especially in industries which are active in R and D activities themselves Nadiri, 1993. However, most studies pertain to advanced OECD countries and it is
debatable whether similar strong effects are present in countries which operate far from the world technology frontier and perform little R and D.
10
Unfortunately, the data base for this paper does not allow us to examine these assumptions further
here. Apart from spillovers across sectors, the conventional shift-share method also
ignores externalities within a sector. Output growth and productivity growth in a sector is assumed to have no causal link. This is a potentially serious omission as
possible virtuous circles between output growth and productivity growth within a branch might exist. This effect is known as the Verdoorn effect Verdoorn, 1949.
If resources shift to branches with a higher Verdoorn elasticity, one part of the productivity improvements will be included in the dynamic shift effect, but
another part in the intra-branch effect. Hence the contribution of structural change as measured by the shift-share analysis is underestimated. This might provide an
explanation of the lack of empirical support for the structural-bonus hypothesis we found so far.
7. The Verdoorn effect and the modified shift-share analysis
In this section we try to incorporate the Verdoorn effect in our measurement of the contribution of structural change to productivity growth. Verdoorn’s Law is an
empirical generalisation that states that growth of output is positively related to the growth of productivity. Causation obviously runs from the latter to the former,
11
but also the other way around, which is important for the discussion here. Originally, Verdoorn 1949 was concerned with finding regularities between growth
rates of output and productivity of similar industries in different countries or time periods, a line of research further developed by Kaldor 1966. The unit of analysis
was the total economy or the manufacturing sector. Fabricant 1942 was the first to apply this idea in a cross-industry, rather than a cross-country, perspective,
followed by others such as Salter 1960. In this paper, we follow the lead of Fabricant and focus on inter-industry differences in the relationship between
growth of output and productivity using a pooled dataset for four Asian countries and three subperiods. Nevertheless, we refer to this relationship as the Verdoorn
effect rather than Fabricant’s effect because it is better known under the former name.
A number of arguments have been put forward to explain the positive impact of output growth on productivity growth. Originally it was attributed to static scale
effects caused by processes of labour division and specialisation both within firms
10
In India and Indonesia, private RD expenditures are still very low. In South Korea and Taiwan, they only started to grow in the 1980s see Timmer 2000, Table 8.1.
11
This effect is not only direct by generating higher output for a given set of inputs, but also indirect by attracting more demand through lower output prices.
and between industries, an idea already put forward by Adam Smith and developed further by Young 1928. Besides static effects, Kaldor 1966 also explicitly referred
to dynamic increasing returns caused by learning by doing in the sense of Arrow 1962 and incremental technical progress. Growth of output also means faster
addition of new, superior machinery, better possibilities to utilise technologies at the appropriate scale and shortened lags in application of new knowledge. These
processes may be particular strong in countries that are far from the global technology frontier and industrialise mainly on the basis of borrowing foreign technologies.
Rapid output growth also exerts more effort into improving machinery and materials used in the expanding sector, which is known as Schmookler’s demand-driven
technological progress.
To take into account the Verdoorn effect, we propose the following modification of the conventional shift-share analysis. Due to the Verdoorn effect, branches that
grow faster than the manufacturing average enjoy an extra source of productivity growth compared to slow-growing branches. This extra productivity growth should
be attributed to the effects of structural change. To take this into account we modify the shift-share analysis presented above as follows:
TR 0 E=A:−
i
r
i
{A :
i
− o
i
Y :
i
− Y
: } 8
with o
i
the Verdoorn elasticity of branch i, defined as the elasticity of TFP growth on output growth. Thus defined, the total reallocation effect TRE is positive if factor
inputs shift to branches with a higher level, or growth rate, of productivity as in the original decomposition, or with higher Verdoorn elasticities. If one compares the
redefined total reallocation effect with the original definition in Eq. 6, it can be seen that if output growth is equal in all branches, the adjusted TRE is similar to the
original TRE. This does not mean that the Verdoorn effect is not present in this situation, but stresses only that this effect has the same productivity-enhancing effect
in all branches. Hence, there is no reason to attribute part of this productivity growth to structural change. Similarly, it can be easily seen that if the Verdoorn elasticity
is the same for all branches, the adjusted TRE is equal to the original TRE because
i
r
i
Y : =Y:. Productivity gains due to the Verdoorn effect in sectors with above
average growth are balanced by productivity losses in the sectors with less than average growth. Hence, only if Verdoorn elasticities differ across branches, does the
modified shift-share analysis generate different results compared to the conventional analysis. Therefore we used our data set to estimate the Verdoorn relationship at the
manufacturing branch level, looking for significant differences.
The empirical work of Verdoorn was critised on several grounds, surveyed in-depth by McCombie and Thirwall 1994. First of all, Verdoorn’s original
specification focused on labour productivity growth and ignored the role of capital accumulation. However, it is clear that growth of capital input will explain part of
labour productivity growth, apart from the scale effects discussed above. Following Kaldor 1966, Fingelton and McCombie 1998 argue that this omission is not
serious if the capital – output ratio is more or less constant. However, while this assumption might hold for developed countries, capital – output ratios in rapidly
growing developing countries show a clearly increasing trend. Taking the role of capital into account would suggest the substitution of TFP growth for labour
productivity growth in the original Verdoorn law.
TF : P=a
+ b Q
: 9
In Eq. 9, total factor productivity growth is modelled as a linear function of output growth and b
indicates the Verdoorn elasticity. However, the specification suffers from spurious correlation because TFP growth is defined as output growth
minus an index of input growth Eq. 3 and hence, output appears on both sides. To remove this spurious correlation, McCombie and De Ridder 1984 suggested
the following regression model
TF : I=a
+ b Q
: +u 10
with TF : I=6L:+1−6K:, a
= − a , b
= 1 − b
and u a normal distributed error term.
12
For the purpose of the modified shift-share analysis we are interested in obtaining the Verdoorn elasticity for each manufacturing branch seperately, rather
than for total manufacturing. To this end branch dummies are introduced to allow for differences in the regression slope across the 13 branches.
TF : I=a
+ b Q
: +b
1
d
1
Q : +···+b
12
d
12
Q : +u
11 with d
i
is 1 for branch i and 0 otherwise. Data on value added growth and total factor input growth is averaged over 10-year periods and pooled for India,
Indonesia, South Korea and Taiwan. In total 126 observations are used to estimate Eq. 11 with ordinary least squares. The results are given in Table 3a. The overall
explanatory power is rather high R
2
= 0.74. As may be seen from Table 3, the
intercept i.e. exogenous technical progress comes up positive and significant. The estimate for the slope coefficient can be found in the row for the machinery and
transport equipment branch. This branch is taken as the base as it appears to have the highest coefficient of all branches. The Verdoorn coefficient is highly significant
and indicates a Verdoorn elasticity of 0.53 1 − b
. Importantly, the elasticity in other branches is lower, especially in the metal branch and the non-metallic mineral
products branch 0.33 and the electrical machinery branch 0.35.
13
Only the elasticity in these branches is significantly different from the base at 90 in a
two-tailed test, as indicated by the t-values in Table 3. The estimates for the Verdoorn elasticity are close to those found in earlier
studies. Using a similar approach, McCombie and De Ridder 1984 found esti- mates between 0.3 and 0.4 for the manufacturing sector in US states. Using
cointegration techniques, Harris and Lau 1998 found Verdoorn effects between 0.3 and 0.5 for manufacturing in UK regions. Both studies focused on total factor
productivity growth rather than labour productivity.
An objection to the specification above is that it assumes that all countries have access to the same technology Rowthorn, 1975. However, part of the total factor
12
All growth rates are in logarithms.
13
The Verdoorn elasticity for branch i is derived as 1 − b + b
i
.
386 M
.P .
Timmer ,
A .
Szirmai Structural
Change and
Economic Dynamics
11 2000
371 –
392
Table 3 Estimation of the Verdoorn elasticity for 13 manufacturing branches, four Asian countries, 1963–1993 three pooled sub-periods
a
Variable c South Korea and Taiwan,
a All countries b All countries,
including level dummy including level dummy
Coefficient t-value
Verdoorn t-value
Coefficient Verdoorn
Coefficient Verdoorn
t-value elasticity
elasticity elasticity
− 0.55
− 0.0231
Intercept −
1.58 0.0220
3.94 −
0.0045 0.22
0.499 0.1084
0.89 0.360
0.2372 0.0285
1.73 Q.d
1
0.168 Food,
beverages and
tobacco 0.0260
0.27 0.442
− 0.0193
Textile mill −
0.18 Q.d
2
0.424 0.0907
0.90 0.437
products 0.1062
1.38 0.362
0.1499 1.55
1.56 0.255
0.399 0.1284
Q.d
3
Wearing apparel
Q.d
4
0.503 0.0013
0.02 0.467
− 0.0408
− 0.52
0.446 0.0246
Leather 0.32
products 0.0562
0.63 0.412
0.0017 0.02
0.29 0.403
0.501 0.0273
Q.d
5
Wood products
0.62 0.459
0.0927 0.90
0.375 0.1101
Paper, 0.93
Q.d
6
0.295 0.0686
printing and
publishing 0.0237
0.26 0.444
− 0.0849
Q.d
7
− 0.79
0.1050 0.490
1.11 Chemical
0.423 products
0.11 Q.d
8
0.517 0.0097
0.11 0.458
0.0477 0.49
0.357 0.0106
Rubber and plastic
products 0.332
0.1406 1.51
0.327 −
0.0042 Q.d
9
− 0.04
Non-metallic 0.409
0.1960 1.98
mineral products
Q.d
10
2.21 0.332
0.1515 1.82
0.316 0.1395
1.51 0.265
Basic and 0.1954
fabricated metal
387 M
.P .
Timmer ,
A .
Szirmai Structural
Change and
Economic Dynamics
11 2000
371 –
392
Table 3 Continued c South Korea and Taiwan,
Variable a All countries
b All countries, including level dummy
including level dummy Coefficient
Coefficient t-value
Verdoorn t-value
Coefficient t-value
Verdoorn Verdoorn
elasticity elasticity
elasticity 7.21
0.528 0.5321
8.47 Q.d
10
0.468 0.4721
0.5951 7.84 0.405
Machinery and
transport equipment
0.1233 1.66
0.345 0.1014
1.27 0.304
Electrical Q.d
11
0.1756 2.24
0.352 machinery
0.466 0.0736
1.00 0.394
0.0467 0.0623
0.55 Other
0.358 Q.d
12
0.79 manufact-
uring TFPlev
0.0656 4.19
0.0900 3.97
Initial TFP level
127 Number of
75 127
observations 0.8026
R
2
0.7356 0.7713
a
Part a presents results of estimating Eq. 11 using all data for all four countries. Part b and c present results of estimating Eq. 12 using all data for all four countries part b and data for South Korea and Taiwan only part c. Dependent variable in all cases is total factor input growth. The Verdoorn
elasticity for branch i is derived as 1−b +b
i ,
where b is the slope coefficient for the machinery and transport equipment branch and b
i
is the slope dummy coefficient for branch i.
Significance at the 10 level in a two-sided test. Significance at the 5 level in a two-sided test.
Significance at the 1 level in a two-sided test.
productivity growth might be due to a catch-up phenomenon as described by Gerschenkron 1962. Technological backward countries might improve productivity
by taking over new technologies from technology leaders. More specificically, the further away from the technology frontier, the stronger this effect will be. Hence the
initial level of productivity in a particular branch should be taken into account. Timmer and Szirmai 1999 provide estimates of the manufacturing productivity gap
between the Asian countries and the US, the overall world productivity leader. They used industry-specific purchasing power parities to convert national levels into a
common denominator. Timmer 2000 extends their analysis and provides compari- sons by manufacturing branch. Using this data, we re-estimated Eq. 11 including
for each branch the level of total factor productivity relative to the US at the beginning of each sub-period TFPlev.
TF : I=a
+ b Q
: +b
1
d
1
Q : +···+b
12
d
12
Q : +gTFPlev+u
12 The results are presented in Table 3b. It shows that the coefficient of the initial
level of relative TFP is positive and highly significant. This indicates that the Gerschenkron effect has an important influence separate from the Verdoorn effect.
Manufacturing branches with low relative TFP levels have the highest rate of exogeneous technical change. The intercept ceases to be significant. Importantly,
estimates of the Verdoorn elasticities are affected as well. For example, the slope coefficient of food manufacturing increases hence the Verdoorn elasticity declines,
which can be explained by the fact that the productivity gap with the US is especially large in this branch in all Asian countries.
A similar regression is run for the East Asian countries separately to see whether these countries are different in terms of branch Verdoorn elasticities. The results are
given in Table 3c. They indicate that branch elasticities are different, especially for the food-manufacturing branch that has a much lower Verdoorn elasticity. However,
it remains true that the significance of the differences between branch elasticities is rather low. At 90, only the elasticity of the food branch is significantly different
from the elasticity in the machinery branch. Even the electrical machinery branch does not appear to be special in terms of its Verdoorn elasticity.
As outlined above, if branch elasticities do not differ from each other, the results of the modified shift-share analysis will be the same as those of the conventional
analysis. Nevertheless, we would like to have an indication of the probable bias in the empirical results when Verdoorn effects are ignored. Therefore, we use the branch
estimates of the Verdoorn elasticities in our decomposition formula Eq. 8. The results are presented in Table 4.
Two sets of results are presented. In column 3 we use the Verdoorn elasticities estimated from the complete data set, including the initial level of relative TFP
Table 3b. In column 4, specific East Asian elasticities are used, taken from Table 3c. The results from the conventional shift-share analysis are given in column 2
and can be compared with the new results that include Verdoorn effects. It follows that the conventional method produces biased results, but not always against the
structural-bonus hypothesis. The highest effects are found for the East-Asian countries, especially for South Korea during 1963 – 1973. However, only in the
Table 4 Total reallocation effect on aggregate TFP growth including Verdoorn effect average annual growth
rates
a
TFP growth due to reallocation including Verdoorn effects TFP growth
annual 1 Verdoorn elasticities
Verdoorn elasticities Verdoorn elasticities
same for all branches for East-Asia
from pooled dataset 3
4 2
b
India, registered sector −
0.1 1973–1982
0.5 0.0
0.1 0.1
2.9 1982–1987
0.0 3.5
0.1 1987–1993
2.0 0.0
0.0 1973–1993
Indonesia, medium and large scale sector 0.8
0.0 0.0
1975–1982 −
0.1 −
0.1 3.8
1982–1987 −
0.3 3.7
− 0.1
1987–1993 −
0.1 1975–1993
2.6 −
0.1 South Korea, firms with fi6e employees or more
1963–1973 −
0.7 8.3
− 0.3
− 0.9
1973–1982 −
0.4 −
0.1 −
0.5 −
0.4 −
0.1 0.0
0.0 1982–1987
5.7 0.2
6.3 0.2
0.3 1987–1990
− 0.4
− 0.2
− 0.4
1963–1990 4.5
Taiwan, all firms 3.3
0.2 0.1
0.4 1963–1973
0.2 0.0
0.0 −
0.1 1973–1982
− 0.3
− 0.2
0.0 4.0
1982–1987 0.6
0.7 0.7
0.8 1987–1993
2.0 0.3
0.1 0.2
1963–1993
a
Source, decomposition of total factor productivity growth into part due to total factor productivity growth in branches intra-branch effect and shifts of factor inputs between branches shift effect
according to Eq. 8, using estimates of Verdoorn elasticities from Table 3. Figures may not add up due to rounding.
b
This column is the same as column 3 in Table 2.
latter case was the difference with the original reallocation effect \ 0.2 points. It appears that the differences in the Verdoorn elasticities across branches are much
too small for factor reallocation to have a significant impact on aggregate TFP growth rates. Whether or not Verdoorn effects are taken into account, structural
change did not provide a bonus to aggregate productivity growth.
8. Summary and conclusions
