human capital accumulation and depreciation

Agricultural & Applied Economics Association

Human Capital Accumulation and DepreciationAuthor(s): Daniel McFaddenSource: Review of Agricultural Economics, Vol. 30, No. 3 (Fall, 2008), pp. 379-385Published by: Oxford University Press on behalf of Agricultural & Applied Economics AssociationStable URL: http://www.jstor.org/stable/30225880 .

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Review of Agricultural Economics-Volume 30, Number 3-Pages 379-385 DOI:10.1111/j.1467-9353.2008.00411.x

Human Capital Accumulation and Depreciation*

Daniel McFadden

In the spirit of T. W. Schultz's contributions to the theory and measurement of human capital, this article discusses the dimensions of human capital, and the technologies used for its accumulation and maintenance. The article emphasizes the role of health as a dimension of human capital that influences the efficiency of acquisition and maintenance of cognitive skills, and the relationship between worker productivity and depreciation of cognitive skills over the life cycle.

My first contact with Ted Schultz came when I visited the University of

Chicago during the 1966-67 academic year. He was on leave most of that year, but I met and talked to him about development and growth. I was impressed by Ted's wisdom and prairie practicality, a refreshing counterpoint to the edgy gamesmanship of Milton Friedman and George Stigler. Ted's strongest influence on me was indirect, through his avatar Zvi Griliches, who taught me the importance of understanding data and the economic circumstances that produce it. A casual observer might think that the econometrics I have developed and taught over my academic career is in the opposite corner from the Schultz-Griliches school, but while we did dispute the productivity of mathematical models and econometric theory, there was never any disagreement on the objectives and re- quirements of sound empirical economics.

Given the centrality of human capital in Ted Schultz's interests, and the importance of his contributions, it is natural in this lecture to comment on this subject. I will refer to the extensive and penetrating research on human capital accumulation, but concentrate my remarks on the aspect that touches my own research on health dynamics, the maintenance and depreciation of human skills as we age.

When economists introduce the concept of physical capital, they recognize that it is an aggregate that includes durable equipment, fixed plant, intangibles such

* Daniel McFadden is the Cox Professor of Economics at University of California, Berkeley

*This lecture was given as the T.W. Schultz Award Lecture at the Allied Social Sciences Association Annual Meeting, New Orleans, LA, 4-6 January 2008.



380 Review of Agricultural Economics

as intellectual property, and for some purposes, endowments of resources such as mineral deposits and arable land. They are used to the idea that multiple production processes may be available for capital accumulation, such as building fish stocks from fingerlings grown naturally or in hatcheries, the idea that technology and factor substitution influence the cost and productivity of real capital stocks, and the idea that aging, wear, and obsolescence cause stocks to depreciate in value. Economists are accustomed to the capital accumulation equation,

(1) d K/dt = I - 8K

that says that the rate of change in capital stock equals investment less depreciation, with depreciation a constant fraction 8 of the capital stock, but recognize that while this may be a satisfactory approximation for physical capital at the level of an industry or the aggregate economy, it may be a poor representation of the process of accumulation and depreciation of specific capital components.

Turn now to human capital, recognized by Ted Schultz (1960, 1961, 1962, 1963, 1967) and his contemporaries1 as the stock of skills and knowledge accumulated by workers through education, on-the-job training, and self-improvement. How good is the analogy between physical and human capital? Is equation (1) a rea- sonable description of the accumulation of human capital? Can human capital be reasonably approximated as unidimensional, or does it really need to be treated as multidimensional? What technologies are involved in human capital maintenance and depreciation?

In his seminal 1961 paper, Ted Schultz described human capital investment as occurring in several distinct dimensions: health (longevity, strength, stamina, vigor, vitality, acuity), general training and knowledge (provided by formal education, employer training, and self-instruction), and job-specific skills (provided by employer training and experience). To this list can be added socialization and motivation, provided by informal education and experience that contribute to the ability of individuals to work in teams. This suggests that human capital may best be pictured as having hedonic attributes that interact in accumulation and depreciation. For example, a healthy consumer with stamina and acuity will acquire job-specific skills more rapidly and maintain them more easily. Then, investment in nutrition and socialization may be important complements to investment in schooling and training. Economists have noted that healthier consumers with higher probabilities of a long working life have higher expected payoffs from skill acquisition, but increased efficiency in skill acquisition may be even more important in determining the return to training. It is also clear that the comparative importance of different attributes of human capital varies by job-- strength and stamina are more important for a farm worker than for a computer programmer.

Consider human capital accumulation. Ben-Porath observed that the individual, "has to participate in the creation of his human capital. His own abilities, innate or acquired, the quality of co-operating inputs, the constraints and op- portunities offered by the institutional setup all determine the technology." This technology encompasses "a wide spectrum of activities including formal education, acquisition of skills on the job, child care, nutrition, health, etc." For example, important and convincing research by Jim Heckman shows that the socialization



Human Capital Accumulation and Depreciation 381

provided by early education enhances the economic productivity of later investment in training.2 Research results by Case and Paxson; Case, Lubotsky, and Paxon; Bhargava, and Bhargava et al. link productivity to childhood nutrition, showing that investment in health is an important component of human capital accumulation. Health economists have found it useful to employ the concept of health capital.3 In my own research, I factor health capital into dimensions such as cardiovascular capital, cognitive capital, etc., with these capital factors having different, but interactive, processes for accumulation and decay.4

Economists have given less attention to the process of human capital depreciation, and technologies for human capital maintenance. Natural questions to ask are how human capital at various stages in the life cycle can be measured, using current wages, aptitude tests, etc.; the degree to which the depreciation of human capital components is an exogenous consequence of aging or can be controlled through work, study, and behavioral choices; and the degree to which depreciation is predictable or random. At least for the health component of human capital, the evidence suggests that behavior is important, wear-and-tear depreciation is significant, maintenance through health care matters, and while the probabilities of health events vary systematically with age, realized health states are substan- tially random.5

To examine the question of depreciation of human capital more closely, consider cognitive skill, the human capital component most closely associated with formal education. One simple view is that accumulation of this capital component is described by equation (1), with investment I equal to the number of hours of classroom instruction the individual receives each day, 8 interpreted as a rate at which acquired knowledge is forgotten or becomes obsolete, and K interpreted as cumulative hours of formal education, depreciated. This framework leads to the treatment of depreciated education as a factor of production, and to measurement of the returns to education as a conceptually straightforward, although econometrically challenging, task. It also implies that over the life cycle, human capital stock peaks at a fairly young age, even when on-the-job training is ac- counted for. Then, wage rate profiles that do not peak until late in working life are interpreted as back-loaded, giving rise to interesting economic analysis of the incentives in employment contracts. Immediate questions raised by this approach are the role of individual aptitude, which may determine the efficiency with which hours of schooling are transformed into useful cognitive skills, the rate at which acquired skills depreciate, and the pattern of depreciation of cognitive skills with age and behavior. If the human capital of an individual follows "one-hoss shay" rather than exponential depreciation, then back-loading of wage contracts is less severe and easier to explain.

Psychologists factor cognitive skill intofluid intelligence, measured by processing speed on tasks such as nonsense syllable recall, and crystallized intelligence, measured primarily by vocabulary.6 These skills are quite heterogeneous across individuals at any given age. They are fairly highly correlated with each other, and controlling for age are positively associated with education. However, their profiles over the life-span, illustrated in figure 1, indicate that there is no simple causal arrow from education to these skills. Fluid intelligence rises from birth, peaks around age fourteen, well before the end of formal education, and declines steadily over the rest of life. Crystallized intelligence continues to accumulate




Figure 1. Fluid and crystallized cognitive skills

EDUCATION

CR YSTAL L

IZED

0 14 28 42 56 70 84 AGE

beyond the end of formal education, is increased by mental exercise, and shows little depreciation until about age sixty-five when health conditions such as strokes and dementia begin to take a toll. Decay in fluid intelligence is tied to physiolog- ical aging of the brain, particularly in motor coordination. These cognitive skills are aspects of human capital, and the lesson from this figure is that human capital is a complex product of natural endowment and decay, augmentation through investment in education and training, and endogenous decay influenced by usage and maintenance. Further, the mix of cognitive skills changes with age, and this interacts differently with productivity in different occupations, so that crystallized cognitive skill makes agricultural economists and professional golfers productive workers long past the age when fighter pilots and professional basketball players who require high fluid cognitive skill have retired.

Thinking about depreciation of crystallized and fluid cognitive skills, and other components of human or physical capital, it is clear that the conventional equation (1) assumption of a constant rate of decay is problematic. An exponential failure time distribution, corresponding to a constant hazard rate, holds for in- candescent light bulbs, but typically not for machines with built-in redundancy or capacity for repair. Depreciation is sometimes pictured as being like evaporation from a reservoir, but even here the process is not so simple. A reservoir has finite capacity, and water added beyond capacity is spilled. Natural replenishment may decrease with age, accelerating net loss and requiring more investment in maintenance and replenishment. The rate of evaporation depends on the ratio of surface area to volume of the reservoir, as illustrated in figure 2. In a cylindrical reservoir, evaporation is independent of volume, so the evaporation rate 8 increases as the volume of water stored decreases. In a conical reservoir, evaporation is proportional to the square root of volume. Generally in convex reservoirs, the rate of depreciation is highest when the stock is small. Alternatively, if one has a flute-shaped reservoir, then evaporation produces exponential depreciation that




Figure 2. Reservoir shapes and rates of depreciation

D = Depreciation, K = Capital Stock

y

ii~iiiiii~iii~iii~ii~iii~iiiiiii

Cylinder Cone Exponential flute

D indep. of K D ~ K112 D= 5K

y = 2eh

fits equation (1). The usefulness of equation (1) as an economic approximation comes from the fact that if one replicates many times reservoirs of any shape, then depreciation will be roughly proportional to the number of reservoirs and the total stock of water they impound. However, as the discussion above indicates, this aggregate empirical law may be a poor approximation to the human capital depreciation profile of an individual.

Consider health capital more generally, including components such as cardiovascular capital. Most of these components display low, nearly constant hazard rates for health problems at younger ages, then increasing hazard rates as people age. This seems analogous to evaporation from a convex reservoir. Peoples' natural replenishment and repair processes may be sufficient to keep health capital near capacity when they are young, but with aging the capital stock diminishes and more frequent maintenance is required. People repair or work around fail- ing optional equipment, but when the power train goes, it's goodbye Charlie. While I have been talking specifically about health capital, some of these obser- vations may apply to other dimensions of human capital. The concept of human capital developed by Ted Schultz and his contemporaries is a powerful tool for understanding and quantifying the role of education, nutrition, experience, and training in determining worker productivity. In the study of technology, human and physical capital can be usefully treated as complementary factors of production. However, just as the aggregate concept of physical capital may be a poor representation of the life-cycle characteristics of individual machines, the human capital of individuals comes in dimensions with life-cycle profiles that have distinct features. Economists should be cautious about borrow- ing the usual tools of capital theory and applying them to individuals without carefully thinking through the question of how accumulation and depreciation of specific skills work, and how different components of human capital interact. A broader examination of the technologies underlying accumulation and depreciation of human capital components, and of the mapping from human capital components to worker productivity in different occupations, may provide new ways of studying and interpreting returns to education, childhood nutrition,




and health maintenance. This is a research agenda that Ted Schultz would approve.

Acknowledgments The preparation of this article was supported by the E. Morris Cox fund at the University of Califor-

nia, Berkeley, and by the Institute on Aging of the National Institute of Health. I thank James Heckman for useful comments.

Endnotes 1Friedman and Kuznets, Becker (1962, 1964, 1967), Mincer (1958, 1962, 1970), and Ben-Porath. 2Carneiro and Heckman, Heckman and Masterov, Cunha and Heckman, and Heckman. 3Grossman (1972, 1976), Davis, Ram and Schultz, Lee, and Cutler and Richardson. 4Heiss, McFadden, and Winter; Schultz 1980. 5Case and Deaton. 6Cattell, John and Cole, and Staudinger, Cornelius, and Baltes.

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