* Eldon Smith Professor of Economics, Pomona College. Please do not quote without permission of the author.
 Comments by Frank C. Wykoff on Barbara Fraumeni, “Expanding Economic Accounts ...”

 Barbara Fraumeni has produced yet another major advance in the construction of the Jorgensonian System of Accounts In-progress (here after referred to as JASI). This paper adds to a long line of contributions in which Jorgenson and his associates are constructing an entire sys-tem of production accounts with considerable detail and which may be applied to empirical re-search into innumerable social issues. Advancing the great empirical work of  NBER, Kuznets, Goldsmith, Denison and others, this Jorgensonian effort is truly remarkable in its scope, care and detail and most importantly in its consistent adherence to sound economic theory. If the sound blend of theory and evidence, econometrics at its best, were shown as high-light films then this project would be the trailer.

JASI Modeling of the Labor Input

In this paper, Fraumeni produces a system of human capital accounts for the US ex-ploiting the concepts of human capital developed by Gary Becker. I would argue that the Frau-meni human capital framework is a perfectly logical and natural extension of the physical capital model developed by Jorgenson and Associates. First, I will explicate this framework and second argue that this perspective leads to several questions about the execution of the model in this pa-per and several suggestions for modifications.

Fraumeni blends Becker’s analysis of human capital, family decision making and the use of time into the Jorgensonian accounting framework by extending the methodology for physical capital to that for human capital. Fraumeni actually goes beyond the standard physical capital model of Jorgenson in several directions when applying it to human capital, and here I think some problem arise.

Fraumeni confronts two inherent realities of economic behavior that guarantee that much of her analysis will find critics.  The first of these two problems is that a good deal of human capital is generated and consumed outside of normal market channels so that imputations are required to determine values and imputations always attract critics. The second is that adding increments of human capital into a person frequently occurs at the same time as consumption of the resulting services, thus complicating the question of the appropriate accounting partition between consumption and investment. This is not a problem for capital goods measurement, be-cause capital goods, in the Jorgenson model, are produced, priced from a market transaction and then used in production. There is no question about the use of the unit of capital after it is pro-duced, marketed and priced.

Is Labor Different from Capital?

Before dealing with these problems, though, let me begin by reflecting on the core con-cept inherent in the Jorgenson accounting framework, and in fact core to virtually all growth and productivity models that include labor and capital as inputs in a production function. This core concept is that labor and capital, although marketed differently, are essentially the same. That is, even though capital assets are ordinarily acquired by the owner-user and labor services are hired by the user from the owner, one can in fact analyze the role of labor and capital in a parallel fashion by distinguishing in both cases, labor and capital, between stocks and flows. The stock of capital (usually owned by the user) sends off a flow of capital services which enter the contem-porary production function. The latter service flow must be imputed as a rule because while the acquisition of the capital asset is normally a market activity the consumption flow of the services normally occurs outside the market (and inside the firm). The stock of labor (usually owned by the laborer) also sends off a flow of labor services which enter the contemporary production function. In the case of labor, unlike capital, the flow of services employed by users (firms) is almost always acquired within a formal market context whereas the value of the stock of labor from which these flows emerge must be imputed since it is not ordinarily acquired in a private market.

Once the appropriate measures of the service flows are developed, virtually every analy-sis of production functions treats labor and capital as two separate but essentially identical serv-ice flows. The measure of the service flows may take account of quality change, but, even here, once this is done, labor and capital are symmetrical if not identical. I would like to suggest that in the final analysis this approach may miss something very fundamental about how labor and capital differ and that this difference may be at the heart of our inability of understand growth.

Douglas Hofstadter challenges the reader, in chapter 3 of Godel, Escher and Bach, to solve the “MIU puzzle,” in which one is instructed to write down sequences of the three letters M, I and U, obeying a few seemingly innocuous rules. The goal of the puzzle is to achieve a par-ticular sequence. It soon becomes evident to virtually any reader that this exercise can lead to an endless looping of sequences of the 3 letters without ever “solving” the puzzle within the rules of the game. Any human being will know to quit doing something which involves a simple endless loop by, in Hofstadter’s words, “leaping out of the pattern.”

Machines, though, can be designed to continue in such “closed loops” endlessly. Hu-mans could only be induced to such senseless activity through extremely potent positive or negative incentives. Hofstadter’s point, that humans differ from machines because humans can “leap out of the pattern,” implies to me that in the final analysis humans cannot be modeled into a deterministic functional relationship if one is to capture their inherent unique quality – humans must be able to “leap out of the pattern.”

Dale W. Jorgenson is one of the profession’s stellar examples of the unique superiority of the individual human intellect’s capacity to surpass machines, even when the latter take the form of government statistical agencies. In the late 1960s the thirty year-old Jorgenson began to develop a comprehensive conceptual system of economic accounts, linking inter-temporal movements in stocks of wealth to flows of income and expenditures over time. As fodder for his econometric analysis of production behavior, Jorgenson quickly realized the value of a more co-herent system of accounts than the accounts then produced by statistical agencies. As is often the case with brash, brilliant young scholars, Jorgenson encountered resistance to his data inquisition from senior members of his guild and their network of supporters in the statistical agencies. A classic case of entrenched powers protected their turf, the “conventional wisdom.”

Jorgenson, though, like our Hofstadter reader, and as impatient as he was brash, “leapt out of the pattern” and began to develop his own national accounting system, JASI. Because this effort was to be so monumental, Jorgenson needed to develop a virtual statistical agency of re-searchers who could implement and advance his agenda. These researchers could not be ma-chines who would simply replicate endless loops but scholars in their own rights with the so-phistication, skill, training and eventually experience to implement this remarkable man’s re-search agenda. It is no accident that in references to the work of Jorgenson and his many collabo-rators, writers are starting to refer to Jorgenson and Associates. Jorgenson has created, perhaps become, a virtual statistical agency of his own, Jorgenson Associates (hereafter J&A.) Does this man’s work suggest the uniqueness of labor as opposed to capital? I think so, but first let’s turn to the JASI itself.

JASI – A New System of Economic Accounts

Consider a model of the conceptual genesis of the official national income and product accounts (NIPA) that prevailed when Jorgenson turned to the official statistical agencies to test his theories of private domestic investment in the nineteen sixties. Underlying the accounts was a circular flow view of the economy. In Figure 1 note that we can measure two flows of economic activity, each at two different points in the flow process.

The circular flow model depicts two flows – an outer clockwise flow of dollars and a corresponding inner counterclockwise flow of physical goods and services. The outer clockwise flow of money consists of a flow of income payments from firms to households and a flow of expenditure payments from households to firms. The inner counterclockwise flow of physical goods and services consists of a flow of factor input services from households to firms (in ex-change for income) continuing with a flow of output products and services from firms into households (in exchange for expenditures.) One can, and the NIPA do, measure each of the two flows at the top and at the bottom of the cycles. This results in two sets of balanced accounts. Note that empirically each item in each account is a value measure, where I use the word value in the Debruevian sense as the product between price and quantity.

Figure 1
 For a simple economy without government and a foreign sector, but with saving and in-vestment, we can depict the four measures implied by the circular flow model. Letting V repre-sent value and using subscripts as follows: c for consumption, i for investment, s for saving, g for output goods and services, l for labor, m for materials and k for capital, we have Figure 2. Note from Figure 2, that all four total measures of economic activity are equal. Nominal income equals the value of input services equals the value of the output flow equals the value of expen-ditures.
The focus of the NIPA framework is clearly on flows of contemporary economic activ-ity. This apparently reflects the predominant influence of Keynesian flow models on economic thinking from the middle of the thirties throughout much of the sixties.  Jorgenson, who it will be recalled, began his research agenda in the early sixties with investment theory focused initially on the input side of the counterclockwise loop. It became evident to Jorgenson that markets han-dled capital and labor inputs differently. Markets directly generate the value flow data for the labor input, the cost of labor – wages plus benefits in exchange for hours worked. Capital, how-ever, was different, because it usually was marketed, if at all, as an asset and then used by the owner within the firm away from the easily observable market place. This meant that one could not directly observe the cost of using capital from the market in the same way one could observe the compensation of labor as payments for labor services.

Figure 2

Clockwise Flows
   bottom        top
Expenditures  ?    Vc + Vi  =  Vc + Vs    ?  Income
 

Counterclockwise Flows

   bottom          top

 Output    ?    ?sectors Vg,i   =  Vl  + Vk  + Vm + a  ?  Input
 

 Jorgenson’s first brilliant insight, for solving the different market treatment of labor and capital, was to recognize that capital users must be “acting as if” they were incurring a cost for using capital services corresponding to the wage they were paying for labor services. He called this cost (or price) of using capital services the user-cost-of-capital which we shall depict as c. Thus, the problem of interpreting input flow data begins with partitioning input values into price and quantity components as follows:
(1)  Vk = c ? k   and  Vl = w ? l
where c is the user-cost-of-capital, w is the wage rate, k is quantity of capital services and l the quantity of labor services. We use lower case letters to represent flow concepts as opposed to stock concepts. The dot can represent a dot-product when there are multiple capital and labor inputs so that c, k, w, and l are vectors of user-costs, capital service flows, wages and labor service flows.

In J&A’s model all the adjustments initially are made on the price side, not the quantity side, so that the flow of capital services, k, is proportional to the stock of capital, K, which can be thought of as the number of units of capital, just as the flow of labor services is total human-hours worked, l, by the number of workers, L. (It turns out that these concepts are a little vague at this point, so we will have to return to this later.)

In addition to needing to partition flows of value data into price and quantity compo-nents, J&A also realized that investment flows and flows of capital services were different. The first related to additions to the stock and the second to consumption of the stock, thus J&A real-ized that a Keynesian flow model was inadequate for analysis of capital goods. J&A had to ac-count for flows and for stocks in the same model, and the flow and stock measures had to be consistent over time. As always J&A turned to economic theory for a modeling framework for his system of accounts. Here again one sees the reliance on theory to ground measurements. It is this grounding which causes J&A’s measurement decisions to hold up under withering attacks by opponents. While critics may not like outcomes J&A get from the analysis of the data, they can-not attack the measurement decisions on theoretical grounds as they are always theoretically consistent.

The famous Hicksian week illustrates the Jorgenson model linking stocks and flows. In Figure 3 we illustrate this Hicksian week. The Hicksian week begins on Monday morning with an initial stock of wealth, WEALTHt, consisting of the stock of all physical (non-human) capital assets, Kt, all materials, Mt and all human capital assets, Ht. Economic activity takes place throughout the week by owners of the stocks of assets providing flows of services in exchange for factor payments which generate income, and this income is, in turn used for either consump-tion or saving throughout the period, the saving going to capital accumulation. At the end of the week, economic agents prepare to begin the next week with a new stock of WEALTHt+1 which reflects both their initial wealth and the flow of economic activity throughout the week. Recall that in Lord Hicks’ model, income is Haig-Simons income, defined as the amount one could consume throughout the week keeping wealth intact, thus increments to wealth must reflect in-come minus consumption.
 
 

Figure 3
Hicksian Week
 
   Monday          Friday
        ?  ? Circular flow  ? ?

 [WEALTHt]       ?   Haig-Simon income flows ?   [WEALTHt+1]

      production: inputs?outputs
 [Kt + Mt + Ht]    ?    ? [Kt+1  Mt +  Ht+1]
           income/expenditure

 To show that the new human capital model of Fraumeni is a logical extension of the J&A physical capital model, we first review the highlights of J&A’s physical capital model. In particular, we first explain exactly how J&A measure the initial stocks of capital, contemporary flows of capital, and the final stocks, each stock and flow having to be appropriately partitioned between prices and quantities, all in an inter-temporal consistent fashion which is implied by the Hicksian week.

The J&A Capital Model

We start by defining the stock of physical capital at the beginning of the week. Because capital is consumed over time, one must distinguish at any one point in time the different vin-tages of capital in the stock. This is the key problem encountered as a result of the inherent het-erogeneity of capital, i.e., capital assets differ by age, type and model. J&A define:
(K.1) ?(s) ? the efficiency function
where s= 0, 1, 2, . . ., T
?(0) = 1 and ?(T+1) = 0
where s indexes age and T is the age of the oldest surviving vintage of capital. The effi-ciency function indicates the in-use productive efficiency of an age-s unit of capital relative to a unit of new contemporary capital.  To aggregate different vintages of capital at a point in time one must first weight each vintage of capital by its relative efficiency value,  ?, before aggre-gating.
(K.2) ?t =  s=0?s=T ?(s) ? Kt-s
The capital aggregate ?t is quantity of the entire stock of capital at time t measured in new-machine unit equivalents, i.e., efficiency units. The efficiency function, or sequence, de-clines with age according to loss in productive efficiency until T+1 when capital is retired from service. The efficiency function turns out to play a central role in the J&A models because it provides the linkage between stocks and flows and between prices and quantities. That is, both problems Jorgenson set out to solve, partitioning value measures into prices and quantities and constructing a coherent set of stock and flow accounts, can be solved with the use of the effi-ciency function.

How does one measure productive efficiency of different assets, i.e., how does one measure the ? - function? Here, again, J&A apply neoclassical economic theory. In this case J&A apply the equilibrium condition that marginal rates of substitution equal relative prices. In the case of capital, this equilibrium condition yields
(K.3) ?(s) ? MRSs,0  =  c(s)/c(0)
where MRSs,0 is the marginal rate of (technical) substitution in production between an age-s unit of capital and a new (age-0) unit of capital, i.e., ?(s) is the number of units of output that can be produced, at the margin, by an incremental unit of age-s capital relative to that of a unit of new capital.  Equation (K.3) states that the efficiency function, which measures the rela-tive in-use productive efficiency of two different units of capital is, for the optimizing producer, the marginal rate of technical substitution in production which this producer equates to the ratio of the costs to him of using these two different units of capital, their relative user-costs.

Equation (K.3) is referred to as the duality relation, because it links the optimal quanti-ties to the optimal prices, the latter of which are dual to the former. There is nothing mysterious or esoteric about this relation. It is a standard marginal decision made by the optimizing pro-ducer, and it is absolutely central to the J&A framework, because it enters into the relations be-tween different asset prices, different quantity measures, and into the linkage between different stocks and flows.
Consider first prices. Let q(0,t) represent the contemporary market-observed price of new capital goods, i.e., the asset price of 1 unit of new (age = 0) capital in period-t. Similarly, the asset price of an age-s asset at time-t is q(s,t). These asset prices, again under optimizing condi-tions, are related to the future flow of user-costs on the assets. In particular,
(K.4) q(s,t) =  x=0?x=T-s  c(s+x, t+x) / (1+r)x
where r is the interest rate. Equation (K.4) states that the purchase price of the asset at any time in its life cycle is equal to the present discounted sum of future user-costs on the asset. In other words, at any point in time, the present value of the flow of the user-cost of the asset throughout the future is equal to the price of acquiring ownership of the asset at time t. Equation (K.4) is called the fundamental price equation, and it reflects the standard competitive neoclassi-cal equilibrium condition.
Assuming that the efficiency function is stationary, we can solve equation (K.3), the du-ality condition, for c(s+x ,t+x) in (K.4) to derive:
(K.4’) q(s,t) = x=0?x=T-s ?(s+x) c(0,t)/ (1+r)x
Notice that, given the interest rate, r, the change in asset price as it ages depends only on the efficiency function, ?(s). Taking first differences of (K.4), or (K.4’), one can easily derive the famous Jorgenson user-cost-of-capital equation:
(K.5)   c(s,t) = r?q(s,t)  +  [q(s,t) - q(s+1,t)]  -  [q(s+1,t+1) - q(s+1,t)].
Equation (K.5) permits, in principle, imputation of the unobserved user-cost-of-capital from observed asset prices. On the right hand side of (K.5), the first square bracketed term is the change in asset price as age increases, economic depreciation, and the second square bracketed term is the change in asset price as time advances, asset revaluation. If depreciation and re-valuation both occur at constant rates, ? and ? respectively, then we have
(K.5’) c(s,t) = (r + ? - ?) ? q(s,t).
Turning now to quantities, we begin with the following fundamental quantity equation,
(K.6) ??t ? ?t+1 - ?t =  ?t - ?t
Equation (K.6), the capital accumulation equation, states that the change in capital stock over the course of the Hicksian week is equal to gross new increments of capital during the week, ?t, minus requirements for replacing worn out capital, ?t. Note that ? and ? are quanti-ties (more specifically quantity concepts), not values nor prices, measured in new machine equivalents, so that the value of new investment in period-t,
Vt = q(0,t) ? ?t
If there are multiple new investment goods produced in period-t, then q and ? are re-spective price and quantity vectors, and V is the dot product, which is the total value of invest-ment expenditures in period-t.
The efficiency function entered into the fundamental price equation and also enters into the fundamental quantity equation by inserting equation (K.1), into equation (K.6)
(K.7)    ?? t =  ?(0)Kt+1 + {s=1?s=T ?(s)Kt+1-s - s=0?s=T ?(s)Kt-s}
Equation (K.7) has two distinct parts, new increments of capital or gross investment in units of new capital, which is ?t, and in curly brackets replacement requirements, ?t. If we de-fine the mortality sequence as the decline with age in productive efficiency, we have
(K.8) m(s) = [?(s+1) - ?(s)],
then we have
(K.7’) ??t = ?t - s=0?s=T m(s)Kt-s
Equation (K.7’) makes clear that the inter-temporal change in the capital stock consists of gross additions to capital during the week minus new capital required to replace loss in pro-ductive efficiency from aging capital, as a result in loss of efficiency, or mortality.  This com-pletes the capital model employed by J&A to obtain coherent stock and flow, price and quantity measures of capital. Central to every measure is the efficiency function.

Applying the J&A Capital Model to Labor

Corresponding to each capital (hereafter “machines”) equation, (K.1) through (K.8), is a human capital equation for labor, because in each instance J&A rely on neoclassical production theory. While the J&A abstract theoretical structure applied to human capital measurements is consistent with the machines model, the empirical problems encountered are quite different. Three distinctions between labor and machines present difficulties in adapting the machines model to human capital. First empirically, unlike in the case of machines, flow user-costs (wages and fringes) of labor are market observed whereas human capital asset prices are not. Thus, whereas J&A had to impute non-market user-costs for machines from market-observed acquisi-tion prices, the exact opposite is the case for labor. User-costs are observed but asset prices must be imputed.

Second, the production of human capital is more complex than the production of ma-chines for several distinct reasons. Machines ordinarily are produced, and then used seriatim, but human capital is acquired, used, re-acquired, used some more and so on, thus, one cannot as eas-ily assume the human capital is simply produced and then there. While there may be some mod-est break-in period for machines, essentially once produced their service flow begins at its peak and then, unless a one-horse-shay, starts to decay. Humans, on the other hand acquire skills, knowledge and experience on the job, so that their relative in-use productive efficiencies proba-bly will rise then fall. In fact, the patterns may be even more complex than that.

To further complicate matters, acquisition of human capital occurs in several very differ-ent ways – fertility, informal rearing, formal education, on-the-job training, for instance.  Even more difficult is dealing with the fact that the process of production of human capital tends to be extra-market. Even Gary Becker would not claim that reproductive decisions, family rearing, and formal educational systems occur in competitive markets that simply produce human capital as-sets, so the costs of production are going to require controversial imputations of extra-market activity.

As if these realities did not create enough problems, the production process of human capital involves the use of the time of the unit of human being produced (or educated and trained), so that the output-unit of human capital is produced in part by itself. No one worries about the time materials are tied up in the production of machines, except in short run investment models, but the use of time in the production of human capital directly effects its availability to the market and involves an important economic calculus. The decision to invest in human capital is made by the  owner of the asset thus is not market observed and this decision maker is also the consumer of final product. This forces one to make precise distinctions between consumption and production in the use of time.

To illustrate how Fraumeni deals with these various difficulties, we begin by building the human capital model by developing the humanc capital equation corresponding to each ma-chine equations (K.1) - (K.8).  As with machines, J&A begin by dealing with the heterogeneity problem. Corresponding to the capital efficiency function, ?(s), is
(H.1) ?(h) ? efficiency function for human capital,
where h = 0, 1, . . ., A
where h indexes humans by age, and where A is age of the “oldest” worker.
One can normalize ?(0) = 1 and ?(A+1) = 0. In the case of machines it is fairly straight forward to normalize the efficiency sequence on the newest machine, so that  ?(0) = 1, but with human capital, the choice of normalization is less obvious. While arbitrary, a natural normaliza-tion is to set the efficiency of one new entrant of labor into the production function to 1, so that h=0 in the period a new worker enters the labor force. (Just as there are different types of new machines produced in each period, there will be different types of new workers in each period, so that in both cases, machines and workers, one has to aggregate across heterogeneous types. In the case of machines, we distinguish drill presses, offices, and automobiles. In the case of workers, the variations occur across skill and education level, possibly sex, weight, whatever.)
Thus, corresponding to machine equation (K.2) is
(H.2) ?t = s=0?s=A ?(s) Ht-s
? is the quantity of human capital at time period-t measured in new-entrant equivalents, i.e., efficiency units.
 
The form of the efficiency function for machines has been controversial. Is it one-horse-shay, linear, geometric, or what?  The human capital efficiency function is surely going to be even more controversial as it is much more complex. The sequence of labor efficiencies is likely to rise as workers gain in on-the-job training, maturity, experience, and so forth. Eventually, de-pending on the tasks, the human capital efficiency function is going to decline as the ravages of age begin to offset the accumulation of wisdom. At least in the case of labor, though, we have the advantage that the duality condition applies to observable market wages (and fringes), so that when we impose the duality condition, that the marginal rate of technical substitution in produc-tion between two units of labor, one vintage-h at time-t relative to a new vintage of worker at time-t, we have
(H.3) ?(h) ? MRSh,0 = w(h)/w(0),
where clearly w(h) refers to the flow earnings of a unit of labor, age-h, in period-t. Thus, as long as one is dealing with hired or employed workers, one can directly observe movements in wage ratios over different workers and determine the form of the labor-efficiency sequence. It need not be inferred from asset prices or from imputed user-costs.
As in the case of capital, the duality condition links quantity and price measures through the efficiency function. We turn now to the equivalent of machine equation (K.4), the funda-mental price equation (H.4). Fraumeni calls this the “lifetime income approach.” It states that the human capital asset price is the present discounted value of the future flow of earnings per pe-riod:
(H.4) p(h,t) = x=0?x=A w(h+x, t+x)/ (1+r)x
   Equation (H.4) links the asset-price or stock price or “lifetime income approach” of a unit of vintage-h human capital in period-t to the future flow of wages to be earned by that unit of human capital. Substituting equation (H.3) into (H.4) yields:
(H.4’) p(h,t) = x=0?x=A-h ?(h+x) w(0,t)/(1+r)x
As in the case of machines, we see that the human capital efficiency function enters into the fundamental price equation (H.4’) and the fundamental quantity equation (H.2). One can also derive a user-cost-of-human-capital formula corresponding to (K.5), but in this instance, since labor compensation is market determined, this equation need not be used to impute the cost of using workers. However, it does point to the relationship between wages and inter-temporal in-fluences on worker efficiency which point to some difficulties with Fraumeni’s empirical im-plementation of the J&A model.
(H.5)  w(h,t) = r?p(h,t)  +  [p(h,t) - p(h+1,t)]  -  [p(h+1,t+1) - p(h+1,t)]
or in continuous time
(H.5’) w(h,t) = r ? p(h,t) + ?p/?h - ?p/?t
The cost of using (or the wage paid to employ) a unit of age-h human capital (an hour of work provided by an age-h worker) contains three terms: (1) the opportunity cost of the worker’s time, r?p, plus (2)  maturity (improvements or decrements in productive efficiency) of a worker as the age index advances, given time-t, ?p/?h, minus (3) the revaluation of a given age of hu-man capital between periods as a result of human capital gains or losses from time t to t+1, ?p/?t. If maturity of workers with age occurs at a constant rate ? and if changes between periods in the cost of labor are constant at rate ?, then:
(H.5’’) w(h,t) = (r + ? - ?) ? p(h,t).
As noted above, one need not impute wages from r, ?, and ?, since wages are market determined. However, since relative wages are used to construct the number of efficiency units of human capital across heterogeneous workers, via equation (H.1), the duality relation, aggre-gation takes place over the number of units each multiplied by the efficiency term for that type of worker, ?(h). This means that corrections for age and year differences have been accounted for by the efficiency index, thus no further corrections are appropriate on the quantity side of the ledger.  In fact, if one were to adjust quantities for age and date effects, then this would be like double counting – correcting twice for differences on the quantity side.

We turn now to the quantity equations beginning with the human capital accumulation equation corresponding to equation (K.6).
(H.6) ??t  ? ?t+1 - ?t = ?t - ?t
where ?t is period-t acquisitions of labor into the human capital stock and ?t is period-t replacement requirements. Here one has to be quite careful what one means by new acquisitions. In the case of machines, the clear intent is acquisition of the finished machine by the producer of the product for whom the machine is an input in production. Since machine production itself and use of the machine as an input occur seriatim, this is not a problem. With human capital, though things may be more complex. Should not new acquisitions refer to already produced units of human capital entering into production of goods and services in time period-t? Once we have constructed the efficiency functions for aggregation, then all we need to know is how many workers of each type, age, etc. are available for production in period-t. Thus, the number of new workers entering the production process at the beginning of period-t is ?t and the aggregate number of units of workers measured in efficiency units is ?t.
Replacement requirements for human capital, like requirements for machines is deriv-able from equation (H.2) the quantity of human capital, in production, equation. In particular,
(H.7) ?t = h=0?h=A d(h) ??t-h
where d(s), corresponding to the mortality function for machines, is the rate at which in-use productive efficiency of a unit of human capital changes with age (matures).
(H.8) d(h) ? [?(h+1) - ?(h)].
Thus, replacement requirements of human capital depend only on the changes, of in-use productive efficiency of the human capital inputs. Note that replacement requirements are not always positive, because maturity can increase or decrease in-use productive efficiency.

Fraumeni vs. J&A Analysis of Human Capital
 
The various measures suggested by the above analysis are somewhat different than what Fraumeni measures on the human capital side. These differences mainly reflect the decision by Fraumeni to measure much more than J&A had measured on the capital stock side. First, she constructs aggregate measures of the total stock of human capital alive in period-t whether in-volved in production or not. Second, she accounts for the use of time by every unit of human capital throughout its life span and third, she includes measures for maintenance and repair of human capital once in place. Thus, rather than being concerned only with additions to and dele-tions from the in-use productive efficiency of the period-t employed work force, she is concerned with period-t births, rearing, education, health care, and so forth.

Rather than dealing with a constant flow of services from the stock of capital, as J&A do with machines, Fraumeni sets out to measure the entire use of human time. This means she must account for all uses of time, not just work, but sleep, eating, leisure and so forth. She also prices leisure time. This is not something J&A had to deal with in analysis of machines, and is clearly very difficult to do, because markets do not directly price leisure time. The corresponding prob-lem with non-human capital is dealt with in the utilization literature,  but as far as I know, J&A did not deal with utilization issues.

Fraumeni then adjusts for unwanted changes in productive efficiency while in place (health care). Here again, J&A did not integrate maintenance and repair into analysis of ma-chines in production.  As a consequence of this much broader objective, Fraumeni encounters many difficulties not dealt with in J&A analysis of non-human capital assets. Many of the solu-tions to these new problems are going to be controversial and are certainly arguable.

It seems to me that Fraumeni has undertaken a much more difficult task than J&A un-dertook in measuring machinery, equipment, structures and other non-human physical capital input flows. In the usual, and I think simpler, J&A framework, information on births, rearing and education only enters into construction of the efficiency function, when it cannot be observed directly from wages. But, with wages, all we need to know is the number of new workers in pro-duction each period of each type. Exactly how best to integrate maintenance and repair issues into the J&A framework is also not exactly clear to me. Feldstein and Rothschild (1974) believed it was not possible. It seems to me that both health care issues and the time Fraumeni refers to as “maintenance time” such as sleep, eating and so forth both should enter as maintenance and re-pair components, but it not obvious to me how this should be done. It seems to me that this can only be done if one models in some form. The reason is that capital acquisition, whether ma-chines or capital, involve an expected flow of services, including an expected flow of down times and maintenance and repair (or in the case of humans, health care) expenses. Deviations from expected will change asset valuations, but not, it seems to me, normal patterns of mainte-nance and repair, so I would want to develop the theoretical expectations model on which I based integration of health care and other maintenance activities into the model.

Finally, the decision to account for the entire use of human time raises lots of problems. J&A model the quantity of capital services to be proportional to the stock of capital, the latter and former both measured in efficiency units. J&A do not worry about idle capital. They do not feel they have to account for the use of machine time. An implicit assumption here is that firms will do the optimal thing with the use of their machinery, so that variations in intensity of use are of secondary importance in the accounting model. Here, though Fraumeni is accounting for how each efficiency-unit of labor spends its time once in place. It seems to me a viable research strat-egy might be to replicate the simpler J&A framework for non-human capital in the human capital case and then to extend measures of both inputs into the more complex environment of worrying about utilization, maintenance and repair, down time, and so forth.

Conclusion – Humans vs. Machines

I would like to end by reasserting my view on the core question raised earlier in the pa-per regarding the appropriate treatment of human and machine. Let’s assume that the various measurement issues raised by Fraumeni’s overarching treatment of humans’ use of time could be resolved, either by applying similar methods to non-human capital or by scaling back the treat-ment of human capital, so that it is more consistent with J&A treatment of machines. The ques-tion still remains that after all adjustments are made to get the services of machines and the services of humans measured in the proper efficiency-corrected units, can we then just view these two aggregates as entering the production process symmetrically? Everyone does it, but still, I am uneasy about It.

Doesn’t Professor Jorgenson himself serve as a perfect illustration of the unique ability of humans to “leap out of the pattern,” as Hofstadter (1979) pointed out. It seems to me that hu-mans can, and do, via Schumpeter’s creative destruction, constantly “leap out of the pattern” and generate new approaches to the provision of goods and services from inherent scarcity. This hu-man quality is unique and must be modeled differently in the final analysis from machines if we are to understand the complex evolution and growth of economic activity. In some very funda-mental sense, humans alter the process so that we are unlikely to be able to analyze long range economic activity if we model humans and then put them on automatic pilot as we do machines.
 
 

 References

Becker, Gary S., “A Theory of the Allocation of Time,” Economic Journal, Vol. LXXV, Sep-tember, 1965.

__________, Human Capital, University of Chicago Press, Chicago, IL, 1975.

__________, The Economic Approach to Human Behavior, University of Chicago Press, Chi-cago, IL, 1976.

Berndt, Ernst R. and Melvyn A. Fuss, “Economic Capacity Utilization and Productivity Meas-urement for Multiproduct Firms with Multiple Quasi-Fixed Inputs,” NBER Working Paper no. 2932, Cambridge, MA, April, 1989.

Christensen, Laurits and Jorgenson, Dale W., “US Income, Saving, and Wealth, 1929-1969” Re-view of Income and Wealth, Vol. 19, December, 1973.

Eisner, Robert, The Total Incomes Systems of Accounts, The University of Chicago Press, Chi-cago, 1989.

Feldstein, Martin and Michael Rothschild, “Towards an Economic Theory of Replacement In-vestment, Econometrica, 42, May, 1974, pp. 393-423

Hall, Robert E., “Technical Change and Capital from the Point of View of the Dual,” Review of Economic Studies #35, pp. 34-46, 1968.

Hall, Robert and Dale W. Jorgenson, “Taxation and the Theory of Investment Spending,” American Economic Review, #57, pp. 391-414, May, 1967.

Hofstadter, Douglas R., Godel, Escher, Bach: An Eternal Golden Braid, 1979.

Hulten, Charles R., “The Measurement of Capital,” in Berndt, Ernst R. and Jack E. Triplett (eds.), Fifty Years of Economic Measurement: The Jubilee of the Conference on Research in In-come and Wealth, NBER Studies in Income and Wealth, Vol. 54, Chicago University Press, Chi-cago, 1990.

Jorgenson, Dale W., “The Economic Theory of Replacement and Depreciation,” in Econometrics and Economic Theory, Essays in Honor of W. Sellykraerts, McMillan, New York, 1973.

Jorgenson, Dale W. and Barbara Fraumeni, “The Output of the Education Sector,” in Zvi Grili-ches (ed.), Output Measurement in the Service Sectors, NBER Studies in Income and Wealth, Vol. 56, Chicago University Press, Chicago, 1992.

Triplett, Jack E., “What’s Different About Health? Human Repair and Car Repair in National Accounts,” NBER, Cambridge, MA, unpublished manuscript, May, 1998.