In this paper, we develop a measure of industry specific human capital using the Tobin's qtheory. The measure is derived from a structural model of heterogeneous knowledge labor,which is homogeneous physical labor embodied with industry specific human capital

Tang, K.K.

Tseng, Y.

University of Queensland eSpace

Constructing a measure of industry−specific human capital
using Tobin's q theory 
Kam−Ki Tang Yi−Ping Tseng
School of Economics, University of Queensland Melbourne Institute of Applied Economic and Social
Research, University of Melbourne
Abstract
In this paper, we develop a measure of industry specific human capital using the Tobin’s q
theory. The measure is derived from a structural model of heterogeneous knowledge labor,
which is homogeneous physical labor embodied with industry specific human capital.
We would like to thank Alicia Rambaldi for her constructive comments.
Citation: Tang, Kam−Ki and Yi−Ping Tseng, (2004) "Constructing a measure of industry−specific human capital using Tobin's
q theory." Economics Bulletin, Vol. 10, No. 1 pp. 1−7
Submitted: November 14, 2003.  Accepted: February 27, 2004.
URL: http://www.economicsbulletin.com/2004/volume10/EB−03J40002A.pdf
 1
1. Introduction 
Increasingly, “human capital” has assumed a central place in various level of analysis of 
economic growth and development. At an individual level, human capital is influential in 
determining a person’s income, employment status and labor mobility (e.g., Heckman, Lochner 
and Taber 1998). Macroeconomists have also identified human capital’s important role in 
enhancing a country’s overall economic performance (Barro 1999). In turn, the development and 
promotion of human capital has become a central feature of international policy discussions (e.g., 
OECD 1994). 
Accurate measures of human capital are an essential prerequisite for the scientific discussion of 
growth and economic performance, as well as for the proper evaluation of education, training, 
and industry policies. However, there are some practical complications. The term human capital 
covers a wide range of elements including: knowledge accumulated via education; skills 
acquired by training; experience gained during employment; ideas and inventions developed in 
research, or even personal networks established in the workplace. This conceptual depth imposes 
obvious limitations on the definition of a single summary measure of human capital.    
This dilemma has lead researchers to employ a range of indicators for human capital. For 
example, the most commonly used measure of general human capital is educational attainment. 
Both Barro and Lee (2000) and de la Fuente and Demenech (2000) have made concentrated 
efforts to build accurate, cross-country databases for educational attainment. The specific 
dimensions of human capital are then accounted for by other indicators such as: average years of 
schooling; test scores; labor market experience; and cognitive ability. However, integrated 
approaches to measuring human capital are becoming more common. Fernandez and Mauro 
(2000) draw on Jorgenson’s seminal work to devise a human capital index that weights labor 
inputs by educational attainment and wages. Hanushek and Kim (2000) also accounts for the 
heterogeneity of labor quality at the cross-country level. 
In comparison, quantitative assessment of industry-specific human capital (ISHC) is far less 
developed, despite empirical evidence indicating that it is an important determinant of inter-
industry wage differential and labor mobility (Neal 1995; Kim 1997). The difficulty with 
measuring industry-specific human capital is the lack of a good proxy for the effects of 
experience and benefits of training. 
Against this background, this paper aims at developing a measure of ISHC from a structural 
model of knowledge labor. The essence of the paper is to establish the theoretical linkage 
between unobserved ISHC and observed return to industry experience. The link is the Tobin’s q 
of ISHC. In our model, ISHC is interpreted as experience and know-how, in contrast to the 
interpretation of idea and invention in the growth literature, but compatible to the interpretation 
of skill in labor economics. Our method thus provides a complementary measure of human 
capital to the traditional method of using education attainment. 
Tobin’s q theory has been widely used in examining physical capital investment and firm 
performance. However, little attempt has made to apply the Tobin’s q theory in human capital 
assessment. Therefore, this paper can be viewed as a new application of the Tobin’s q theory. 
 2
2. Theoretical Model 
Our model distinguishes between knowledge labor and physical labor. Production of an industry 
requires knowledge labor specific to that industry. A heterogeneous knowledge labor is a 
homogeneous physical labor that has accumulated ISHC. Labor accumulates ISHC through a 
learning-by-doing process, which incurs an implicit learning cost, akin to the installation cost of 
physical capital (Lucas 1967; Hayashi 1982). 
The objective of a representative household is to maximize its intertemporal utility function 
( ),  
t
U C L e dµτ τ∞ −∫   subject to 
 
Z Z
i i
i
W L rA PC A+ = +∑   (financial budget constraint) (1) 
 1 i
i
L L= +∑   (labor supply constraint) (2) 
 
1i iZ
i i iL Z L
β β−=  (composition of knowledge labor) (3) 
 1 2
Z Z
Z i i
i i
i
JL J
Z
φ = +    (gross investment in ISHC) (4) 
 
Z Z
i i i iZ J Zδ= −  (accumulation of ISHC) (5) 
where µ is the subjective discount rate; C is consumption; P is a price index; L  is leisure hours; 
A is financial asset holding; iL  and 
Z
iL  are the physical and knowledge labor hours deployed in 
industry i, respectively; ZiJ  is fixed formation of ISHC − iZ ; and Ziδ  and Ziφ  are the depreciation 
rate and learning cost coefficient of ISHC, respectively. Time subscript t is omitted for notational 
cleanness. 
Equation (1) is the financial budget constraint of the household, who distribute physical labor 
hours amongst various industries. Equation (2) is the total time constraint, which is normalized to 
one. Equation (3) indicates that knowledge labor is a Cobb-Douglas combination of both ISHC 
and physical labor.1 The multiplicative functional form of ZiL  implies that ISHC has to be coded 
into a physical labor for it to be operational. Equation (4) indicates that more ISHC will be 
acquired as a result of longer accumulated working hours in an industry. The inputs of physical 
labor in production and human capital accumulation are not exclusive, signifying that the latter is 
                                                 
1 With a Cobb-Douglas function, allowing iβ  to differ across industries will not change the equilibrium ISHC 
intensity of an industry. 
 3
a learning-by-doing process.2 Gross investment in ISHC is partially consumed as learning costs − 
( )2
2
ZZ
ii
i
J
Z
φ , which is implicit due to the learning-by-doing mechanism and, thus, does not enter 
the household’s budget constraint. Since the learning cost is a quadratic function of ZiJ , 
investment in ISHC is irreversible. 
The Lagrangian of the optimal control problem is 
 ( )
1( , ) 1
1
2
A Z L
i i i i
i i
Z Z
Z Z Z J Z i i
i i i i i i i
i i
h U C L W Z L PC rA L L
JJ Z L J
Z
β βλ λ
φλ δ λ
−   = + − + + − −      
    + − + − +       
∑ ∑
∑
 
. 
Solving the optimization problem, we obtain, amongst other first order conditions, 
 1
Z Z
Zi i
iJ
i i
J
Z
λ φλ = +  (6) 
where Ziλ  is the shadow value of ISHC, and Jiλ  is the shadow cost of gross investment in ISHC. 
The first order condition in relation to Ziλ  can be integrated to give: 
 
1 2
( )( )
2
i
Z
i
Z Z
s tZ A Z Ji i i
i i i is t
i i
L JW e ds
Z Z
β
µ δφλ λ β λ
−
∞ − + −
=
      = +          ∫ . (7) 
Equation (7) states that the value of a unit of ISHC at a given time equals the discounted valued 
of its future marginal value. The first term inside the bracket is the value of the financial reward 
of increasing the supply of knowledge labor. The second term is the value of the reduction of 
learning cost in ISHC accumulation. Therefore, the ratio of Ziλ  to Jiλ  can be naturally 
interpreted as the Tobin’s q of ISHC: 
 
Z
Z i
i L
i
q λλ≡ . (8) 
                                                 
2 The process can be modified into learning-by-training by specifying a share of physical labor hours spent on 
human capital investment. As long as the share is constant, it will not change the properties of the model. 
 4
 In the case of physical capital, Tobin’s q can be measured by the market value of outstanding 
securities of a firm divided by the replacement cost of its net assets.3 Nevertheless, the market 
value and replacement cost of ISHC are not directly measurable. Therefore, proxies have to be 
called in for empirical work. The closest proxy for Ziq  is probably the wage differentials between 
staffs with industry experience and those without, after controlling for other characteristics: 
wage rate of experienced staff1 1 marginal return to industry experience.
wage rate of inexperienced staff
Z
iq − = − =  (9) 
The imputed value of Ziq  has a central role in the estimation of ISHC, as shown below. 
3. Industry-specific Human Capital Index 
Using (4) − (8), it can be deduced that at steady state 
 
2
(2 )
i
i Z Z Z
i i i i
ZISHC
L δ φ δ≡ = +  (10) 
 1
Z Z Z
i i iq φ δ= + . (11) 
Here we define i
i
Z
L
 as industry-specific human capital intensity − iISHC .4 To empirically 
construct iISHC , we need to know the value of either 
Z
iδ  or Ziφ . However, the values of both 
parameters are unobservable. A solution is to impose a theoretical relationship between the two 
parameters. 
Firstly, for a given finite value of Ziφ , as Ziδ  tends to zero, iZ  will tend to infinitely large. 
Therefore, industry i will dominate the economy; this thus violates our competitive market 
framework. To exclude this scenario, it is necessary to specify that a sector that can accumulate 
more ISHC (i.e. a small Ziδ ) incurs greater learning costs (i.e. a large Ziφ ). Secondly, the 
                                                 
3 Under the assumptions of competitive output and capital markets, and linear homogenous production and 
adjustment cost functions, marginal Tobin’s q is equivalent to average Tobin’s q (Hayashi 1982). While the former 
is not observable or measurable, the latter is. In our model, the labor market is competitive and the learning cost 
function is linearly homogenous. 
4 In the case of heterogeneous labor input, (10) can be generalized to i ij ij
j
ISHC ISHCθ≡∑  where ijθ  is the 
weighting of the j-th type workers in industry i. ijθ  can be measured by the share of wage bills: 
/Z Z Z Zij ij ij ij ij
j
W L W Lθ = ∑ . 
 5
following inequalities must prevail: 1 0Ziδ≥ ≥ ; 0Ziφ∞ > ≥ ; and 1Ziq∞ > ≥ .5 To satisfy the 
above inequalities, as well as capture the negative relationship between Ziδ  and Ziφ , we postulate 
that 
 
( 1) ; 1
( 1)
Z
i Z
i
q q
q
δ φ
−= >− + . (12) 
Substituting (12) into (11), we get 
 ( 1)
Z Z
i iq q q δ= − − . (13) 
q  is the upper bound of Ziq . This can be seen from that if 0
Z
iδ → , then Ziφ →∞  and Ziq q→ . 
On the other hand, if 1Ziδ → , then 0Ziφ →  and 1Ziq → . That is, if ISHC is costless to 
accumulate but quick to depreciate, industry experience will not be valued at all. 
Substituting (12) and (13) into (10), we obtain a measure of ISHC intensity: 
 
2( 1)
( )(1 )i Z Zi i
qISHC
q q q
−= − + . (14) 
A condition for iISHC  to be strictly monotonic increasing in 
Z
iq is 3 1q> > .6 The value of q  
can be specified arbitrarily (within the inequality constraint). Choosing different values for q  
will affect the scaling of the measurement but not the ordering. To guarantee q  being the upper 
bound limit, we can choose a value according to the greatest observed value of Ziq . Econometric 
estimations of wage equations suggest that return to experience typically is only about a few 
percentage points per annum; see, e.g., Preston (1997) and Chang and Miller (1996). Therefore, 
using this specification method, it is likely to assign q  a value between 1 and 1.1, and the 
inequality 3 1q> >  will be comfortably satisfied. 
4. Conclusions 
In this paper, we integrate together two prominent theories in economics − Tobin’s q theory and 
human capital theory − to develop a measure of ISHC. The measure is derived from a dynamic 
optimization model of heterogeneous knowledge labor. Making use of the concept of Tobin’s q, 
we construct a measure of ISHC in terms of marginal return to industry experience. Lastly, while 
                                                 
5 These imply 1iISHC∞ > ≥ . 
6 This is because 1Ziq ≥  and 2 22( 1)( 1 2 )( ) (1 )
Z
i i
Z Z Z
i i i
ISHC q q q
q q q q
∂ − − − −=∂ − + . 
 6
the model is constructed in terms of ISHC, the whole framework is equally applicable to firm 
specific human capital. The only modification will be to measure Tobin’s q in terms of marginal 
returns to firm experience. 
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