-> (P0n0+ Ppnp + Psns + Ptnt)/P P0/P n0+…+Pt/P nt-> π0n0+…+ πtnt = 𝑛R What is the share of by each quintile? Q1 Q2 Q3 Q4 Q5 0 + 0.18 ∗ 8 13.34 = 0.108 0.2 ∗ 13 13.34 = 0.195 0.2 ∗ 13 13.34 = 0.195 0.1 ∗ 13 + 0.1 ∗ 18 13.34 = 0.232 0.2 ∗ 18 13.34 = 0.270 Associate the cumulative share of population (sorted in quintiles) with its cumulative share of total education. Cumulative share of population 0 0.2 0.4 0.6 0.8 1 Cumulative shares of education 0 0.108 0.303 (= 1.08 + 0.195) 0.498 0.730 1 At this point we can draw the Lorenz curve (blue one)-> associate the cumulative shares of education corresponding to the shares of population. The next step is to match social status with performance score, in the example we can see: The first column (coverage) indicates the percentage of the sample students which made the test (the remaining having probably dropped out) The second and third columns indicate, country by country, the percentages of country students belonging to bottom and top international deciles (the most disadvantaged and most advantaged students internationally) The lines on the right indicate, country by country, the mean scores by the various international quantiles. The data in the Figure tell us three main things: a) In every country the status matters, meaning that as we climb up in the distribution of status we also climb up in test scores (with very few exceptions) b) But also countries matter for performance: students belonging to the bottom international decile, for instance, by no means have similar test scores (e.g. Domenica Republic VS Macao) c) The learning gap of the disadvantaged students varies substantially across countries. This is better clarified if we consider performances in the national distributions of status • We may say, therefore, that some school systems ‘compensate’ better than others the disadvantages of students of ‘low’ status • The report classifies countries according to the percentage of variation in performance explained by socio-economic status: those with less than OECD average (12%) have more ‘equitable’ schools At the same time, we can also classify the same countries according to performance: those with more than OECD average are more ‘efficient’. Finally, we can combine these two classifications. We may extract from data a rather strong positive correlation between socio-economic status and test scores. The most reliable is the estimate -> the higher the slope, the most the index of social, economic status matters. Comparing PISA 2009 with PISA 2018, it turns out that inequality of learning (as expressed by test scores) is by no means declining. Differences in performance by students -> 12% measures how much it matters for final performance to come from a low or a higher social-economic condition. Never forget: PISA data set -> international data (different in nationalities, in social condition, many other things but we consider only national differences and on social condition). On the right of the line there are countries that are more equitable, school system that compensates socio-economic status better. The weight of being a low socio-economic status is low, explains less the differences in performance. Socio-economic status means less here. Having equitable school system in which people independently of social condition learn relatively little is not a good thing, a good school system should perform 2 goals: being equitable and being efficient. Horizontal line -> students on average perform better than OECD average (relatively efficient school system). Empirical strategies: mere pictures of situation, go beyond of statistic and establish correlation between variables. 1. Analysis of data set. Problem: individual observation that differs (as time goes on, never happens that variable changes: with individual observation we have big problem of distinguishing and separating the effect of different characteristics on certain variable that you wish to explain. Main things change at once) 2. Field experiment. What does field experiment consist on? Divide your object of analysis in two group (the treatment group) and the other is the controlled group. Parents education and children: positive correlation but shift according to the number of siblings (family size). As family size increases, the level of education might decrease. How to distinguish the effect of parent education and size of the family on children education? A digression: understanding regression results, some minimum knowledge Imagine we have a dataset with n observation (e.g. a large sample of people from different countries at different times), each concerning M variables (e.g. school attainments of 30 years old, the characteristics of their family of origin, their present occupational status, and many others) We designate one variable to be the dependent variable, denoted by y (e.g. attainments) and we want to study the effect of other variables on it. On the basis of an economic or social theory, we select these other 𝑚 ≤ 𝑀 variables, which we call ‘independent variables’: 𝑥0, 𝑥5, ⋯ , 𝑥; We want to explain a measure of attainments -> variable y. We want to study the effect of other variables on it. Distinguish specific individual effect in a sense of decomposing the effect of all these variables on y. We observe across the individuals, differences in y (different school attainment), we must look at a lot of different variables -> across individual observation, all the variables change at once. See the specific effect of each variable. At this point we need theory -> need to form some hypothesis of which variable might be relevant for school attainment. Theory gives always hypothesis to be tasted empirically (logical conclusions). Denoting by i a generic observation, our data set (D) will be therefore 𝐷 = [𝑦<; 𝑥0,< , 𝑥5,< , ⋯ , 𝑥;,<], 𝑖 = 1,2,⋯ , 𝑛 Certain collection of elements: yi = value of independent variable in observation i. We divide the variables in two groups: dependent or independent variables. Take record of value of each variable. We have a set of an observation, each observation concerns one independent variable and m. Regression analysis elaborates on these data aiming at finding significant correlations between y and each x. In principle, it is as if we could by elaborating data take all x as constant except one, and see the specific effect on y. Very often in the economics of human capital we encounter linear regressions called OLS (Ordinary Least Squares). At the basis of an OLS regression there is a linear regression equation 𝑦< = 𝑎 + 𝛽0𝑥0< +⋯+ 𝛽;𝑥;< + 𝜀< We use the observation in the regression equation. This equation has a series of parameters that are the object of our estimation. Using this particular method, we find the best fit parameters. A is a constant, the beta are parameters that tell us wheatear the correlation is positive or negative. Example: how strong is the influence of being male or female in school attendance. Term of error: the fit is not perfect. In the equation we must add the term of error or residual. This estimation is clearly never perfect. The observed data differ from the estimation, they differ in value expressed on the error. Statistical analysis can tell us two main things: a. What fraction of the observed variability of y across observations is explained by the regressors (this is 𝑅5, the ‘coefficient of determination’). We see across persons different level of educational attainments, and we want to explain variability of a sort of regression: we need to calculate the percentage of variability that we are able to explain using regression (coefficient of determination) b. Depending on the distribution on the error term we must establish how reliable is each parametria. 0.05 is the probability that you are misinterpreting the data (very low). How reliable is each parameter (𝑎, 𝛽0, ⋯ , 𝛽;) used in the estimation (𝑝 − 𝑣𝑎𝑙𝑢𝑒 or 𝑡 − 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠): to this purpose, we impose that the probability that a coefficient be statistically significant is sufficiently high (say, 95%): in this case, it should be 𝑡 > |1.96| which amounts to 𝑝 < 0.05 In every OLS regression, we have: - A dependent variable - A set of independent variables - A constant term (a) and a set of parameters 𝛽 - The number of observations - The 𝑅5 for the entire regression - A statistical indicator of ‘reliability’ of each parameter (in parenthesis) The key to solid results from a regression is an appropriate blending of independent variables. For this reason, regressions from the same dataset are often replicated with different choices of independent variables. Decomposing the socio-economic status We should now try to decompose the overall effect of social stratification on education. We follow a recent study by two sociologists on inequality in educational attainments in Britain. They recorded the educational attainments at 34 years of ages of a sample of three cohorts of people who were aged 10 (or 11) in 1946, 1958 and 1970 respectively. The characteristics of their parents at these three dates are also recorded, and particularly their education, occupation and social status. Seven levels of attainments (qualifications) are distinguished, as in the table. Then these qualifications (dependent variable) are regressed on parental education, social status, and occupation (independent variables), the main results are in the tables: women and men Small differences concerning the regression of women and men. Some parameters are not statistically significant, the authors tried to argue that this might be a problem with this kind of occupation. Family size: the existence of a correlation between educational choices and family size (the so- called quantity-quality tradeoff) has long been debated, since the 1800s, as if a fixed budget from investment was to be divided in smaller parts. Positive check: infant mortality. What limits the increase of population is infant mortality -> dark picture of prospect of humanity. Preventive check: people also favored by increasing levels of education planned to have smaller families in which children may have higher human capital (nutrition, health and education). According to the literature, fertility choices may depend on the desired quality of the children and the resources (income, time) that they would attract, not the other way round. GNP – Gini index: logarithm of inequality-adjusted real GNP Poverty: child mortality rate in the first year (per 1,000 births) Family size: fertility rate (potential children per woman) Population growth: crude birth rate (per 1,000 inhabitants) Social environment: share of the corresponding population over 15 with some primary education Educational resources: students per teacher in primary education Threshold value of t statistic is 1.96. When t is bigger than 1.96, the coefficient is statistically significant at (95?) 99% of probability. t statistic is each coefficient in parenthesis. Female enrolment rate is reduced: income of poor families might have diminished, as a consequence, families have to sacrifice at primary level the education of daughters. Estimation of secondary education enrolment – fixed effect, 1960-95 Reduction in female enrolment is greater than the total enrolment. There should be some borrowing constraint at work. Education and racial discrimination: a basic model Wage for one kind of worker (with certain educational attainment) = marginal productivity in value for that kind of task, qualification = betaHi (linear function of the amount of human capital). The relationship between wage and Human capital is not linear in reality -> increasing wage premium to the most skilled workers, starting from a given qualification and then it falls around the possible qualifications. For any given amount of hc, the beta constant variable as it might be is the same or not the same for different people. In topic 2 we have seen that under competition the wage offered by firms is equal to the value of marginal productivity; and that marginal productivity depends on human capital We find that wage gaps associated with characteristics have nothing to do with productivity and human capital: - Gender (there is a gender wage gap: reducing and narrowing in the course of time but it is relatively lower in the most advanced countries. This problem of decomposing the gender wage gap is very lively topic of research) - Nationality or ethnicity (“race”) -> second generations of immigrants. As generations go ahead, we ask about why should immigrants learn less, suffer from an earning gaps on a given level of qualifications. In principal the observed racial wage gap may depend on: 1. Racial bias in schooling (children that belong to racial minority in certain country might decide to study less) 2. Racial bias in learning (for any given level of schooling, their knowledge is less accomplished, less solid than for other with the same educational attainments) 3. Racial discrimination in the labour market 1 and 2 bring us back to the problem of the influence of different social status on education. Racial bias in schooling may depend on a composition effect concerning a series of family characteristics: - Family income - Family size - Parental occupation (and education) Racial bias in learning may depend on a composition effect concerning the same and other family characteristics: - Parental education (and occupation) - Family education resources - Location (centre VS periphery, urban VS rural) An interesting question is whether there is also a racial bias in intergenerational mobility. Poor people are locked in a situation on which they cannot escape, if they have low social origin and social origin matters a lot it is very likely that they remain in the same social level than their parents. Even with the same qualification level, minorities (and women) can be less to be hired in skilled tasks than the majority group (and men) and a lower demand determines a lower wage. A person from a given minority is less likely to be hired in skilled tasks than the majority group. If there is a preference by employers for majority members -> lower demand for that kind of workers and this gap in demand determines in the labour market also a gap in the wage. This gap in demand translates itself in gap in the wage, that preference determines a lower wage and high rate in unemployment. To some extent is some “pure” discrimination: different wage for same task (in particular in private sector) To some other extent is some “segregation”: different task for same qualification level Discrimination (in a wide sense) can be the result of two different mechanisms a. Consumers, co-workers and employers may have adverse “tastes” for some minorities (taste-based discrimination) b. Employers may have preconceptions concerning the “true” skill level of racial minorities (for any given educational attainment) Example: We have a certain distribution on people who graduated, they wanted to be hired in certain firms. How good is this person that is in front of me? The employers might only have in mind the probability of distribution. About the preconception -> the probability of minority to be skilled is lower, unskilled graduates can be also in the majority groups. Probability distribution that that person be skilled or unskilled, I can compare to different distributions. Pre conceptions are not a matter of tastes, are not completely arbitrary. In our understanding they are based on different distributions. The interesting question about preconceptions: labour market discrimination may interact with educational choices via a lower return on education: minorities will anticipate the discrimination/segregation in the labour market and rationally decide to educate less or put less effort on education. In this case, some negative stereotypes, based on skin color may spread throughout society. In this case, some negative stereotypes, based on skin colour may spread throughout society. Negative stereotypes lead to a racial bias in labour demand, at each educational level, called ‘statistical discrimination’: an individual worker is discriminated on the basis of preconceptions concerning her/his ethnicity ... ... and he/she either remains unemployed or accepts a lower wage than other (majority) workers At the same time, however, it also leads to lower efforts and resources devoted to learning by minorities (and to lower educational attainments as well). Ironically, the negative stereotypes can be self-confirming and minorities can be trapped in a vicious circle! In what follows we shall present a simple model of statistical discrimination, in which the racial wage gap is explained by preconceptions concerning the qualification of a member of a minority group. Labour market discrimination: a basic model Let A denote majority group and B denote a minority group. Employers have pre-concepts on B qualification for tasks requiring higher skills. Let us assume that there are two tasks, unskilled and skilled. Every worker can be assigned to an unskilled task, since employers have no discriminatory feelings, the choice is completely colour-blind. By contrast, for skilled tasks the employers must ascertain (by means of a test, interview and on-the-job monitoring) whether the worker is qualified or not, incurring a cost, say k. The ex-ante probability that an applicant be qualified depends on group membership: in the employer’s judgement, it is lower for B than A workers: 𝜋+ > 𝜋= Let Ps denote the productivity of worker qualifies for a skilled task. If WA, WB are the two wages, the expected returns from hiring an A or a B are respectively (𝑃> −𝑤+)𝜋+ for A and (𝑃> −𝑤=)𝜋= , for B with 𝜋=<𝜋+ At the same wage, an employer would exclude hiring any ‘B’ Ps is marginal product if qualified, wage paid for that work is WA He would consider to hire both some ‘B’ and some ‘A’, if (𝑃> −𝑤+)𝜋+ = 𝑘 = (𝑃> −𝑤=)𝜋= A little calculation shows that the wage gap (WA – WB) is (𝑤+ −𝑤=) = 𝑘 g 𝜋+ − 𝜋= 𝜋+𝜋= h The proximate determinants of the racial wage gap The paper focuses on test scores around the end of secondary education in a panel of late teens on one side, and on the wage gap in their late twenties on the other. The main premise is that the choice of postsecondary education and of a job in the decade in between, strongly depends on both the quality of previous schooling and of labour market prospects. Such choices would not be good ‘independent variables’ in a regression, because they are ‘endogenous’. In other terms, the amount of human capital attained in the late teens determines the effectiveness of further investments in human capital, like further study or work experience The true exogenous variables taken to explain the wage are therefore: ethnicity, gender, age and test scores. Note that these variables, unlike postsecondary schooling and early work experience, are independent of labour market discrimination. The wage gap cannot be explained by these variables (the residual) is the measure of labour market discrimination. Discrimination remains something that we cannot explain. The dependent variable here is wage, to be more precise the logarithm of wage. What are the factors affecting the wage, including ethnicity that is our main target? What is regressed is not the natural measure of wage but they consider the log of the wage. The dependent variable is expressed in logarithm and the coefficient can be interpreted as %, percentage of each independent variable. The table is distinguished in two parts -> men and women. Regression 1 is connected with regression 4. The independent variables in these two regressions: black (dummy means a variable on-off), Hispanic, age… The number (- .244) is a coefficient of regression. The coefficient here (beta1) is the percentage impact of being black on the wage, in this case the impact ins negative, so there is a wage gap. Y = log, X1 = black and Y1 = a + beta1X1 + … + E1 According to this regression, the wage of black person (male) is lower than one quarter. Being black determines a wage cut -> nearly 25%. The number in parenthesis (.026) is the standard error = measures of how beta1 is statistically significant. T statistic of a certain beta is beta over standard error. This should be greater than 1.96 if we decide that 96% criteria of probability the number is correct. If you find in parenthesis the standard error, we have to consider the ratio of corresponding beta and standard error. X2 = age. Beta3 is 0.48 -> our interpretation is that increasing age produces increasing wage. A unit increasing age determinates increasing in wage by 4.8%. Regression 1 and 4 are called unadjusted (wage gap) because you do not take into account neither the learning achievements (X4) nor the schooling level and attainments (X5). If we ignore productivity, this are proxy probability of being productive, or having a sort of productivity -> we just observe that being a black gives disadvantages of nearly 25% compensating, controlling for age. Second regression for men is 2 and for women is 5: we consider race, age and high grade by 1991 (the coefficients in columns 2 and 5 are the percentage differences in wage controlling for both age and educational attainments: wage gap adjusted by school grade). Beta 5 is positive coefficient (.061) -> part of explanation of wage. The interesting thing is when we control for schooling, the coefficient -.196 and -.155 change. Moving from regression 1 to regression 2 we have started to decompose the unadjusted wage gap, while in the 1st regression nearly 25% of the gap is explained by race, here nearly 20% of the gap is explained with race. The decisive step is to move on with this direction. The study grade might be contaminated by a sort of self-selection. The idea of the authors is to try a 3rd regression which is the results: they include the test score as regression. They exclude the educational attainment of the regression; the interesting thing is that the residual and what remains of discrimination effect drops down to 17.2%. This is explained by the fact that blacks have lower scores in the tests. People who find disadvantages in learning will suffer from a wage gap later on when they go in labour market. This evidence naturally raises the question of why blacks acquired lower skills than whites in compulsory schools. Two possible answers: - They underinvested because their expected return to schooling was lower (by labour market discrimination), no evidence in support of this hypothesis is found in this study, but the hypothesis of discourage children reasonable? - Their investment has been less effective due to disadvantages in schooling: detailed evidence in support is given by the study Beta 1 in table 5 is not a percentage. All these social aspects matter. Some conclusions: it is well known that since the 1980s there has been a fanning out of the upper tail of the distribution of earnings in the US (as well as in many other advanced economies) which suggest that the value of high skills has increased a lot. And we have seen that the racial wage gap has increased substantially in the same period. Our study suggest that the two phenomena are linked: ethnic minorities did not take advantage from an increasing return to high education because their social status was not conductive to “making the most” of schooling. The authors are able to decompose the wage gap and assign it to learning gap. The residuum unexplained is due to labour market discrimination. Upper high school = people of racial minority might not decide to stop studying or with little effort because they are anticipating future discrimination in labour market (there might be as well statistical discrimination). Very much depend on pre market factors -> the authors focused on these factors that have a lot to do and are explained by different conditions. Kind of school that they attended (ghetto schools -> risk of having them, schools of different qualities). What the study does not say is whether Blacks deliberately underinvested in human capital because of negative stereotypes. A field experiment on stereotypes concerning acquired skills Bertrand & Mullainathan, ‘Are Emily and Greg More Employable than Lakisha and Jamal: A Field Experiment on Labor Market Discrimination’, American Economic Review, 2004 Discriminatory feelings by employers, assuming the same level of skills (or the same level of skill as documented by the achievements), the article aims to establish whether the level of consideration of black and with is the same or not. The article is based on different methodologies and consist in field experiment. In order to implement them empirically -> two possibilities: use data set, a high number of observations in which individual observation is different in characteristics, we choose one observation as main choice but since observations are different, we need to control for the other characteristics. The second methodological possibility is to contrast with experiment: we want to explain whether there is difference in attention (racial bias in the consideration that employers give to applicants for a job). Whatever the level of skill we are looking for the very basis of what in the market place can became a wage gap. There is a racial bias in which demand given the kind of vacancies that are to be covered, there is a higher demand (preference in demand in whites rather than blacks). The present study addresses directly the question of whether US employers have a prejudice against Afro-Americans (test-based discrimination) or perhaps, more likely, they take it for granted that race signals as lower productivity (statistical discrimination). Its main findings is that differential treatment by race still appears to be prominent in the US labour market. The experiment consists in sending nearly 5,000 fictitious resumes in response to over 1,300 employment advertisements in newspaper of Boston and Chicago. There are vacancies that have to be covered and in response to this call for applications the authors wrote a number of fictitious resumes. They selected ads concerned four occupational categories: sales, administrative support, clerical services and customer services. Four resumes were sent for each ad: two were of high quality, and two were of a lower quality. Different quality (i.e. level of human capital) was important in order to infer information on racial gap in the return to investment in human capital. Establish whether the investment in human capital by different races had respectively the same kind of appreciation by employers evaluating. Our target is to establish: if more attention is given and variation of interest is sensitive of level of presumed human capital that can be extracted by the characteristics. For each quality, one resume was randomly assigned to a white-sounding name and the other to a black-sounding name. Giving the information about racial belonging: the first name of the applicant (names that are typical for whites and for blacks). We have all of these resumes and we want that the quality of the resumes be exactly the same for whites and black. In the response you have clear idea of how race matters. The research eliminates any difference of characteristics except race (as inferred by names) -> then the responses in terms of call backs. The data consist in analysis of call backs. Each resume combines a series of characteristics, some of them are measured like years of experience in natural measures. Years of experience -> 7.84 number of year experience in all 5,000 resumes, in parenthesis we have the standard deviation (5.04)