increase in schooling levels seems to correspond to the growth in labor productivity over this period. Moreover, as productivity and educational levels were growing
and converging among OECD countries, so was their RD intensity of production. We now turn to regression analysis to analyze these relations more systematically.
3. Catch-up models
For heuristic reasons, I begin the econometric analysis with the catch-up model. As noted in the Section 1.2 above, this approach implies that education should be
interpreted as a threshold effect and leads to an econometric specification in which the rate of productivity growth is a function of the le6el of schooling. Of course,
one is still left with the difficulty of deciding which year to use for the educational variable. When productivity growth is measured over a short period of time, the
model would suggest using educational attainment as of the beginning of the period. However, when productivity growth is measured over a long time period,
educational levels will likely be rising and initial education may not be relevant for characterizing the ability of the work force to adopt new technology toward the end
of the period. In this case, one might use the average educational level over the period. Of course, as a matter of practicality, one is limited in choice by the
available data.
The basic model specification is as follows: lnRGDPW
1
RGDPW t
1
− t
= b
+ b
1
RGDPW +
b
2
INVRATE + b
3
RDGNP + b
4
EDUC + o 1
where lnRGDP
1
RGDP t
1
− t
is the annual rate of growth in real GDP 1985 dollar equivalents per worker from time 0 to1; RGDP
is RGDP near the beginning of the period; INVRATE is the average investment rate, defined as the
ratio of investment to GDP, both in 1985 dollar equivalents, averaged over the period of analysis; RDGNP is the average ratio of RD expenditures to GNP,
averaged over the period; EDUC is a measure of educational input; and o is a stochastic error term.
10
Mankiw et al. 1992 provide some theoretical justification for this approach, deriving this specification from an augmented Solow model.
However, one can also be agnostic about the theoretical foundations of the model. The convergence hypothesis predicts that the coefficient b
1
will be negative that is, countries further behind near the beginning of the period will show more rapid
increases in GDP per worker. The coefficients of the investment rate b
2
, RD intensity b
3
, and education b
4
should be positive. Results are shown in Table 8
10
In order to partially allay the criticisms of Friedman 1992, I use the value of RGDPW near the beginning of the period rather than RGDPW
in the regression analysis. See his comment for more details. I also use labor productivity growth as opposed to the growth in GDP per capita, as has been
used in most previous studies, including my own, or GDP per adult, as used in Mankiw et al. 1992. As a result, the results reported here will differ somewhat from those of previous studies.
455 E
.N .
Wolff Structural
Change and
Economic Dynamics
11 2000
433 –
472
Table 8 Regressions of the annual growth in real GDP per worker RGDPW on Initial RGDPW, the investment rate, RD, and educational enrollment and
attainment levels, all OECD countries, 1950–1990
a
Adjusted R
2
Standard error Relative
Sample size INVRATE
Education variable RD
Education variable R
2
RDGPW
55
A RD 6ariable
:
RDGNP 0.0056
24 −
0.017
d
0.74 0.73
7.99 0.0051
24 0.78
0.80 −
0.016
d
0.063
c
2.38 8.35
0.80 0.064
c
0.0050 24
0.314
b
0.83 −
0.018
d
8.20 1.80
2.51 0.070
d
0.82 0.0047
23 PRIM-ENRL
1965
0.336
b
0.018
b
− 0.018
d
0.86 8.77
2.88 1.90
2.04 0.82
0.074
d
0.0048 23
PRIM-ENRL
65–91
0.366
c
0.031 0.85
− 0.018
d
2.93 2.16
1.66 8.12
0.0051 23
SCND-ENRL
1965
0.79 0.83
− 0.018
d
− 0.001
0.317
b
0.065
c
2.34 1.75
0.11 7.24
0.0051 23
SCND-ENRL
65–91
0.79 0.059
b
0.308 −
0.019
d
0.83 0.004
2.01 1.72
0.38 6.81
0.85 0.81
0.0049 22
UNIV-ENRL
1965
− 0.017
d
0.078
c
0.318 0.026
7.60 2.80
1.72 1.23
0.0048 22
UNIV-ENRL
65–91
0.82 0.86
0.033 −
0.021
d
0.073
d
0.274 2.93
1.51 1.72
7.92 0.86
0.032 0.0043
22 PRIM-ATTN
1970
0.233 0.033
c
0.89 −
0.024
d
8.93 2.79
1.42 1.28
0.83 0.057
c
0.0047 22
PRIM-ATTN
1979
0.358
b
0.016
b
0.86 −
0.020
d
2.36 2.07
8.72 1.84
0.85 0.039
0.0044 22
PRIM-ATTN
60–79
0.264 0.029
c
0.88 −
0.022
d
8.92 1.60
1.59 2.54
0.80 0.064
c
0.0051 22
SCND-ATTN
1970
0.408
b
− 0.009
0.84 −
0.017
d
5.62 2.47
0.78 2.09
0.79 0.064
c
0.0052 22
SCND-ATTN
1979
0.362
b
0.000 0.83
− 0.019
d
2.41 1.84
0.10 6.61
0.0051 22
SCND-ATTN
60–79
0.80 0.84
− 0.017
d
− 0.008
0.421
b
0.061
c
5.67 2.31
2.03 0.66
0.0051 22
UNIV-ATTN1
970
0.80 −
0.017
d
0.352
b
0.060
c
0.83 −
0.020 2.21
1.87 0.68
5.39
456
E .N
. Wolff
Structural Change
and Economic
Dynamics
11 2000
433 –
472
Table 8 Continued INVRATE
R
2
Adjusted R
2
Standard error Sample size
Education variable RD
Relative Education variable
RDGPW
55
0.83 0.79
0.0052 23
UNIV-ATTN
1979
− 0.019
d
0.362
b
0.065
c
0.002 6.44
0.10 1.91
2.29 0.0051
− 0.018
d
23 0.059
b
UNIV-ATTN
60–79
0.364
b
− 0.016
0.84 0.80
0.49 5.35
2.10 1.93
0.79 0.058
c
0.0051 23
MEAN-EDUC
1965
0.334
b
− 0.002
0.83 −
0.019
d
2.10 1.86
0.64 8.00
0.0051 23
MEAN-EDUC
1970
0.79 0.83
− 0.018
d
− 0.001
0.330
b
0.060
b
7.84 1.76
1.97 0.28
0.0048 23
MEAN-EDUC
1975
0.82 −
0.020
d
0.067
c
0.85 0.016
0.228 2.75
1.31 1.70
8.56 0.80
0.072
c
0.0050 23
MEAN-EDUC
1980
0.338
b
0.004 0.84
− 0.018
d
7.97 0.96
1.92 2.68
0.80 0.072
c
0.0050 23
MEAN-EDUC
1985
0.338
b
0.005 0.84
− 0.018
d
2.69 1.92
7.97 0.99
0.79 0.065
b
0.0051 23
MEAN-EDUC
65–85
0.312 0.000
0.83 −
0.018
d
7.57 2.07
1.72 0.05
0.068
c
0.82 0.0048
23 BL-EDUC
1960
0.354
b
− 0.001
− 0.015
d
0.85 1.65
2.10 5.42
2.78 0.81
0.069
c
0.0049 23
BL-EDUC
1965
0.349
b
− 0.001
0.84 −
0.016
d
5.34 2.72
2.02 1.36
0.83 0.80
0.0050 23
BL-EDUC
1970
− 0.016
d
0.068
c
0.326
b
− 0.001
5.08 0.79
1.84 2.59
0.84 0.81
0.0049 23
BL-EDUC
1975
− 0.015
d
0.072
c
0.325
b
− 0.001
2.77 1.88
4.86 1.24
0.82 0.078
d
0.0047 23
BL-EDUC
1980
0.358
c
− 0.001
b
0.85 −
0.014
d
4.13 3.09
2.15 1.84
0.85 0.81
0.0048 23
BL-EDUC
1985
− 0.014
d
0.343
b
0.075
d
− 0.001
4.17 2.93
1.57 2.03
0.81 0.072
c
0.0048 23
BL-EDUC
60–85
0.344
b
− 0.001
0.85 −
0.015
d
4.60 2.02
2.85 1.48
B RD variable: SCIENG 0.0049
23 −
0.017
d
PRIM-ENRL
65–91
0.058
c
0.025
b
0.035 0.84
0.80 1.75
1.71 7.90
2.17 0.77
0.055
b
0.0053 24
SCND-ENRL
65–91
0.013 0.000
0.81 −
0.017
d
6.76 1.87
0.93 0.00
457 E
.N .
Wolff Structural
Change and
Economic Dynamics
11 2000
433 –
472
Table 8 Continued Education variable
R
2
Adjusted R
2
Standard error Sample size
Education variable Relative
RD INVRATE
RDGPW
55
0.84 0.80
0.0051 22
UNIV-ENRL
65–91
0.071
c
− 0.020
d
0.005 0.037
7.36 1.65
0.29 2.38
0.86 0.83
0.0046 22
PRIM-ATTN
60–79
0.031 −
0.022
d
0.009 0.031
c
1.18 0.70
8.38 2.52
0.78 0.041
0.0054 22
SCND-ATTN
60–79
0.028 −
0.012 0.82
− 0.016
d
4.76 1.28
1.47 0.78
0.83 0.78
0.0053 22
UNIV-ATTN
60–79
0.035 −
0.015
d
0.026 −
0.039 4.87
1.07 1.07
1.61 0.77
0.060
b
0.0052 23
MEAN-EDUC
65–85
0.013 0.000
0.81 −
0.017
d
1.82 0.99
0.25 7.66
0.0048 23
BL-EDUC
60–85
0.82 0.85
− 0.013
d
− 0.002
c
0.031
c
0.056
c
4.06 2.19
2.14 2.10
a
Note: The absolute value of t-ratios are shown in parentheses below the coefficient estimate.See footnotes to Tables 2 and 3 Tables 4–7 for sources and methods. Key:Dependent variable: lnRGDPW
90
RGDPW
50
40.RGDPW
t
: GDP per worker in year t, measured in 1985 international prices in units of 10 000.Source: Penn World Table Mark 5.6.Relative RGDPW
55:
RGDPW level of the country relative to the RGDPW level of the U.S. in 1955.Source: Penn World Table Mark 5.6.INVRATE: Ratio of investment to GDP both in 1985 dollar equivalents averaged over the regression period.Source: Penn
World Table Mark 5.6.RDGNP: Expenditure for RD as a percentage of GNP. Source: UNESCO Statistical Yearbook,1963–1990.SCIENG: Scientists and engineers engaged in RD per 10 000 of Population. Source: UNESCO StatisticalYearbook, 1963–1990.PRIM-ENRL
t
: Total enrollment of students of all ages in primary school in year t as aproportion of the total population of the pertinent age group. PRIM-ENRL
t−t’:
Average primary school enrollment rate in t and t.SCND-ENRL
t:
Total enrollment of students of all ages in secondary school in year t as aproportion of the total population of the pertinent age group. SCND-ENRL
t-t’
:Average secondary school enrollment rate in t and t.UNIV-ENRL
t
: Total enrollment of students of all ages in higher education in year t as aproportion of the total population of the pertinent age group. UNIV-ENRL
t-t’
:Average tertiary school enrollment rate in t and t.PRIM-ATTN
t:
Proportion of the population age 25 and over who have attended primary schoolor higher in year t.SCND-ATTN
t
: Proportion of the population age 25 and over who have attended secondary schoolor higher in year t.UNIV-ATTN
t
: Proportion of the population age 25 and over who have attended an institution ofhigher education in year t.MEAN-EDUC
t
: Mean years of schooling of the labor force in year t, from Kyriacou 1991.MEAN-EDUC
t−t’
: Average years of schooling from t to t.BL-EDUC
t
: Mean years of schooling of the of the total population aged 25 and over in year t,from Barro and Lee 1993. BL-EDUC
t-t’
: Average years of schooling from t to t.
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.
for all OECD countries over the 1950 – 1990 period and for a variety of educational measures.
11
The RGDPW level of the country relative to the U.S. level is by far the most powerful explanatory variable in accounting for differences in labor productivity
growth among OECD countries. By itself, the catch-up variable explains 74 of the variation in RGDPW growth over the 1950 – 1988 period. The coefficient of
INVRATE is positive and significant at the 5 level or greater except in three cases where it is significant at the ten percent level. The average investment rate, together
with the catch-up variable, explains 80 of the variation in RGDPW growth. RD intensity is significant at the 10 in almost all cases.
The educational enrollment rates have positive coefficients in all but one case and of these are significant in only one case — the primary enrollment rate in 1965,
which is significant at the 10 level. This is the most unlikely case, since primary education enrollment rates show little variation among OECD countries.
The attainment rates by level of schooling have positive coefficients in only half the cases. While the coefficients are insignificant for secondary and university
attainment, they are significant for primary school attainment levels at the 5 level for 1970 and the average rate over the 1960 – 79 period and at the 10 level for
1979. The results for primary education are unexpected, because this is the level of schooling that would appear to have least relevance to the types of sophisticated
technology in use among OECD countries in the post World War II period. Also there is little variation in this measure among OECD countries, except for Greece,
Portugal, and Turkey the three non-industrial market economies. However, even when these three countries are excluded from the sample, the coefficient remains
significant at the 5 level. I shall comment more on this result in the conclusion.
Because of the anomalies in this data series discussed above, I have also used the average value of the attainment rates over the four periods, 1960, 1970, 1979, and
1996. When there are missing values, I use the average of the data points that are available. This method has the added advantage of eliminating most of the missing
observations for 1970. However, the results are virtually unchanged. The coefficient of the average primary attainment rate is significant at the 5 level, while that of
the secondary and tertiary attainment rates remain insignificant.
The next two panels show results for mean educational levels. The first of these is based on the Kyriacou data on average schooling for the labor force. The
coefficients of these educational variables are positive in only four of six cases and not significant in any. The second panel uses the Barro-Lee data on average
education for the adult population. The coefficients of these variables are all insignificant and, indeed, all have negative values.
At first glance, the disparity in results for these two measures of mean schooling is, to say the least, disquieting. However, it should be noted that the schooling of
the labor force should, in principle, have more relevance to the growth in labor productivity than the educational attainment of the total adult population, and the
regression results confirm this. Still, one would have expected a fairly high
11
It was not possible to run regressions on the ISDB-14 country sample over the 1950-95 period because of its small sample size.
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
