correlation between these two indices of educational achievement. Instead, the correlation coefficients are rather low for example, 0.54 between MEAN-EDUC
75
and BL-EDUC
75
. It appears more likely that differences in sources and methods used to construct the two series are responsible for the discrepancy in econometric
results. The results are quite similar when SCIENG, the number of scientists and
engineers engaged in RD per 10 000 population, is substituted for RDGNP, as shown in Panel B of Table 8. The coefficients of the variable SCIENG are generally
somewhat less statistically significant than RDGNP, as are the coefficients of INVRATE. However, the coefficients of the education variables are essentially
unchanged.
12
An anonymous referee suggested that the use of cross-sectional regressions, where variables are averaged over time, might cause relatively low variability of the
education variables and thus result in low significance levels. In Table 9I use pooled cross-section, time-series data for the 24 OECD countries and periods 1960 – 1973
and 1973 – 1990. Due to data limitations, the only education variables that could be used are the enrollment rates. The regression results are similar to those in the
cross-section analysis of Table 8. The coefficients of the enrollment rates remain insignificant. In fact, for the secondary and tertiary levels, the coefficients are
negative. The catch-up term is less significant than before because of the shorter time period, as are the R
2
and adjusted R
2
statistics, but the investment rate variable is stronger. There is little change in the RD variables.
4. Human capital models
I next turn to the human capital model, which posits a positive relation between the rate of productivity growth and the rate of change of schooling levels. For this,
I use the same specification as Eq. 1, except that I substitute the change in educational level for the educational level itself. The model becomes:
lnRGDPW
1
RGDPW t
1
− t
= b
+ b
1
RGDPW +
b
2
INVRATE + b
3
RDGNP + b
4
DEDUC+o 2
where DEDUC is the change in level of schooling. Results are shown in Table 10 for all OECD countries over the 1960 – 1990 period. I have used this shorter period
instead of 1950 – 1990, since data on schooling levels are not available for the 1950s for the full set of OECD countries.
The results are again disappointing. Of the 12 forms used, the coefficient of the change in schooling is positive in all cases but statistically significant in only two:
the change in university enrollment rates at the 10 level and the change in
12
When both RDGNP and SCIENG are omitted from the equation, both the coefficients and significance levels of the educational variables remain relatively unchanged. Various combinations of the
educational variables were also included in different regression specifications, with no material difference in results.
460
E .N
. Wolff
Structural Change
and Economic
Dynamics
11 2000
433 –
472
Table 9 Pooled cross-section, time-series regressions of the annual growth in real GDP per worker RGDPW on initial RGDPW, the investment rate, RD, and
educational enrollment levels, all OECD countries, 1960–1973 and 1973–1990
a
R
2
Adjusted R
2
Standard error Sample size
Education variable RD
Relative RDGPW
55
Education variable INVRATE
A RD 6ariable
:
RDGNP 0.45
0.41 0.0145
46 −
0.032
d
0.145
d
0.691
b
4.77 1.72
3.01 0.46
0.41 0.0146
46 PRIM-ENRL
− 0.032
d
0.149
d
0.723
b
0.021 3.06
1.78 4.69
0.80 0.52
0.157
d
0.0132 46
SCND-ENRL 0.591
− 0.013
0.56 −
0.021
d
2.80 3.58
1.62 1.54
− 0.024
d
0.0142 0.103
b
44 UNIV-ENRL
0.818
b
− 0.031
0.51 0.46
1.53 1.96
2.01 2.96
B RD 6ariable
:
SCIENG 0.43
0.38 0.0150
46 PRIM-ENRL
0.029 −
0.027
d
0.021 0.127
c
0.89 4.23
0.76 2.57
0.0131 46
SCND-ENRL 0.53
0.57 −
0.018
d
− 0.011
0.052
b
0.137
d
3.18 2.83
1.80 1.61
0.0143 44
UNIV-ENRL 0.46
− 0.019
d
0.51 0.058
b
0.064
b
− 0.028
2.87 1.07
1.83 1.45
a
Note: The sample consists of pooled cross-section, time-series data for periods 1960–1973 and 1973–1990. The absolute value of t-ratios are shown in parentheses below the coefficient estimate. See Table 8 for definitions of the variables.
b
significant at the 10 level, two-tail test.
c
significant at the 5 level, two-tail test.
d
significant at the 1 level, two-tail test.
461 E
.N .
Wolff Structural
Change and
Economic Dynamics
11 2000
433 –
472
Table 10 Regressions of the growth in GDP per worker RGDPW on initial RGDPW, the investment rate, RD intensity, and the change in educational
enrollment and attainment levels, all OECD countries, 1960–1990
a
Standard error Sample size
Relative RDGPW
65
Education variable INVRATE
RD Education variable
R
2
Adjusted R
2
A RD 6ariable
:
RDGNP 0.0048
23 0.369
c
DSCND-ENRL
91–65
0.325 0.055
c
− 0.018
d
0.85 0.82
8.49 2.21
2.17 1.65
0.0047 22
DUNIV-ENRL
91–65
0.83 −
0.022
d
0.058
c
0.86 0.489
b
0.467
c
2.36 2.57
1.87 8.10
0.74 0.050
0.0052 21
DSCND-ATTN
96–60
0.187 0.127
0.80 −
0.017
d
0.53 0.74
5.82 1.65
0.76 0.052
b
0.0050 21
DUNIV-ATTN
96–60
0.131 0.877
0.81 −
0.015
d
4.98 1.93
0.55 1.27
0.80 0.060
c
0.0050 23
DMEAN-EDUC
85–65
0.347
b
0.037 0.83
− 0.018
d
8.21 2.30
0.93 1.94
0.79 0.061
c
0.0051 23
DBL-EDUC
85–60
0.324
b
0.019 0.83
− 0.019
d
2.29 1.82
0.58 7.90
B RD 6ariable
:
SCIENG 0.0048
23 0.045
c
DSCND-ENRL
91–65
− 0.017
d
0.031
b
0.454
c
0.85 0.82
8.69 2.11
2.14 2.09
0.0052 22
DUNIV-ENRL
91–65
0.79 0.83
− 0.019
d
0.353 0.022
0.044 1.49
7.30 1.26
1.54 0.0052
21 DSCND-ATTN
96–60
0.74 −
0.014
d
0.045 0.79
0.210 0.016
1.56 0.59
0.96 3.84
− 0.011
d
0.0049 0.054
b
21 DUNIV-ATTN
96–60
0.026 0.967
0.82 0.77
1.65 0.96
3.16 2.04
0.77 0.052
b
0.0052 24
DMEAN-EDUC
85–65
0.014
b
0.026 0.81
− 0.017
d
8.09 1.85
1.10 0.64
0.83 0.79
0.0051 23
DBL-EDUC
85–60
0.018 −
0.017
d
0.015 0.049
b
1.22 1.78
0.45 7.60
a
Note: The dependent variable is lnRGDPW
90
RGDPW
60
30. The absolute value of t-ratios are shown in parantheses below the coefficient estimate. See Table 8 for definitions of the variables. In addition, a ‘D’ indicates the annual change in the variable over the period.
b
significant at the 10 level, two-tail test.
c
significant at the 5 level, two-tail test.
d
significant at the 1 level, two-tail test.
secondary school attainment rates at the 5 level with SCIENG as the RD variable. One possibility, at least for the educational attainment rate and the
Kyriacou mean schooling level data, is that the anomalies in the basic data are undermining the regression results the enrollment rate data seem sensible, as do the
Barro-Lee mean schooling levels. I eliminated all observations that seemed to be unreasonable and reran the regressions. The results were virtually unchanged.
Another possibility is that there is both a threshold effect, as well as a positive influence of the growth in human capital on labor productivity growth. The same
6 equations were re-estimated with initial level of schooling also included results not shown. In all twelve cases, the change in schooling remains insignificant
including the case of the university enrollment rate.
A second dataset covering the period from 1950 to 1989 for six OECD countries France, Germany, Japan, the Netherlands, the U.K. and the U.S. was also used,
derived mainly from data provided in Maddison 1987 Maddison 1991 Maddison 1993a,b. These sources provide figures on actual capital stocks, as opposed to
investment rates. As a result, following Mankiw et al. 1992, it is possible to use a Cobb-Douglas production function, augmented with human capital, as follows:
LPRGRTH
t h
= b
+ b
1
RELTFP
t h
+ b
2
KLGRTH
t h
+ b
3
EDUCGRTH
t h
+ o
t h
3 where LPRGRTH
t h
is country h’s annual rate of labor productivity growth, RELTFP
t h
is country h’s total factor productivity TFP relative to the U.S. level at the start of each period, KLGRTH
t h
is country h’s rate of capital-labor growth, and EDUCGRTH
t h
is the annual rate of growth in mean education in country h, and e¨ is a stochastic error term.
13
The regression analysis is conducted as a pooled cross-section covering six countries and four time period — 1950 – 1960, 1960 –
1973, 1973 – 79 and 1979 – 1989. As with the Penn World Table Mark 5.6 data, the results see Table 11 generally
show no statistically significant effect of the growth in mean education on the growth in labor productivity. Indeed, the coefficient of educational growth is
negative in the first two specifications. When a term for initial education is included the third specification, the coefficient on educational growth turns positive but
remains insignificant. However, one surprise is that the coefficient on initial education EDUC
is negati6e and significant at the one percent level. Even when the variable for the growth in mean education is dropped, the coefficient on initial
education remains negative and significant at the one percent level result not shown. One possible reason is that the variable for initial education picks up part
of the catch-up effect note that the coefficient and significance level of RELTFP both fall when EDUC
is included in the equation. In other words, a low initial schooling level is directly associated with a low initial TFP level.
I next included a 6intage effect in Eq. 3. This is measured by AGEKCHG
t h
, the annualized change in the average age of country h’s capital stock over period t see
13
TFP is defined as ln TFP
t h
= ln Y
t h
− a ln L
t h
− 1 − aln K
t h
, where Y
h
is the total output of country h, L
h
is labor input, K
h
is capital input, and a is the international average wage share.
463 E
.N .
Wolff Structural
Change and
Economic Dynamics
11 2000
433 –
472
Table 11 Regressions of annual labor productivity growth LPGRTH on the relative TFP level, capital-labor growth, RD intensity, and the growth in mean
education, six OECD countries, 1950–1989
a
R
2
Adjusted R
2
RELTFP Standard error
KLGRTH Sample size
EDUCGRTH EDUC
AGEKCHNG RDGDP
0.68 0.65
0.011 24
0.300
c
− 0.051
d
3.96 2.64
0.68 0.63
0.011 24
− 0.051
d
0.304
c
− 0.107
3.68 2.57
0.18 0.46
0.41 0.014
24 −
0.716 0.534
d
4.20 0.96
0.80 0.75
0.009 24
0.289
d
− 0.031
c
− 0.007
d
0.353 2.97
0.68 3.30
2.39 0.202
d
0.80 0.75
0.009 24
0.597
b
− 0.045
d
− 0.049
d
6.74 7.33
1.79 3.17
− 0.042
d
0.202 0.94
0.92 0.005
18 −
0.027
b
0.372
d
0.558 0.33
1.64 1.99
3.05 4.97
a
Note: t-ratios are shown in parentheses below the coefficient estimate. Observations are for France, Germany, Japan, the Netherlands, the U.K. and the U.S. for four time periods: 1950–1960, 1960–1973, 1973–1979, and 1979–1989. The data source is Maddison 1991, unless otherwise indicated.
Key:RELTFP: percentage difference of country’s TFP from U.S. TFP at the beginning of the period.KLGRTH: country’s annual rate of capital-labor growth.EDUCGRTH: country’s annual rate of growth in mean education. Sources. 1950 and 1973: Maddison 1987. 1989: Maddison 1991. 1960
interpolated from data from Christensen et al. 1980. 1979: interpolated from data in Maddison 1987.EDUC
0:
country’s level of mean education at the beginning of the period.AGEKCHNG: annualized change in the average age of country’s capital stock over the period.RDGDP: Ratio of RD expenditures
to GDP, averaged over the period. The data are not available before 1960. Sources. 1960–1983: Maddison 1987; 1984–89: UNESCO Statistical Yearbook, various years.
b
significant at the 10 level.
c
significant at the 5 level.
d
significant at the 1 level.
Wolff, 1994, for more details. The results specification 5 do show a very strong vintage effect the coefficient of AGEKCHG is negative and significant at the one
percent level. Moreover, the coefficient of the growth in mean education is positive and now significant at the 10 level. Moreover, when initial education is included,
its coefficient, while still negative, is no longer statistically significant results not shown. In the final specification, I included RD intensity, though this variable is
available only for 1960 and later. In this case, the coefficient of the growth in mean education becomes insignificant.
14
5. Interactions with technical change
