342 M
.A. Carree et al. Economics Letters 66 2000 337 –345
is far higher than the other industries. These are ‘tobacco’ ISIC 314 and ‘petroleum refineries’ ISIC 353. These two industries are capital-intensive and provide only a fraction of total manufacturing
employment. The ‘tobacco’ industry is a somewhat special case as it is confronted with relatively high taxes resulting in higher value of sales. The correlations computed in Section 4 are based upon each of
the industries in Table 1 with the exception of ‘total manufacturing’ ISIC 3 and ‘other manufacturing’ ISIC 39. However, we will also discuss results when leaving out the two industries
with the lowest average employment, viz. ‘tobacco’ ISIC 314 and ‘petroleum and coal products’ ISIC 354. The first industry is affected by high sales taxes while the second industry is not observed
in two of the 18 countries.
4. Results for 28 OECD manufacturing industries
The convergence estimates for labor productivity are presented in Table 2. In the second column of the table the estimate of
b is presented followed in the third column by the corresponding t-value. For
i
‘total manufacturing’ ISIC 3 the estimated rate of b-convergence is about 0.2. It is significantly
different from zero i.e. no convergence only at the 10 significance level. Ten out of 28 industries have a rate of
b-convergence of labor productivity that is significantly in excess of zero at the 1 significance level. This number increases by six when considering a 10 significance level. The
fourth and fifth column of Table 2 show the value of the standard deviation of the logarithm of labor productivity in the years 1972 and 1992. A decrease of this value indicates that productivity
differences across countries have declined over this 20-year period. In the sixth column the S -statistic, introduced in Eq. 5, is presented. According to this statistic only seven industries show
1T
a significant F-convergence at the 10 significance level. The results for labor productivity show that
s-convergence is indeed a sufficient but not necessary condition for
b-convergence. Each industry showing a significant positive value of the S -statistic
1T
also has a significant positive value of b . However, there are also industries [‘industrial chemicals’
i
ISIC 351 and ‘rubber products’ ISIC 355] which show significant b-convergence but have an
ˆ increase in the value of
s . This may be interpreted as evidence for regression to the mean. The
it
ˆ ˆ
correlation between the estimated values of b and s 2 s is quite strong: 20.78. When leaving out
i iT
i 1
the ‘tobacco’ ISIC 314 and ‘petroleum and coal products’ ISIC 354 industries, this correlation is 20.76.
The results confirm the finding by Bernard and Jones 1996a,b and Gouyette and Perelman 1997 that labor productivity in the manufacturing sector is only slowly or even not at all converging.
3
However, they also show that the spread of the speed of convergence across industries is large. We
3
The standard likelihood ratio test of the equality of the b ’s across industries has a value of 49.3 larger than the critical
i 2
value of the x 27-distribution corresponding to the 1 significance level. This not only shows that the speed of
convergence is not identical across industries, but it also indicates the presence of a possible ‘aggregation bias’ see Theil, 1954, for the pioneering work on the problems of aggregation over micro units. The unweighted average of the estimates
of b across industries is 0.326. When weighted with employment this average decreases somewhat to 0.282. Both exceed the
i
estimated b-convergence for the entire manufacturing industry ISIC 3. Hence, the slow rate of convergence found for the
manufacturing sector appears to be partly due to an ‘aggregation bias’.
M .A. Carree et al. Economics Letters 66 2000 337 –345
343 Table 2
a
The rate of convergence of productivity in manufacturing industries ISIC
b t
s s
S
b 1
T 1T
a
3 0.195
1.79 0.232
0.212 0.71
c c
311 2 0.416
4.37 0.326
0.227 2.78
313 0.230
1.65 0.335
0.318 0.36
314 0.006
0.05 0.853
0.948 23.69
a
321 0.307
1.76 0.256
0.252 0.09
c a
322 0.519
3.50 0.403
0.307 1.75
c a
323 0.751
4.25 0.363
0.272 1.71
c b
324 0.448
3.55 0.491
0.367 2.01
c c
331 0.477
5.77 0.442
0.273 4.04
332 0.043
0.29 0.424
0.478 21.56
c
341 0.437
3.12 0.200
0.159 1.49
a
342 0.207
1.81 0.283
0.259 0.68
a
351 0.473
1.85 0.282
0.325 20.62
352 0.121
0.62 0.279
0.327 21.21
353 0.215
1.04 0.717
0.818 20.79
a
354 0.378
1.85 0.796
0.785 0.07
c
355 0.594
2.57 0.282
0.286 20.06
356 20.069
20.19 0.217
0.390 N.A.
361 0.176
1.08 0.314
0.331 20.37
c b
362 0.513
3.72 0.311
0.229 2.05
c
369 0.345
2.58 0.337
0.285 1.12
c c
371 0.753
5.11 0.480
0.307 3.16
372 0.225
1.09 0.488
0.551 20.72
a
381 0.327
2.00 0.321
0.301 0.39
382 0.061
0.46 0.331
0.357 20.87
383 0.168
1.13 0.225
0.230 20.16
c
384 0.495
3.12 0.301
0.244 1.28
b
385 0.396
2.18 0.307
0.290 0.32
39 0.106
0.63 0.582
0.642 20.82
a
For the industries corresponding to the ISIC codes, see Table 1. The superscripts a, b and c mean significant convergence at the 10, 5 and 1 significance levels. N.A. means ‘not available’.
claim that one of the reasons for this spread is the variety in the complexity of production technologies, or the existence of knowledge and capital barriers. A possible proxy for the complexity
of production technologies is the level of labor productivity. Industries with high levels of labor productivity use, on average, technologies of a higher complexity and capital intensity than industries
with a low level of labor productivity.
The relationship between the rates of b-convergence and s-convergence on the one side and the
logarithm of labor productivity in 1972, m , on the other side is computed by the correlation
1i
ˆ ˆ
ˆ ˆ
coefficients of b with m and of s 2 s with m . We also employ b weighted with the reciprocal
i 1i
iT i 1
1i i
of its standard error, i.e. the t-value t . The correlation between the estimated values of b for the 27
b i
i
industries and their m
is –0.27. The correlation between the t-values of b and m
is somewhat
1i i
1i
ˆ ˆ
stronger: –0.36. For the variable s 2 s
we find a correlation coefficient of 10.47. These three
iT i 1
correlation coefficients change somewhat to –0.18, –0.28 and 10.42, respectively, when the
344 M
.A. Carree et al. Economics Letters 66 2000 337 –345
4
‘tobacco’ ISIC 314 and ‘petroleum and coal products’ ISIC 354 industries are excluded. That is, we find evidence for industries with a relatively high labor productivity having a low rate of
5
especially s-convergence of productivity. This is in line with high knowledge or capital barriers
preventing quick catch-up.
5. Conclusion
