Discussion Papers In Economics
And Business

What decreases the TFP ?
The aging labor and ICT imbalance

Tatsuyoshi Miyakoshi and Pekka Ilmakunnas

Discussion Paper 09-03

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANWhat decreases the TFP ?
The aging labor and ICT imbalance

Tatsuyoshi Miyakoshi and Pekka Ilmakunnas

Discussion Paper 09-03
February 2009

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANWhat decreases the TFP ?
The aging labor and ICT imbalancebyTatsuyoshi Miyakoshi, Osaka University
andPekka Ilmakunnas, Helsinki School of Economics

Abstract
The purpose of this paper is to investigate what decreases TFP, why TFP has decreased insome countries and how large the decreases of TFP are. We focus on the quality of laborand capital inputs and use cross country data for the manufacturing industries of someOECD countries. We provide a comprehensive empirical investigation based on two
hypotheses, substitutability and complementarity of labor input age and skill categories.
Further, we provide an aging index, which tells how much the share of ICT capital should
be increased to counterbalance decreases of TFP caused by the aging of the labor input.

Keywords: TFP; quality of labor and capital, substitutability and complementarity of age
and skill groups, aging index
JEL Classification Number: O11; J00;J80;O40.
Earlier versions of this paper were presented at the seminars in Tohoku University andOsaka University. We are very grateful toYoshiro Tsutsui, Mototsugu Fukushige, Hiroshi
Yoshida and participants at the seminars for their helpful comments. The research of thefirst author was supported by Grant-in-Aid 20530271 from the Ministry of Education,
Culture, Sport, Science and Technology of Japan.
Correspondence:
Tatsuyoshi Miyakoshi, Prof. of Monetary Economics
Osaka School of International Public Policy, Osaka University
1-31, Machikaneyama-machi, Toyonaka, Osaka, 560-0043, Japan.
tel:+81-6-6850-5638; fax:+81-6-6850-5656;E-mail: miyakoshi@osipp.osaka-u.ac.jp1

1.

Introduction

As empirically found by Lebow (1993), Sbordone (1996) and Basu and Fernand (2001),
among others, the Total Factor Productivity (TFP) accounts for a large percent of growthwithin economies and behaves pro-cyclically in a business cycles. The TFP is often seenas the real driver of growth within an economy. Basu and Fernand (2001) provide fourchannels from the TFP to the business cycle which lead to pro-cyclical productivity:
technology fluctuation that affect both productivity and output; increasing returns andimperfect competition that cause productivity to increase with an increase in inputs;
variation of utilization rate of inputs over the business cycle; and reallocation of
resources between sectors or firms with different productivities. In (at least some) of thechannels the TFP changes are exogenous shocks for the business cycle.
The next logical step is to investigate what causes the TFP changes and why the
TFP has decreased in some countries. Since Japan has experienced a long period of slow
growth, it serves as a good example of attempts to explain the productivity slowdown.
Hayashi and Prescott (2002) found that the low TFP accounts well for the Japanese lost
decade of growth, and conjectured that the low TFP growth was the result of a policy thatsubsidized inefficient firms and declining industries. This policy resulted in lower TFP
because the inefficient producers produce a greater share of the output. Though manyother papers have mentioned the TFP decrease in the business slump, they have notinvestigated what decreased it. Exceptions are Nishimura et.al. (2005), who found that
efficient firms in terms of TFP exited while inefficient ones survived, implying that thenatural selection mechanism of economic Darwinism is not working properly. Further,
this phenomenon is observed mainly for new entrants and contributes substantially to afall in macro TFP after 1996. The work of Fukao, et.al (2005) is in the same strand. They
focused on the aggregation aspect of the production function. Caballero et al. (2008)
argue that bank credits to insolvent borrowers depressed job creation and destruction andled to lower productivity. Jorgenson and Motohashi (2005), Jorgenson and Nomura(2005), and Hayashi and Nomura (2005) mostly expand a single-sector growth model ofHayashi and Prescott to a multi-sector model, focusing on the relationships between
information technology, labor input and the TFP through the price mechanism. They did
not include the idiosyncratic characters like aging and skill levels directly into thephysical inputs of labor and capital, and did not estimate the effect of each factor on the
TFP. This alternative aspect is one of determinants for the TFP but has not been analyzed
yet. The quality of labor as a determinant of productivity has been suggested in the microcontext by Griliches (1967) and Hellerstein and Neumark (Hellerstein et al., 1999,
Hellerstein and Neumark, 1999), among others.
The purpose of this paper is to investigate what decreases the TFP, why the TFP
has decreased in some countries and how the TFP can decrease through aging. We focus
on the quality of labor and capital inputs, and incorporate the aging of the physical labor
input and the information technology component of the physical capital input in theframework used by Hellerstein et al. (1999) and Ilmakunnas and Maliranta (2005). We
then can identify the effect of each labor characteristic on the TFP, while we have no
growth theory basis used by the previous researches. We also provide a comprehensive
investigation based on two hypotheses of the relationship between workers of different2ages and skills, substitutability and complementarity, by using cross country data. This isdifferent from the literature on worker characteristics and productivity, where perfect
substitutability of labor categories is assumed and the analysis is conducted with single
country micro data. We finally suggest a new measure, the Aging Index, to measure howmuch of the decrease of the TFP can be attributed to the aging of the labor input. We use
cross country data for the manufacturing industries of some OECD countries.
We find that (i) Based on the perfect substitutability hypothesis among age groups,
the low TFP is related to the aging of the labor input and to insufficient information
technology content in the capital input. The aging of the labor input improves
productivity only in the low skilled labor category, but contributes negatively to
productivity in the medium to high skilled labor category. However, the total labor effecthas still been positive in all of the countries examined. Due to the imbalances of theeffects of aging and ICT (Information and Communication Technology), the TFP has
since 1990 increased in Austria, Finland, Netherlands, and USA, while it has stagnated or
decreased in Australia, Denmark, and Japan. (ii) Based on the complementarity
hypothesis among the age groups, the increased share of the old workers has improved
the productivity of the young and mid-aged workers in the low skilled labor category,
while it has had no effect in the medium to high skilled group. The aging process has had
positive effects in the low-skilled labor group in Japan and Finland, consistent with theresults based on the perfect substitutability hypothesis. However, the test results for bothhypotheses support the complementarity hypothesis in the low-skilled labor group andthe perfect substitutability one in the medium to high skilled labor group, respectively.
(iii) Both countries with a low value of the Aging Index (Finland and USA) and with ahigh value of the index (Austria, Netherland and UK) have successfully increased theshare of the ICT to overcome the aging problem. Exceptions are Japan, Australia andDenmark.
With these findings we provide a new explanation of a low TFP, which differsfrom the previous viewpoints suggested in the literature. Moreover, we provide anempirical study of why the TFP has stagnated or increased in some countries, based on
the idiosyncratic feature in aging labor and ICT imbalance.
This paper is organized as follows. In Section 2, we sketch the model. In Section
3, we investigate what cause the low TFP, by using OECD panel data. In Section 4, we
empirically investigate why TFP has decreased in some countries. In Section 5 weprovide the analysis based on the complementarity hypothesis. In Section 6, we propose
the Aging Index reflecting the aging of the labor input and using the index we investigate
which countries are in a serious aging problem. Finally, in Section 7, we provide
concluding remarks.

2. Production Function: quality adjusted labor and capital input
We can formulate a Cobb–Douglas production function with capital and labor inputs:

Y  AK  L  A0 exp( t t ) K  L(1)

3

Where the trend  t is allowed to vary over time and A0 is constant over time. The TFP is
defined as output unexplained by inputs, i.e., described as follows:ln(TFP )  ln(Y )   ln( K )   ln( L )  ln( A0 )   t t(2)

The TFP change can be explained by the changing time trend  t . However, thisformulation cannot tell what kinds of economic factors affect the TFP change. In what
follows, we investigate whether this kind of factors can be found in the characteristics ofthe labor and capital inputs.
The productivity varies by worker characteristics like age and skills. These can be
included in the production function in several alternative ways. One alternative, whichdates back at least to Griliches (1967) and has more recently been popularized byHellerstein and Neumark (Hellerstein et al., 1999, Hellerstein and Neumark, 1999) isbased on the shares of different types of employees.1 It starts from the assumption thatdifferent types of employees are perfect substitutes (we call this assumption“substitutability hypothesis”), but may have different marginal productivities. Using age
groups among the low-skilled as an example, divide workers to two categories (e.g.
young (y) and old (o)) with employment shares sly (=Lly/Ll) and slo (=Llo/Ll) where Ll is a
total low-skilled labor input (hours or number of employees). The group y’s and o’s
productivities equal to ly and lo , respectively. Then, the total low-skilled labor input,

considering the productivity difference, is Ll  ly sly Ll  lo slo Ll . If we take group y as
the base group, the relative productivity of group o is measured by a parameterˆ   /  and
lo

lo

ly


(3)
L l  L l  ly ( s ly  ˆlo s lo )  L l  ly (1  (ˆlo  1) s lo ) .
Here L is the quantity and  (1  (ˆ  1) s ) is the quality of low-skilled labor. The

ly

lo

lo

relative increase in productivity when we go from the reference group y to group o isdenoted ˆlo  1 . The term ln( Ll ) could be used as a variable in a logarithmic production
function, but the model would have to be estimated using non-linear methods. The
approach of Ilmakunnas and Maliranta (2005), among others, is to simplify estimation byusing first-order Taylor expansion around (ˆlo  1) slo  0 ,ln 1  (ˆlo  1)slo )  (ˆlo  1)slo(4)

This gives the share of workers in a group directly as a variable in a log-form
production function. The approximation is reasonable unless the relative productivity (of1Related work in the macro growth literature includes Lindh and Malmberg (1999) where GDP
growth is explained by the shares of population age groups. The relationship between the qualityof labor and the productivity can be analyzed also in other ways, for example using averages ofworker characteristics (average age, average education years, etc.), as in Ilmakunnas, et.al. (2004).
Some other forms in which human capital or more specifically education can be included in a
production function has been discussed also in the growth literature (Temple, 2001).

4

the old in this example) is very high and at the same time the labor share is high. Whenthe approximation (4) is used in a Cobb–Douglas production function Y  AK  L* , theestimated model is described as follows, in the case of two work characteristics j (lowskilled (l) and high (h) skilled workers) and three possible age groups n (=young (y),mid-aged (m), old(o))**
ln(Y )     ln( K )   l ln( Ll )   h ln( L h )   lm* s lm   lo* s lo   hm
s hm   ho
s ho

(5)

where Ll and Lh are low-skill and high-skill labor inputs, respectively,  ln( A)   l ln(ly )   h ln( hy ) , A  A0 exp( t t ) , and  *jn   j (ˆ jn  1) .
The productivity also varies by capital characteristics like vintage, the high-tech(e.g. information technology) content of the capital input, etc.. These characteristics canbe included in the production function in several alternative ways, while it is very
difficult to obtain the necessary data. The vintage capital was a main alternative for that,used by Mizon (1974), Malcomson and Prior (1979) and Mcintosh (1986), among others.
However, the accounting value for capital based on the constant capital depreciation
already reflects the vintage. There are also other problems. As pointed out by Caballero(1999), Cummins and Violante (2002), and Mukoyama (2008), the acceleration of
investment-specific technological progress can distort the measurement of the aggregate
capital stock. Accordingly, Mukoyama (2008) writes:“Many economists reported an acceleration of investment-specific technological progress in thelate 1970s. In a recent paper, Cummins and Violante (2002) argued that during this period,
investment-specific technological progress accelerated from an annual rate of 3% to 5%. Our
analysis shows that this acceleration can cause a large change in the rate of replacement. As aresult, with the conventional measurement of capital (the perpetual inventory method withconstant depreciation), the aggregate capital stock is overestimated. This bias has an importantconsequence in measuring total factor productivity (TFP). In the usual growth accounting
exercise, the growth rate of TFP is measured as output growth minus the contribution of thegrowth in capital and labor. When the existing amount of capital stock is overestimated, thecontribution of capital accumulation is overstated. Therefore, the growth rate of TFP isunderestimated.” (Mukyoma, 2008, p.514).

Following this suggestion, we use for the capital input the same kind of
formulation as was used for the labor input in (3), with ICT capital and other capital as
different categories. Then, we can revise a Cobb–Douglas production function as
Y  AK * L* , and the estimated model is in the case of 2 worker skill characteristics in 3
age groups and 1 capital characteristic in 2 groups (Information and Communication
Technology (ICT), and Non-IC Technology (NICT))*q ICTln(Y )     ln( K )   ICT**  l ln( Ll )   h ln( Lh )   lm* slm   lo* slo   hm
s hm   ho
s ho   0
where   ln( A0 exp( t t ))   ln( NICT )   l ln( ly )   h ln( hy ) and(6)

 NICTisthe*productivity for NICT,  ICT
  ( ICT  1) and q ICT  K ICT / K . We have also added an5error term to account for stochastic shocks and left-out variables. If the production
function (6) is true, the TFP defined in (2) can be expressed as:ln(TFP )  ln(Y )   ln( K )   l ln( Ll )   h ln( Lh )
 ln( A0 )   ln( NICT )   l ln( ly )   h ln( hy )   t t

(7)

*
*
*
  ICTq ICT   lm* slm   lo* slo   hm
s hm   ho
s ho   0

TFP can now be explained by the quality of labor (age/skill group shares) and quality ofcapital (ICT capital share), and the time effect  t t . The time effect has no economic
meaning, while it is a proxy for the other economic variables except for the quality of thelabor and the capital. In practice we will model the time effect with year dummy
variables.
To calculate the TFP, we proceed as follows. First, by using (6), we estimate theparameters of the production function and by checking the significance of the estimatedparameters we investigate what affects the TFP and why the TFP has decreased in somecountries. In addition, by using (7), we investigate how much the manufacturing TFPchange is correlated with manufacturing value added growth country by country. Second,
we provide an alternative production function based on the complementarity hypothesisof labor age categories, thereby relaxing the perfect substitutability assumption used in(6).

3. Influential economic factors on TFP
Cross-country data
In the cross-country analysis we use data that are from the EU-KLEMS data base.2 Since
we are interested in the characteristics of the labor and capital input, we include countries
for which the division of the labor input to different age/skill-combinations andinformation on ICT capital are available. Further, we require that the data are available
for a long time period. With these restrictions we end up with data on the aggregate
manufacturing of the following eight OECD countries: Australia, Austria, Denmark,Finland, Japan, Netherland, UK and USA.3 Some of the data are available for the period
2

EU KLEMS Growth and Productivity Accounts: March 2008 Release, available atwww.euklems.net.
3
In addition to these countries, both the labor input file (which includes the information onage/skill shares) and the capital input file (which has information on ICT capital) were at the timeof writing this paper available for Czech Republic, Germany, Italy, Korea, and Slovenia. We
dropped Czech Republic and Slovenia because of the short time periods (from 1995 only),
Germany because of the break caused by German unification, and Italy because the skill sharesdeviate so much from the other countries and show very little variation over time that theclassifications are most likely different. In addition, since Korea has experienced a quite drastic
growth, the time series cannot be regarded as representative of the whole period. When we
include Czech Republic, Germany, Italy, Korea, and Slovenia in the analysis, the main
conclusions are similar but some results are not significant.

61970-2005, but because of missing information on labor characteristics or ICT the period
is shorter for most of the countries.4
We measure output with the volume index of value added, labor input with total hours
worked, and capital input with real fixed capital stock. All of these variables aremeasured in real terms, and since country differences in levels can be accounted for bycountry dummy variables, we need not convert the variables to common currency. The
labor characteristics are measured by the shares in total hours worked of the following
age/skill-combinations: there are three skill types, low-skilled (35% of labor hours in thepooled data), medium-skilled (56%) and high-skilled (9%), and within each skill category
the employees are divided to the young (15-29 year olds), mid-aged (30-49 year olds),
and old (50 years and over). Since the share of high-skilled category is minor, we unify
medium-skilled and high-skilled and create a new category, called ‘medhigh-skilled’(65%). There are hence two skill characteristics divided to three age groups.5 That is,their shares are slm for the mid-aged and slo for the old-aged among the low-skilled ands hm for the mid-aged and s ho for the old among the medhigh-skilled in eq. (6). The
reference groups are the young low-skilled and young medhigh-skilled. As to capital
input, we use information on the share of ICT capital in the total capital stock as thecapital input characteristic. ICT includes computing equipment, communications
equipment, and software. There is therefore one capital characteristic divided to twogroups (i.e., ICT and NICT) in eq. (6) where the share of ICT is q ICT .

Production function estimation and analysis of what affects the TFPTable 1 shows the estimated production function for the country panel on manufacturing
by using (6). To allow for technological differences, we let the coefficient of the ICT
share vary by country, using Japan as the reference country.6
First, we estimate the production function by including country and year dummy
variables as follows:ln(Y ) CY     ln( K ) CY    l ln( Ll ) CY   h ln( Lh ) CY**  *ICT q ICT   C  C q ICT CDC  lm* slm  lo* slo   hm
s hm   ho
s ho

(8)

  C  C CDC   Y Y YDY   CY

4

The data periods by country are the following: Australia 1982-2005, Austria 1980-2005,
Denmark 1980-2005, Finland 1970-2005, Japan 1973-2005, Netherlands 1979-2005, UK 19702005, and USA 1970-2005.
5
In the EU-KLEMS project these data have been used for adjusting the labor input in growthaccounting, assuming that labor compensation corresponds to productivity. In contrast to this, we
use the information on the labor characteristics to estimate their relative productivities.
6
We can allow for heterogeneity across countries by using different kinds of labor input
categories, while we cannot do the same as easily with capital data. Therefore we interact the ICT
share with country dummies to account better for capital-related heterogeneity.

7

where   ln( A0 )   ln( NICT )   l ln(ly )   h ln( hy ) , CD and YD are country and year
dummy variables and suffixes Y and C are from year 1971 to 2005 and from country 2 to8, respectively. We also estimate the production function excluding the year dummy
variables YD from (8). As shown in column (a) and (b) of Table 1, the estimatedcoefficients show that both production functions with and without year dummy variables
are homogeneous with degree one,    l   h  1  0 . 7 Re-estimation with thisconstraint may be necessary, but in the present paper we do not impose it. Also, thosecountries with clearly insignificant coefficients for the ICT share may be combined to thereference group. However, we leave these variables in the equation for the TFP
estimation.
We use the specification without year dummies in column (b) as our basic model.
The coefficients of physical inputs are all significantly positive in column (b). In thelabor groups we use young as the reference group. In the low-skilled category, in (b), themid-aged are equally productive to the young because of the insignificant coefficient but
the old are more productive by ˆlo = (1+0.598/0.092) = 7.5 times8. In the medhigh-skilled
category the mid-aged are more productive than the young by (1+0.472/0.498) = 1.95
times but the old and young are equally productive. These results can be interpreted toshow that in low-skilled jobs the greater physical strength of the young workers is notenough to compensate their lack of experience, whereas in medhigh-skilled jobs the more
recent education of the young and mid-aged compensates for the lack of experience. As aresult, among the medhigh-skilled, the mid-aged are the most productive.
The coefficients of the age categories are illustrated in Figure 1. These figures
show an U-shape for the low-skilled and an inverted U,  -shape, for the medhigh-skilledlabor. The shape of the age-productivity profile in the medhigh skill category is
consistent with some “stylized facts” of the development of productivity by age. The bars
next to the productivity coefficients indicate the average (over countries and over time)share of the category in question. Each share multiplied by the productivity coefficient isclose to zero, which supports the linear approximation shown in (4).
The coefficients of the ICT share show big variations across countries. The
estimation results show that ICT has been more productive in the reference group country
Japan than NICT by (1+4.953/0.508) = 10.75 times (significant at 10% level), whereas
the ICT productivity is lowest in Denmark by (1+(4.953-5.924)/0.508) = -0.91 times andin Australia by (1+(4.953-4.913)/0.508) = 1.08 times. 9 For the other countries (Austria,
Finland, Netherland, UK, USA), the coefficients of the country-specific ICT shares are
insignificant at the 10% level. We can conclude that their coefficients are the same as thatof Japan, with ICT capital more productive than NICT capital. Some of the ICT
coefficients are too large to be quite plausible in the simple model above. It could be thatthe assumption of perfect substitutability of the capital categories is not tenable, or ourapproximation for the logarithmic form is not particularly good. Therefore, we should
7

We can allow for heterogeneity across countries by using different kinds of labor input
categories, while we cannot do the same as easily with capital data. Therefore we interact the ICT
share with country dummies to account better for capital-related heterogeneity.

lo   l (ˆlo  1)  0.598 , since 1  0.092 .
9 lo   C  4.953  5.924  0.971 and therefore ˆ lo  1  0.971 / 0.598  0.91 .
8

8

pay more attention to the relative magnitudes of the coefficients, rather than on theirabsolute values.
We do a robustness check of the results by including the year dummy variables(which play the role of proxy variables for the other economic variables). The results areshown in column (a) of Table 1. The sign of the old medhigh-skilled coefficient ischanged from negative to positive, while it is not significant. The coefficient of the midaged low-skilled stays negative, but is now significant. Also, similar changes happen for
capital characteristics, while the order of ICT productivity among countries is not
significantly changed. Second, while we include 35 year dummy variables, the adjusted
R-squared increases only by 0.01. Finally, the shapes of the age-productivity profiles forthe low-skilled and the medhigh-skilled labor categories are roughly similar to our basic
results. Thus, the results seem robust to including the other economic variables (proxiedby the year dummies).
Insert Table 1 and Figure 1
The TFP is estimated as:ln(TFP ) CY  ln(Y ) CY  ( ln( K ) CY    l ln( Ll ) CY   h ln( Lh ) CY )**    *ICT q ICT   C  C q ICT CDC  lm* slm  lo* slo   hm
s hm   ho
s ho

(9)

  C  C CDC   CY
where the parameters are replaced by the estimates from column (b) of Table 1. The firstrow in (9) shows the estimated TFP. The second row and Table 1 show that the positive
influential economic factors are the share of the old low-skilled worker hours and theshare of mid-aged medhigh-skilled worker hours, whose coefficients are significantly
positive, i.e., they are more productive than young workers in the same skill categories.
Also, the share of ICT in all countries is a positive (or at least non-negative) factor on the
TFP increases except for Denmark. The estimated TFP is shown in Figure 2 (change) and
Figure 3 (level). In Figure 3 the values of ln(TFP) and ln(Y), are rescaled to be zero in1990.
Insert Figure 2 and Figure 3

Business cycles and TFPThe same way as some papers including Lebow (1993), Sbordone (1996) and Basu
(2000), we investigate the cyclicality the TFP by visual inspection of the estimated TFPchange and by calculating the correlation of ln(TFP) and value added ln(Y) changes. We
define TFP to be pro-cyclical if the correlation is above 0.5. The graphs in Figure 2 for all
countries show pro-cyclicality and the correlation with ln(Y) change is at least 0.5 for all
the countries with maximum 0.91 for Japan and minimum 0.50 for Australia, as shown in
Table 2. On the other hand, we report in Table 2 also the average of the ratio (absolutevalue of TFP growth)/(absolute value of input growth) for each country. The input
growth is calculated as  ln( K ) CY   l ln( Ll )CY   h ln( Lh )CY . The figures in Table 2 show

9

that a large portion of the manufacturing value added growth can be explained by the
TFP growth, i.e., the TFP is a main driver of growth.
Insert Table 2

4. Why has some countries’ TFP decreased?
The main results in Table 1 in the context of the aging trend and ICT imbalance
are as follows. The aging trend in a labor skill category means a decrease in the shares ofyoung and mid-aged workers (and their hours of work). Among the low-skilled labor thisnegative aging trend increases the share of the more productive old workers, implying a
positive productivity effect. On the other hand, the aging trend in the midhigh-skilledlabor group decreases the share of the more productivity mid-aged workers with anegative productivity effect. The aging trends can be counteracted by investments in ICT.
The ICT capital is more productive than the NICT except for Denmark, while theproductivity is different depending on the country.
The TFP for each country is explained by the estimated coefficients for equation(9) (Table 1, column (b)) and the share variables of each country. Based on the estimation
result, we check the age shares country by country (Figures 4a to 4c) and consider why
the TFP of Japan, and Australia, Denmark and UK has recently slowed down or that ofAustria, and Finland, Netherlands and USA has increased, as shown in Figure 3. As seenin Figure 4a and 4c, the USA has no aging trend in either labor skill group in the sensethat there is no increase in the share of the old workers’ hours. The recent aging since1990 among the medhigh-skilled labor (seen in Figure4c; Japan, Australia, Denmark,Finland, Netherlands, UK) has caused a reduction of the most productive mid-aged
workers in some countries (Japan, Australia, Finland, as seen in Figure4b), while its
effect has not been strong enough to decrease the share of mid-aged workers in Denmark,
Netherland and UK. On the other hand, the aging of the low-skilled labor has increased
the most productive old workers in some countries (Japan, Finland, Netherlands, and UK
as can be seen in Figure 4a).
The
total
labor
effect,obtainedbysummingalleffects****
lm slm  lo slo  hm shm  ho sho in (9), is still positive (see Table 3) and increasing overtime for all countries (see Figure 4e). In addition to these effects of aging, ICT has had aneffect,  *ICT qICT   C C qICT CDC on TFP in (9). In most cases the total labor effectdominates the ICT effect (column 4 of Table 3). The ICT effect is increasing over time insome countries, but relatively flat in others (Figure 4e). 10 The slow growth of ICT in
Japan (as shown in Figure 4d) has contributed to the stagnating TFP (the share of the ICT
effect is relatively low), whereas for example in Finland the fast ICT growth has
contributed to the larger share of the ICT effect.
Insert Figures 4a,b,c,d,e and Table 3
10Note that in Figure 4e we have scaled the graphs so that they are zero in 1990. Therefore thelevels of the lines should not be compared.

10Thus, in a wake of the aging trend, some countries lose the productive workers(i.e., the mid-aged workers in the medhigh-skilled category), while immigrant countries
like USA are able to appropriately adjust the shares of the young and mid-aged workers
in each skilled category over time. Also, in a wake of information technology trend withhigher productivity, the countries like Finland using the technology efficiently haveobtained a high TFP.

5. Complementarity among labor groups
We already found the contributions of the composition of labor and ICT effects on TFP
in Table 3. A large portion of the TFP can be explained by the labor effect. Next we
examine in detail the complementarity between different age groups. To simplify the
analysis, we reduce the number of groups by using a new age group “y-worker” whichmeans the young and the mid-aged workers combined. We hence have two age groups, yworkers and old workers, divided to low-skilled and medhigh-skilled ones. The increasein the share of the old within the skill groups then shows the aging trend. Related toequation (3), we assume that the y-workers’ productivity is complemented by the oldworkers. Previously we have assumed perfect substitutability of the age groups. In thatcase the relative productivity of the young is independent of the share of the old.
Departing from that assumption we now assume that the y-workers’ relative productivity
ˆ jy ( s jo ) depends on the share sjo of the old workers in each skill category j. This
relationship is represented by a decreasing or an increasing function around s jo  1 , asshown in Figure 5. An increasing function shows complementarity between the agegroups, whereas a decreasing function would imply (imperfect) substitutability of the agegroups. This relationship can be interpreted as a particular character of team work
(discussed e.g. by Benders and Hootegem, 2000, in the context of Japanese working
place). On the other hand, many papers are dealing with the capital - skilled laborcomplementarity (e.g. Yasar and Morrison Paul, 2008), while there are few papers
studying the complementarity of the old workers and young workers. We add a further
assumption about the shape of the complementarity function: ˆjy ( s jo )  1 at s jo  1 eventhough the function may be increasing or decreasing. The y-worker’s productivity
increases or decreases depending on the share of the old workers and finally the
productivities are equal.
Insert Figures 5
Consider the case of low-skilled workers (j=l). We express the function ˆly ( slo ) as a firstorder Taylor expansion around slo  1 :11
11

We can relax the assumption as follows: ˆly (1)  1 when Aly  0 and ˆly (1)  1 when

Aly  0 . The former means that the old improve the young’s productivity, and the latter is the11ˆly ( s lo )  ˆly (1)  Aly ( s lo  1) where ˆly (1)  1(10)Equation (4), productivity, for young low-skill workers can be expressed, by using (10):X(slo )  sly (ˆly (slo ) - 1)  sly (ˆly (1)  Aly (slo  1)  1)   Aly (1  slo )2(11)This formulation satisfies also the approximation in (4). This introduces an interaction
term of the shares of the y-workers and old workers, but since we have only two age
groups, this implies a quadratic form in the share of old workers. We estimate the TFP byinserting this approximation (11) into equation (9).
The coefficients are related to the shape of the productivity of low-skilled labor in (11),due to the first order and the second order conditions:dX(slo )/dslo  2 Aly (1 - slo ) , d 2 X(slo )/ds 2lo  2 Aly(12)This productivity X is a convex function decreasing from a positive value to zero with theincrease of slo when Aly <0, which means that the productivity of y-workers is decreasingin the share of old workers as seen in Figure 5. On the other hand, it is a concave function
increasing from a negative value to zero when Aly > 0, which means the productivity of yworkers is increasing. In particular, Aly = 0 means X = 0, which means that the
productivity of y-workers is equal to that of the old workers. Note that we are not trying
to find a point where the share of old workers maximizes total productivity. For example,
if the function ˆly ( slo ) is quadratic, we would end up with X being a third-orderpolynomial. This could have a (local or global) maximum at some value of slo between
zero and one. Instead, we analyze the shape of the function (and X), and thereby thecomplementarity or substitutability at large values of the share of old workers.
The results are shown in Table 312. The productivity X is significantly concave inthe low-skilled labor category (the coefficient of (1-slo)2 implies Aly =0.354) and zero(insignificant) in the medhigh-skilled labor group (the coefficient of (1-sho)2 implies
Ahy =0.178). Considering these characteristics and the first order condition in (12), we
can find the location of each country by using the average shares of slo and sho. We show
in Figure 6 the cases of Japan and USA, which have the highest and lowest share of old
opposite case. Note that we assume that ˆly (1)  1 is appropriately small in order not to affectthe Aly (slo  1) in (11). Then, we can know whether X is increasing or decreasing, depending on
the sign of Aly : X   Aly (1  s lo ) 2  (1  slo )(ˆly (1)  1) .
12

Note that in (8) the coefficients of labor characteristics should not be very negative, since   j (ˆ jn  1) and the relative productivity ˆ jn is not negative. In contrast, in thejncomplementarity formulation the parameters are slopes of a function and can be large in absolutevalue.

12

low-skilled labor, respectively, among the countries in our data. Moreover, considering
the increase of the share of old workers in both skill groups in Japan (see Figures 4a and4c), the aging trend implies moving towards the right hand side in Figure 6, which
increases the productivity of low-skilled labor and stagnates it in the medhigh-skilledlabor group. On the other hand, the USA has no aging trend and therefore no change inthe labor productivity over time. Similar facts hold in the other countries.13
These results are not inconsistent with the results based on the hypothesis ofperfect substitution. We can reconcile the findings as follows. As shown in Figure 5, theresult that Aly > 0 in the low-skilled labor group means that an increase in the oldworker’s share improves the productivity of y-workers. Further, the result Aly = 0 in themedhigh-skilled labor group means no improvement of their productivity, but they havethe same productivity as the old workers. These results can be interpreted to show that inlow skilled jobs a large number of the old workers can easily transmit their experience tothe young workers (i.e., the age groups are complements), whereas in medhigh-skilledjobs the more recent education of the young brings the same productivity as that of theold and the old cannot improve the young with their experience (i.e., the age groups are
perfect substitutes). Thus, this is the same interpretation as what we drew form our earlier
results.14
The column (a) in Table 4 shows the robustness check with including the year
dummies. Our main implications remain the same. The main difference to column (b) in
Table 4 is that some of the coefficients of the ICT shares change, but even then theirrelative orders of magnitude do not change much.
Insert Table 4 and Figures 6

6. The Aging Index
The ICT effect and the total labor effect on the TFP have positive trends over time asshown in Figure 4e. However, as the aging proceeds more, the labor effect may slow
down, as evidenced by Japan. The labor effect is but moderated by the ICT progress. In
fact, a country with high progress of the ICT needs not pay attentions on aging. How do
we recognize the seriousness for the aging labor problem on the TFP for each country?
Focusing on the moderating effect of ICT progress and using (9), the following change of
the ICT share is needed to make the TFP equal to random shocks ln(TFP )CY  ln(TFP )CY  ln(TFP )CY 1   Y :13

Again, we should not give too much emphasis on the absolute values of the ICT coefficients.
The ICT coefficient for Denmark in column (b) of Table 4 is 1+(5.070-6.759)/0.591 = 1(1.689)/0.591 = -1.86, which is significant. This negative coefficient (negative relative
productivity) is somewhat a problem. The ICT coefficients for Australia and UK are significantly
negative, while the second one plus ICT coefficient is positive and moreover, the first one plus
ICT coefficient is insignificant by t-test.
14
However, the results are not exactly comparable, since in the complementarity analysis wehave aggregated the young and the mid-aged workers (with more productivity than the young) to
the y-workers.

13

q ICT ,Y 

1



*
ICT

*
*
( lm* slm ,Y   lo* slo ,Y   hm
s hm ,Y   ho
s ho ,Y )(13)

where the subscript Y refers to years. Here, the numerator in (13) is change in the termthat we have already defined as ‘total labor effect on the TFP’ in Section 4. q ICT ,Y is thechange of the ICT share which is necessary to stop the TFP decrease (or increase) causedby the change in the total labor effect. Since the ICT productivity parameter  *ICT and thechanges of the labor input shares ( slm ,Y , slo ,Y , s hm ,Y , s ho ,Y ) vary across countries, theterm qICT ,Y in (13) reflects the idiosyncratic index for the necessary increase of ICT
share in each country. Considering the coefficients in Table 1, for example, the index for
Finland for 2005 is q ICT ,Y   (0.0165) /( 4.953  1.658) = 0.0025 percentage points,
where -0.0165 percentage points decrease is the total labor effect on the TFP and
4.953+1.658 is the productivity parameter of the ICT. This value of the index means that
0.0025 percentage points increase of qICT ,Y is needed to stop the TFP decrease causedby the aging effect of labor. Also, for Japan the index for 2005 isqICT,Y   (0.0347) / 4.953 = 0.0007 percentage points, which means that a larger
increase of the ICT share is needed in Finland. This is because the total labor effect isnegative in Finland. In this sense, we call this index is an Aging Index of the country. A
country with ICT share change at least equal to the index is meeting the aging problem.
By using the Aging Index, we investigate which countries are in a serious aging
problem and when. As shown in Figure 7, the aging index of countries with highproductivity of ICT, like Austria, Finland, Japan, Netherlands and USA, is generally
smaller than for the other countries. Also, the index of each country is larger in the recent
years due to aging-caused changes in the total labor effect. In order to overcome thisaging problem, most of the countries have been able to increase the actual share of the
ICT as shown in Figure 7 and as a result, most of the countries have been able to increase
the TFP as shown in Figure 3. Exceptions are Australia and Denmark, which have low
ICT productivity (negative productivity coefficients). In those countries an increase of
ICT share means a decrease of the TFP. Another exception is Japan with the stagnated
TFP, where the actual increase of ICT share has been higher than the required increase of
ICT share (Aging Index), but still relatively low.15

7. Concluding Remarks
The purpose of this paper was to investigate what decreases the TFP and why it has
decreased in some countries, focusing on the quality of labor and capital inputs. We did
this by using cross country data for the manufacturing industries of some OECD
countries.

15

Note that the scales of the panels in Figure 7 vary by country.

14

We found that (i) the low TFP is related to the aging of the labor input and to
insufficient information technology content in the capital input. The aging of the labor
input improves the productivity only in the low skilled labor category, but leads to a fallin productivity in the medium to high skilled labor group. The productivity impact of ICT
capital varies from country to country. Due to these positive and negative effects of aging
and ICT imbalance, the TFP has since 1990 increased in Austria, Finland, Netherland,and USA, while it has stagnated or decreased in Australia, Denmark, and Japan. In
particular, the decrease or stagnation of the TFP initiated by aging is not a problem in an
immigrant country like USA, which is able to adjust to the problem by immigration. (ii)
Based on the complementarity hypothesis, increased share of the old workers in the low
skilled labor group improves the young and mid-aged low-skilled workers’ productivity.
On the other hand, increased share of old medium to high-skilled workers has no effecton the young and mid-aged workers in this skill group. An interpretation of the results isthat the aging of the low-skilled labor improves the productivity of the younger workers
through the old workers’ experience, but in the higher skilled groups the better educationof the young dominates, so no complementarity is found between the age groups. These
results add to the recent results dealing with the complementarity of capital and skilledlabor. (iii) We have calculated the change in ICT which is necessary to compensate forthe aging of the labor input and called this the Aging Index. Both countries with a low
value of the aging index (Finland and USA) and with a high value of the index (Austria,
Netherland and UK) have successfully increased the share of the ICT to overcome theaging problem. Japan, Australia and Denmark are exceptions.16
With these findings we provide a new explanation of a low TFP, which differsfrom the previous viewpoints suggested by Hayashi and Prescott (2002), Jorgenson andMotohashi (2005) and Hayashi and Nomura (2005).

16

The change of the total labor effect for Australia fluctuates between positive and negativevalues, while the size of ICT coefficient is very small compared with the other countries, 0.040 (=4.953 - 4.913) as shown in Table 1. As a result, even small changes in the age effect require largechanges in ICT (see Figure 7). The ICT is therefore not effective for stopping the problem of
aging labor.

15

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17

Table 1. Estimated coefficients of production with country panel data:
Substitutability hypothesis
Dependent variable ln(value added)
Including year
Excluding year
dummies (a)dummies (b)0.092*
0.276*(3.11)(5.27)
0.498*
0.467*(6.58)(4.79)
0.508*
0.325*(5.53)(3.19)ln(Ll) : lln(Lh): hln(K) : Young low-skilled
Mid-aged low-skilled  lm


Old low-skilled lo

Young medhigh-skilled
Mid-aged medhigh-skilled  hm
Old medhigh-skilled ho

Non-ICTICTICT Australia
ICT_Austria
ICT Denmark
ICT_Finland
ICT Netherlands
ICT UK
ICT_USA

Number of significant country
dummies (of 7)

Ref.
-0.477*(-2.60)0.647*(3.21)
Ref.
0.650*(3.51)
0.636(1.61)

Ref.
-0.252(-1.22)0.598*(2.64)
Ref.
0.472*(2.26)-0.602(-1.48)Ref.
-1.623(-0.46)
0.296(0.09)
5.627#(1.83)-0.712(-0.23)5.076*(1.97)
3.267(1.14)
1.366(0.45)
4.702(1.47)

Ref,
4.953#(1.69)-4.913#(-1.77)0.357(0.13)-5.924*(-2.11)1.658(0.69)-1.254(-0.47)-4.187(-1.54)-0.910(-0.33)

6*

6*

Number of significant year
20*
dummies (of 35)
0.69
1.29
H0: +l+h–1 = 0.;t-value
0.96
0.95
Adjusted-R2
244
244
Observations
Notes: t-values in parentheses. * denotes 5% significance, # 10% significance. ‘Ref.' indicates the basegroup. The non-reported constant terms are significant in both columns.

18

Table 2: Correlations and ratios between value added, input and TFP growth rates
Country

AUS
AUT
DNK
FIN
JPN
NDL
UK
USA

Correlations(a) yeardummies
0.39
0.87
0.80
0.70
0.89
0.41
0.59
0.77

Ratios(b) no year
dummies
0.50
0.90
0.85
0.74
0.91
0.69
0.64
0.84

(a) yeardummies
1.60
3.60
5.80
9.60
5.04
5.12
44.70
7.45

(b) no year
dummies
2.77
16.01
6.19
10.78
3.01
2.68
1.63
10.38

Notes: Correlations denote the correlations between TFP growth and GDP growth, and ratios denote theaverage of the ratios (absolute value of TFP growth)/(absolute value of input growth) over time.

Table 3: Composition of labor effect and ICT effect in the TFP(a) year dummies(b) no year dummies
labor
ICT
labor
ICT
AUS
1.36
-0.36
0.98
0.02
AUT
0.81
0.19
0.64
0.36
DNK
1.32
-0.32
0.50
0.50
FIN
0.80
0.20
0.59
0.41
JPN
1.08
-0.08
0.74
0.26
NDL
0.81
0.19
0.49
0.51
UK
0.21
0.79
-0.04
1.04
USA
0.71
0.29
0.56
0.44
Notes: The composition of labor effect is defined as:**** lm* slm   lo* slo   hm
s hm   ho
s ho /( lm* slm   lo* slo   hm
s hm   ho
s ho   *ICT q ICT   C  C q ICT CDC )The ICT effect is 1- the composition of labor effect.

19

Table 4. Estimated coefficients of production with country panel data:
Complementarity hypothesis
Dependent variable ln(value added)
Including year
Excluding year
dummies (a)dummies (b)0.088*
0.052*(3.03)(4.45)
0.437*
0.478*(5.78)(4.95)
0.591*
0.444*(6.47)(4.36)ln(Ll)ln(Lh)ln(K)2Y-worker low-skilled (1-Slo) :-Aly
2

Y-worker medhigh-skilled (1-Sho) : -Ahy

Non-ICTICTICT Australia
ICT_Austria
ICT Denmark
ICT_Finland
ICT Netherlands
ICT UK
ICT_USA

Number of significant country dummies(of 7)-0.631*(-5.55)-0.210(-1.25)-0.354*(-2.87)-0.178(-0.94)Ref.
1.081(0.32)-2.879(0.98)
2.170(0.77)-4.033(-1.41)2.847(1.18)
0.270(0.10)-1.707(-0.61)2.147(0.71)

Ref
5.070*(2.41)-5.459*(-2.81)-0.004(-0.00)-6.759*(-3.46)
1.189(0.66)-1.477(-0.78)-4.568*(-2.37)-1.147(-0.56)6*

6*Number of significant year dummies
12*(of 35)1.54
1.47
H0: +l+h–1=0; t-value
0.97
0.95
Adjusted-R2
244
244
Observations
Notes: see note of Table 1. The non-reported constant term is significant in both columns.

20

Figure 1: Relative productivities of age groups by skill

medhigh-skill

Relative productivity
Skill group share

ll s
ha
re
sk
i

ol
d

m
id
-a
ge
d

f.)
(re
yo
un
g

sh
ar
e
ll
sk
i

ol
d

m
id
-a
ge
d

yo
un
g

(re

f.)

-1

-.5

0

.5

1

1.5

low-skill

Share within skill group21

Figure 2: Growth rates of manufacturing value added and TFP by country

AUT

DNK

FIN

JPN

NLD

-.1 0 .1 .2-.1 0 .1 .2

AUS

1970

1990

2000

2010

USA

-.1 0 .1 .2

UK

1980

1970

1980

1990

2000

20101970

1980

1990

2000

2010

year
dln(Y)

dln(TFP)

Figure 3: Levels of manufacturing value added and TFP by country (1990=0).
AUT

DNK

FIN

JPN

NLD

-1 -.5 0 .5

-1 -.5 0 .5

AUS

1970

USA

-1 -.5 0 .5

UK

1970

1980

1990

2000

20101970

1980

1990

2000

2010

year
ln(Y)

ln(TFP)

22

1980

1990

2000

2010

Figure 4a: Share of old low-skilled labor input by country
AUT

DNK

FIN

JPN

NLD

.8
.2 .4 .6

1970 1980 1990 2000 2010

UK

USA

.2 .4

.6 .8

Share of old low-skilled.2 .4 .6 .8

AUS1970 1980 1990 2000 20101970 1980 1990 2000 2010

year

AUT

DNK

FIN

JPN

NLD

.3 .4 .5 .6 .7.3 .4 .5 .6 .7

AUS

1970 1980 1990 2000 2010

UK

USA

.3 .4 .5 .6 .7

Share of mid-aged medhigh skilled

Figure 4b: Share of mid-aged medhigh-skilled labor input by country

1970 1980 1990 2000 20101970 1980 1990 2000 2010

year

23

Figure 4c: Share of old medhigh-skilled labor input by country
AUT

DNK

FIN

JPN

NLD

0
.3
.2
.1
0

1970 1980 1990 2000 2010

USA

.3

UK

0

.1

.2

Share of old medhigh skilled

.1

.2

.3

AUS

1970 1980 1990 2000 20101970 1980 1990 2000 2010year

Figure 4d: Share of ICT capital by country
AUT

DNK

FIN

JPN

NLD

0 .05 .1 .15 .2

1970 1980 1990 2000 2010

UK

USA

0 .05 .1 .15 .2

Share of ICT capital

0 .05 .1 .15 .2

AUS

1970 1980 1990 2000 20101970 1980 1990 2000 2010

year

24

Figure 4e: Total labor effect and ICT effect by country (1990=0).
AUT

DNK

FIN

JPN

NLD

-.2 0 .2 .4 .6-.2 0 .2 .4 .6

AUS

1970

1990

2000

2010

USA

-.2 0 .2 .4 .6

UK

1980

1970

1980

1990

2000

20101970

1980

1990

2000

2010

year
ICT effectLabor effectFigure 5: Complementary between y-workers (young and mid-aged) and oldworkers
Y-worker’s productivity ˆly ( S lo )ˆly ( slo )  ˆly (1)  Aly ( slo  1)

ˆly (1) 1

1S lo , share of
S lo  125

old low-skilledworkerFigure 6: Complementarity of labor in each skill category

Productivity X(Slo): Aly >0

1

Slo, share ofold workers

0
Japan

USA
Low-skilled labor

Productivity X(Sho)01

Sho, share ofold workers

Medhigh-skilled labor26

Figure 7: Aging Index
AUT

DNK.01 .02-.02 -.01 0-.6 -.4 -.20.2-.005 0 .005 .01 .015

AUS

JPN

NLD

-.005

0

-.02 -.01

0

.005

.01

.01

-.005 0 .005 .01 .015

FIN

1970 1980 1990 2000 2010

USA

-.04

-.02

0

-.005 0 .005 .01 .015

.02

UK

1970 1980 1990 2000 2010

1970 1980 1990 2000 2010

year
Aging Index

Actual change in ICT share27