The influence of income distribution on capital accumulation and
Macro-investment structure: empirical study in China since 1978
Wang Tongsan Cai Yuezhou1
(Institute of Quantitative and Technical Economics, Chinese Academy of Social Sciences)
Abstract: it is proposed that the influence of income distribution on capital accumulation and
macro-investment structure is conducted by the mechanism of “income distribution mode→
income level and income disparity → efficient demand and demand structure → capital
accumulation and macro-investment structure”. Empirical study is made with China’s yearly data
since 1978 to test the above mechanism. It is argued that: (1) The increment of income level and
expansion of income disparity for urban residents might increase both the investment proportion
of heavy industry and its growth rate compared with those of light industry; (2) The increment of
rural income might increase the investment proportion and growth rate of light industry, while the
income disparity of rural residents has little impacts on macro-investment structure; (3) The
macro-investment structure favoring heavy industry is mainly caused by expansion of income
disparity within urban residents.
Keywords: income level, income disparity, capital accumulation, and macro-investment structure
Currently, there exist three structural problems in China’s economy. The first is the high
investment ratio in macro-economy. The second should be the macro-investment structure
favoring the heavy industries. And the third may be the expansion of income disparity in recent
years. These problems are all connected with the problems in income distribution (Wang Tongsan
et al., 2003, 2004). For this reason, we begin with our study from the angle of income distribution,
analyze the influence of income level and disparity on capital accumulation and investment
structure, and then make some empirical study with the data since 1978.
I Income distribution, Capital Accumulation and Sector Structure of
Macro-investment
i Brief Review of Relative Theories
Capital accumulation has always been regarded as the engine of economic development.2 As
a result, researches on capital accumulation and investment structure were usually under the theme
of economic growth and economic development. The purpose of these researches is mainly around
the relationship between capital accumulation (and investment structure) and economic growth (or
development), or on the change of capital accumulation and investment structure in different stage
of economic growth.
Karl Marx has elaborated the relationship between income distribution and capital
accumulation (and investment structure as well) systematically in his famous “On Capital”.3
According to the series theories of Marx (1975), such as distribution theory, reproduction theory,
and two-sector equilibrium model, the distribution mode in capitalism society would certainly
1
2
3
The authors owe greatly to Dr. Guo Meijun for her revision.
See Hayami (2003, p117).
See Marx (1975, pp435-592).
-1-
increase the ratio of accumulation and decrease the share of labor income. With the accumulation
of capital, the production capacity expands, while the labor income share decreases, which leads
to the insufficiency of consumption. The above two relationships form the basic contradiction of
capitalism society, which may cause economic crisis. Although Marx was intended to illustrate the
essence of reproduction and distribution in capitalism society, it still can be regarded as one of the
earliest important researches on the relationship between income distribution and capital
accumulation. It implies a mechanism of “income distribution mode→income level→consumption
and accumulation ratio”.
During the middle of last century, some classical theories of development economics also
related capital accumulation to income distribution. Arthur. Lewis, Simon. Kuznets and Rostow
are among the pioneers.
Lewis’ dual economy model (Lewis 1955, 1989) was built under the framework of classical
economics. It presumes that “Supply creates demand”, and thus neglects the situation of
insufficient effective demand. Under the circumstance of unlimited labor supply, the income level
of workers (in both subsistence sector and modern sector) is only to maintain subsistence or just a
bit higher. And their consumption would mainly be primary products, not the consumption goods
from modern sector. As for the capitalists, their consumption would also be limited because they
were eager to accumulate as much as possible. As a result, the production of modern sector would
mainly be used to meet the investment demand, and the production structure would favor the
capital goods. Eventually, the sector structure and macro-investment structure would also favor the
heavy industries. The Lewis dual economy model also implies the transmission mechanism of
“ distribution mode → income level → aggregate demand and aggregate supply → capital
accumulation and macro-investment structure”.
Kuznets (1955, 1989), Rostow (2001) studied the effects of income distribution on capital
accumulation and investment structure in different stages of economic development.
Kuznets advanced the famous “Inverse U theory” in his celebrated article “Economic Growth
and Income Inequality” in the year 1955. According to his theory, income inequality would
increase in the early stage of economic development. After reaching a climax, the income
inequality would move towards equality. Later, Kuznets (1989) did a lot of empirical study on the
characteristics of economic growth and economic structure for different countries. It comes out
that economic growth is usually accompanied with frequent change of aggregate production,
which reflects the change of demand structure. While the change of demand structure can be
caused by the improvement of average output (or income level) to a great extent.4 Kuznets did not
mention the effects of income distribution (including income level and income disparity) on
capital accumulation and macro-investment structure explicitly, but the above two researches also
implied a mechanism of “economic development→change of income level and income disparity
→change of demand structure→change of production source”.
Rostow (2001) divides the social development into five stages. In his opinion, a necessity for
take-off is the increase of producing investment rate, for example, the investment rate should
increase from less than 5% to over 10%. The supply of capital in the stage of take-off is usually
obtained form the control of income flows. Actually, Rostow regard the economic development as
the result of income transferring, which means the transferring of income from those not using for
4
See Kuznets (1989, p434).
-2-
producing to those having such purpose.5 Rostow’s opinion is intrinsically consistent with what
implied in Lewis’ dual structure model.
Wang Tongsan et al. (2003, 2004) points out some of the problems in China’s economic structure,
including the high investment rate, macro-economic structure favoring heavy industries and the
expansion of income disparity. Wang Tongsan et al. (2003, 2004) argued that the structural
problems should be solved by income distribution (policies).
ii The Influencing Mechanism that Income Distribution Affects Capital Accumulation and
Macro-investment Structure
According to the former analysis on several related theory, we may summarize the
influencing mechanism by which income distribution affects capital accumulation and
macro-investment structure as follows: (1) The change of income level and income disparity
would affect the aggregate consumption and the consumption structure as well. (2) The change of
consumption demands means the change of consumption and investment ratio, which would
change the investment (or accumulation) level in next period; (3) The change of consumption
structure would affect the sector structure of macro-investment by inducing the change of supply;
(4) In an two-sector economy composed of only consumption and investment, the change of
consumption will not only affect the investment rate, but also determine the investment structure
indirectly. In the simple equilibrium equation Y=C+I, the decrease of C would cause the
investment demand in consumable sector (or light industries) to decrease. Then, the investment
share for capital goods (or heavy industries) would increase, which may lead to macro-investment
structure favoring heavy industries.6
In the following three parts, we will test the above mechanism with the dada in China since
1978. Besides, we would also make explanation for the empirical results.
II Relative Variables and Granger Causality Test
i Selection of Variables
The income distribution includes income level and income disparity. The “China Statistical
yearbooks” provides two series, “Per Capital Annual Disposable Income of City Households” and
“Per Capital Annual net Income of Rural Households”, which we choose to represent the income
level. The meaning of income disparity includes not only the disparity between rural and urban
areas, but also the disparity inside rural and urban areas. We will use the ratio of “Per Capital
Annual Disposable Income of City Households” to “Per Capital Annual net Income of Rural
Households” as the income disparity between rural and urban areas. As for the income disparity
inside the two areas, we will directly use their Gini Coefficients.
The concepts of capital accumulation and macro-investment can be treated as the same thing
theoretically. In the “China Statistical yearbooks”, they seem to be corresponded with two related
series, the “Gross Capital Formation” and “Total Investment in Fixed Assets”. Although both of
them can represent the capital accumulation, the former emphasizes the results of accumulation,
while the latter seem to put more on the activity of accumulation. Since the available data range of
“Total Investment in Fixed Assets” is longer, we choose it as the representative of capital
accumulation.
Comparing with the secondary industry, the investment share of agriculture is so low that it
5
6
See Rostow (2001, pp39-40).
Actually, the heavy industries have a characteristic of self-cycling, which can balance the equation.
-3-
almost can be neglected. 7 For this reason, our empirical study will be confined to the investment
of the secondary industry. We divide the secondary industry into light industry and heavy industry,
and take the relative investment share of the two sectors as representative of the macro-investment
structure.
ii Unit Root Test
In the first part of this paper, we have made a judgment on the effects of income distribution
on capital accumulation. Here we would like to use Granger causality test to see whether there
exist causal relationship between the relative variables.
Before we do the Granger Causality Test, unit root test should be done. The procedures of
unit root test are as follows. (1) The test will begin with the original series. If it has unit roots, then
its first-order difference series will be tested. (2) For each series, the test will begin with tendency
and interception, then with only interception, and lastly no tendency and interception. (3) Once the
test refuses the non-hypothesis of “unit root(s)”, it means that the test would be finished, and the
tested series would be regarded to be stable. The results of the tests are listed in table1.
Table1. Unit root tests for relative series
Variable
Order
and
Model
GOR
GOU
INCGAP
INCOR
INCOU
1%
Critical
Value
5%Critical
10% Critical
t-Statistics
Probability
Value
Value
-3.603202
-3.238054
-3.408194
0.0729
-2.632604
-1.308677
0.6092
（0，T）
-4.374307
（0，C）
-3.724070
（0，N）
-2.660720
-1.955020
-1.609070
1.495831
0.9627
（1，T）
-4.394309
-3.612199
-3.243079
-6.807759
0.0001
（0，T）
-4.374307
-3.603202
-3.238054
-3.084395
0.1314
（0，C）
-3.724070
-2.986225
-2.632604
0.071519
0.9568
（0，N）
-2.660720
-1.955020
-1.609070
2.697488
0.9972
（1，T）
-4.667883
-3.733200
-3.310349
-5.935639
0.0012
（0，T）
-4.498307
-3.658446
-3.268973
-1.922070
0.6059
（0，C）
-3.737853
-2.991878
-2.635542
-0.797652
0.8017
（0，N）
-4.498307
-3.658446
-3.268973
-1.922070
0.6059
（1，T）
-4.394309
-3.243079
-3.223834
0.1035
（1，C）
-3.737853
-2.991878
-2.635542
-3.008158
0.0484
（0，T）
-4.374307
-3.603202
-3.238054
-1.430847
0.8260
（0，C）
-3.724070
-2.986225
-2.632604
-0.465920
0.8823
（0，N）
-2.660720
-1.955020
-1.609070
7.332652
1.0000
（1，T）
-4.394309
-3.612199
-3.243079
-2.793580
0.2126
（1，C）
-3.737853
-2.991878
-2.635542
-2.871367
0.0636
（1，N）
-2.664853
-1.955681
-1.608793
-1.049583
0.2566
（2，T）
-4.667883
-3.733200
-3.310349
-2.634416
0.2717
（2，C）
-3.752946
-2.998064
-2.638752
-6.603064
0.0000
（0，T）
-4.571559
-3.690814
-3.286909
1.776810
1.0000
（0，C）
-3.857386
-3.040391
-2.660551
2.173765
0.9998
（0，N）
-2.664853
-1.955681
-1.608793
3.126903
0.9990
-2.986225
-3.612199
7
According to the China Statistical Yearbook, in 2003, the investment in capital construction of farming, forestry,
animal husbandry and fishery is 41.68billion (RMB), only take the share of1.8% in the total investment in capital
construction, which reached 2290.86 billion (RMB).
-4-
INVOH
INVOL
（1，T）
-4.394309
-3.612199
-3.243079
-3.034971
0.1438
（1，C）
-3.737853
-2.991878
-2.635542
-1.606449
0.4640
（1，N）
-2.664853
-1.955681
-1.608793
-0.542518
0.4713
（2，T）
-4.416345
-3.622033
-3.248592
-6.678259
0.0001
（0，T）
-4.571559
-3.690814
-3.286909
1.841589
1.0000
（0，C）
-3.808546
-3.020686
-2.650413
3.546337
1.0000
（0，N）
-2.685718
-1.959071
-1.607456
3.755900
0.9997
（1，T）
-4.394309
-3.612199
-3.243079
-0.259936
0.9871
（1，C）
-3.737853
-2.991878
-2.635542
0.556780
0.9852
（1，N）
-2.664853
-1.955681
-1.608793
1.252158
0.9417
（2，T）
-4.416345
-3.622033
-3.248592
-3.843952
0.0324
（0，T）
-4.394309
-3.612199
-3.243079
0.727141
0.9993
（0，C）
-3.737853
-2.991878
-2.635542
1.625084
0.9991
（0，N）
-2.664853
-1.955681
-1.608793
1.144003
0.9298
（1，T）
-4.394309
-3.612199
-3.243079
1.169953
0.9998
（1，C）
-3.737853
-2.991878
-2.635542
1.848759
0.9995
（1，N）
-2.664853
-1.955681
-1.608793
2.380338
0.9941
（2，T）
-4.416345
-3.622033
-3.248592
-3.137033
0.1216
（2，C）
-3.752946
-2.998064
-2.638752
-2.521754
0.1236
（2，N）
-2.669359
-1.956406
-1.608495
-2.358241
0.0207
Notes:(1) GOR, GOU, INCGAP, INCOR, INCOU, INVOH, INVOL stand for “Gini Coefficient of Rural
Residents”, “Gini Coefficient of Urban Residents”, “Income Disparity between Urban and Rural Area”, “Per
Capital Annual net Income of Rural Households”, “Per Capital Annual Disposable Income of City Households”,
“Investment in Fixed Assets of Heavy Industry” and “Investment in Fixed Assets of Light Industry” respectively;(2)
0,1,2 in the parenthesis of the second row represent that the series tested are original series, first-order difference
and second-order difference respectively, while the N, C, T stands for “ No interception or Tendency”, “Only
interception” and “Both interception and Tendency”; (3)The non-hypothesis was that the series to be tested has a
unit root; (4) Probability is the probability of error when reject the non-hypothesis.
iii Granger Causality Test
To make the series tested stable, we use the first-order or second-order difference of the
correspondent series to do the test. For each couple of variables, we choose one period lag, two
periods lag and three periods lag respectively. The results of the Granger causality test are listed in
table2.
Table2. Results of Granger Causality Test
Independent
Dependent
One period lag
Two period lag
Three period lag
Variables
Variables
F-Statistics
Probability
F-Statistics
Probability
F-Statistics
Probability
DDINCOU
DDINCOR
0.03210
0.85961
1.20050
0.32532
0.66500
0.58727
DDINCOR
DDINCOU
1.02219
0.32408
0.50475
0.61242
0.25419
0.85706
DDINVOH
DDINCOR
0.12850
0.72375
2.11483
0.15129
1.19331
0.34817
DDINCOR
DDINVOH
0.04012
0.84326
0.18812
0.83021
0.80956
0.50942
DDINVOL
DDINCOR
0.00037
0.98491
0.79848
0.46619
0.37827
0.77014
DDINCOR
DDINVOL
1.06927
0.31345
0.50951
0.60968
0.42481
0.73825
DDINVOH
DDINCOU
1.12502
0.30148
0.59997
0.56004
1.54955
0.24573
-5-
DDINCOU
DDINVOH
10.1035
0.00472
7.79116
0.00397
7.09780
0.00392
DDINVOL
DDINCOU
0.00773
0.93084
0.31528
0.73376
1.49941
0.25795
DDINCOU
DDINVOL
5.27931
0.03250
6.75493
0.00694
6.08939
0.00716
DDINVOL
DDINVOH
0.29406
0.59362
4.98717
0.01976
2.00697
0.15932
DDINVOH
DDINVOL
0.15641
0.69667
0.89155
0.42835
0.76674
0.53143
DGOR
DDINVOH
0.05773
0.81257
0.01077
0.98929
0.36920
0.77642
DDINVOH
DGOR
1.05241
0.31720
0.58363
0.56866
0.25484
0.85661
DGOU
DDINVOH
5.32303
0.03187
3.57142
0.05071
1.51259
0.25468
DDINVOH
DGOU
0.33649
0.56834
0.10965
0.89678
0.28272
0.83702
DGOR
DDINVOL
0.01016
0.92071
0.24080
0.78863
0.62877
0.60836
DDINVOL
DGOR
1.35105
0.25878
0.70451
0.50823
0.38307
0.76682
DGOU
DDINVOL
4.02793
0.05846
2.41055
0.11977
1.38102
0.28948
DDINVOL
DGOU
0.03792
0.84757
0.24237
0.78743
1.32993
0.30433
DINCGAP
DDINVOL
1.44678
0.24309
0.35692
0.70495
0.27808
0.84029
DDINVOL
DINCGAP
3.22081
0.08784
3.89597
0.04047
3.11919
0.06008
Notes: (1) The meanings of the variables are the same as that in table1. The “D” before the variables means
“difference”, one “D” for first-order difference and two “D” for second-order difference; (2) Using series of
difference is to guar ant the stability of tested series; (3) The non-hypothesis is “the independent variable cannot
Granger cause the dependent variable”; (4) The meaning of probability is the same as other tables.
According to the results in table2, we may summarize that:(1) There seems to be little
connection between the income level of rural residents and urban residents, since the probabilities
for DDINCOU and DDINCOR are all over0.32. This might be caused by the different income
sources and distribution modes between rural and urban areas, and it also reflects the dual
structure in income distribution. (2) Also based on the probability, the income level of rural
households has little effect on the investment of both heavy industry and light industry. The
income level of rural households is on a low level, and consumption of rural households is mainly
composed of agricultural products. The change of rural income level would not affect the
accumulation by the mechanism we had mentioned in part I. (3) Income level of urban households
has significant effects on the accumulation of light and heavy industry. The income of urban
residents has now reached a fairly high level, so the mechanism that income level affecting capital
accumulation would take effects in this situation. (4) The investment of light industry seems to be
Granger causality of heavy industry. (5) It seems that only the income disparity of urban residents
has impacts on the capital accumulation. The reasons behind are similar to what we have
mentioned above.
Besides, it should be pointed out particularly that the expansion of urban income disparity
would decrease the share of consumption, and result in the macro-investment structure favoring
the heavy industry.
III Co-integration Analyses for Income Distribution and Capital Accumulation
Based on the Granger causality test above, it can be conferred that there exists causal
relationship between the income distribution of urban households and capital accumulation. The
co-integration analyses are to be implemented here to see the possible relations in detail (whether
there are long-term equilibrium).
i Testing and Analyzing
-6-
Take the income level and income disparity of urban households as exponent variables and
the capital accumulation of both light industry and heavy industry as explained variables. The
process and results of the analyses are listed in the following table3. Tests for logarithm series can
be seen in appendix.
Table3. Co-integration analyses for original series
Explained
Exponent
Coefficients
Standard
t-Statistics
Probability
variables
INVOL
C
-66.02226
127.4167
-0.518160
0.6093
GOU
-1537.608
1050.611
-1.463537
0.1569
INCOU
0.485798
0.078239
6.209125
0.0000
GOU
-2023.737
465.5955
-4.346557
0.0002
INCOU
0.513673
0.055937
9.182981
0.0000
C
-379.3309
227.8667
-1.664705
0.1102
T
-30.30703
18.55299
-1.633539
0.1166
GOU
747.4964
1727.993
0.432581
0.6695
INCOU
0.581938
0.095766
6.076658
0.0000
C
-810.4585
221.1396
-3.664918
0.0013
GOU
882.9189
1823.400
0.484216
0.6328
INCOU
1.265892
0.135789
9.322486
0.0000
GOU
-5084.579
1011.123
-5.028646
0.0000
INCOU
1.608073
0.121478
13.23755
0.0000
C
-1456.385
385.4920
-3.777992
0.0010
T
-62.48191
31.38689
-1.990701
0.0591
GOU
5593.962
2923.320
1.913565
0.0688
INCOU
1.464097
0.162012
9.036992
0.0000
INVOL
INVOH
INVOH
INVOH
AIC
SC
0.880039
12.55389
12.69906
0.883696
12.48858
12.58535
0.888153
12.51633
12.70989
0.967530
13.65655
13.80172
0.950710
14.03957
14.13635
0.971235
13.56785
13.76141
R2
variables
INVOL
Adjusted
errors
Notes: (1) C and T stand for interception and time tendency respectively; (2) AIC and SC is shortened for Alkaika
Information Criterion and Schwartz Criterion.
All the residual series in table3 are tested to be stable. Taking Adjusted R2, AIC, SC and the
probability for each coefficient into consideration, two co-integration equations can be derived
from the above result.
INVOLt  -2023.74 GOUt  0.51 INCOUt
(1)
INVOHt  -1456.39-62.481t  5593.96 GOUt  1.46 INCOUt
(2)
It is shown in equation (1) and equation (2) that the investments of both light industry and
heavy industry have long-term equilibrium relationship with the income level of urban residents
and urban income disparity. More detailed, it can be summarized as follows: (1) The income level
of urban residents has positive effects on investment of the two industries, while the influence on
heavy industry is more significant than on that of light industry. With the improvement of income
level, the consumption demands would increase, which promotes the increasing of investment in
light industry and enlarges its supply capacity. The increasing investment in light industry would
in turn forms an extra demand for capital goods, which forces the heavy industry to expand its
production capacity by investment. Moreover, the expanding of capacity means still more
-7-
investment in heavy industry.8 (2) The urban income disparity has negative impacts on the
investment in light industry while positive impacts on that of heavy industry. The expansion of
income disparity would lead the average consuming tendency decreasing ceteris paribus, which
may cut down the share of consumption and reduce the investment in light industry. At the same
time, the share of investment goes up. Since the investment in light industry is reduced,
investment in heavy industry must be greatly improved. As a matter of fact, the heavy industry has
a character of self-recycle to keep the balance of the macro-economy.
ii Error Correction Model
Take the first-order difference series of the above independent variables as the explained
variables, the first-order difference of the dependent variables and the residual as exponent
variables. Different OLS regressions are made with results listed in table4.
Table4. Regression for difference and residual (ECM for equation (1) and (2))
Explained
variables
DINVOL
DINVOL
DINVOL
DINVOL
DINVOH
DINVOH
Exponent
Coefficient
variables
s
Standard
t-Statistics
errors
Proba
Adjusted
bility
R2
0.401723
12.19660
12.34286
0.437971
12.16758
12.36260
0.413780
12.17624
12.32251
0.411911
12.14387
12.24138
0.558136
13.46949
13.66451
0.571881
13.40440
13.55067
DGOU
1170.108
1500.254
0.779940
0.4437
DINCOU
0.534429
0.145967
3.661311
0.0014
RESILNt-1
-0.287900
0.257732
-1.117049
0.2760
C
-56.28861
36.19203
-1.555276
0.1348
DGOU
2247.350
1610.633
1.395321
0.1775
DINCOU
0.805061
0.224264
3.589786
0.0017
RESILNt-1
-0.152105
0.264622
-0.574802
0.5715
C
-34.57179
33.37030
-1.036005
0.3115
DINCOU
0.749329
0.225378
3.324766
0.0031
RESILNt-1
-0.236636
0.263079
-0.899485
0.3781
DINCOU
0.565526
0.139215
4.062261
0.0005
RESILN(-1)
-0.308430
0.254192
-1.213375
0.2373
C
-40.29877
71.72824
-0.561826
0.5802
DGOU
6847.445
3019.352
2.267852
0.0340
DINCOU
1.247906
0.458569
2.721301
0.0128
RESIHTt-1
-0.667341
0.303601
-2.198084
0.0393
DGOU
6187.870
2738.163
2.259862
0.0341
DINCOU
1.043883
0.275636
3.787184
0.0010
RESIHTt-1
-0.736824
0.272924
-2.699744
0.0131
AIC
SC
Notes: (1) “D” means the first-order difference of corresponding variable. (2) RESILNt-1 and RESIHTt-1 is the
one-period lag series of the residuals of equation (1) and equation (2).
Take the factors of Adjusted R2, AIC, SC and the probability for each coefficient into
consideration, the second and sixth model in table4 can be selected as the ECM for equation (1),
(2) respectively.
INVOL t  -56.29  2247.35GOU t  0.81INCOU t
-0.15(INVOL t-1  2023.74 GOU t-1  0.51 INCOU t-1 )
8
(3)
This can be inferred from the fact that the capital invested in heavy industry needs more than one year to be
recovered generally.
-8-
INVOH t  6187.87GOU t  1.04INCOU t -0.74
(INVOH t-1  1456.39  62.48191(t-1)  5593.96 GOU t-1  1.46 INCOU t-1 ) (4)
The above equations indicate:(1) When the system of urban income distribution and
investment (in heavy industry or light industry) deviates from the long-term trend, a short-run
adjustment would pull it back to equilibrium.9 (2) The adjustment for the system of light industry
is smaller than that of heavy industry, as is showed in equation (3), (4). There is nothing strange
because the self-recycling character of heavy industry will definitely accelerate the adjustment.
IV Empirical Study for the Impacts of Income Distribution on Investment
Structure
i Representative Variables for Investment Structure and the Research Process
As mentioned previously, the ratio of investment in light industry to that in heavy industry
can be used as representative of the macro-investment structure. Furthermore, the relative ratio
can be either the ratio of absolute value, or the ratio of increasing rate. They both will be used as
explained variable here.
The exponent variables in the following empirical study are still income level and income
disparity. We will use the method of “from general to specifics” proposed by Professor Hendry.
The initial “general model” may include all possible related variables. Some of the insignificant
variables will be rejected according to the regression results step by step, and finally we will get a
suitable model. The exponent variables include the income level, disparity of both urban residents
and rural residents, and income disparity between rural and urban area as well. Besides, the ratio
of absolute value and ratio of investment index are used as the explained variable respectively, so
the corresponding exponent variables will be absolute value and increasing rate.
ii Test with the Ratio of Absolute Value as Explained Variable
SOI is shorten for “structure of investment”, which is the ratio of investment in heavy
industry to light industry. lnSOI means the logarithm of SOI. Here it is treated as explained
variable. The initial exponent variables include lnGOR, lnGOU, lnINCOR, lnINCOU and
lnINCGAP. The integration test shows that lnSOI is stable series. Since lnSOI，lnGOU，lnINCOR
are all stable, while the other three series are Integration of first-order, we apply co-integration
analyses on these variables. The results of co-integration analyses are listed in table5.
Table5. Co-integration test with lnSOI as explained variable
mode
Exponent
Coefficient
t-Statistics
errors
Proba
Adjusted
bility
R2
l
variables
①
C
14.84672
3.307057
4.489404
0.0003
T
0.064470
0.038498
1.674651
0.1104
LNGOU
1.421092
0.543399
2.615193
0.0170
LNINCOU
0.445324
0.665391
0.669266
0.5114
LNINCOR
-2.042588
0.498528
-4.097239
0.0006
LNGOR
0.284035
0.472195
0.601520
0.5546
LNINCGAP
-2.245932
0.727301
-3.088034
0.0061
C
11.18125
2.588494
4.319598
0.0003
②
s
Standard
9
AIC
SC
0.573867
-1.517102
-1.178384
0.535420
-1.456350
-1.166020
Here we refer to two systems. One is composed of investment in light industry and income distribution in urban
households, which is expressed as equation (1). The other is expressed as equation (2).
-9-
LNGOU
2.020362
0.426984
4.731708
0.0001
LNINCOU
1.352500
0.403441
3.352411
0.0032
LNINCOR
-2.177737
0.513666
-4.239600
0.0004
LNGOR
0.365426
0.490418
0.745132
0.4649
LNINCGAP
-2.633130
0.720007
-3.657087
0.0016
C
9.895852
1.909338
5.182871
0.0000
LNGOU
1.959735
0.414697
4.725702
0.0001
LNINCOU
1.199045
0.343224
3.493474
0.0022
LNINCOR
-1.929553
0.386879
-4.987484
0.0001
LNINCGAP
-2.317932
0.576440
-4.021113
0.0006
③
0.545260
-1.505890
-1.263949
Notes: The explained variable in each model is LNSOI.
The residual series of the above 3 model are all tested to be stable. Considering the factors of
Adjusted R2, AIC, SC and the probability for each coefficient for consideration, equation③ seems
prior to the other two. We may conclude that there exists the following long-term equilibrium
relationship.
lnSOI t 
9.90  1.96ln GOU t  1.20lnINCOU t -1.93lnINCOR t -2.32lnINCGAPt
(5)
iii Test with the Ratio of Increase rates as Variables
Take IROSOI and INDOSOI as explained variable respectively.10 IROG, IROI, IROGR,
IROIR, IROGUR stand for the increase rate of “Gini Coefficient of Urban Residents”, “Income
level of Urban Residents”, “Gini Coefficient of Rural Residents”, “Income level of Rural
Residents” and “Income Disparity between Urban and Rural”. They are all used as the exponent
variables initially. Since the above variables are all stable, we use OLS directly. The results of
regression are listed as table6 and table7.
Table6. Regression with IROSOI as Explained Variables
model
Exponent
Coefficients
variables
①
②
Standard
t-Statistics
Probability
Adjusted
AIC
SC
0.082417
8.135643
8.476928
0.124413
8.062862
8.355392
R2
errors
C
16.54716
12.77128
1.295654
0.2115
T
-0.576926
0.578269
-0.997678
0.3317
IROI
0.956028
0.978962
0.976572
0.3417
IROG
0.251572
0.560067
0.449182
0.6587
IROIR
-2.438471
1.048379
-2.325943
0.0319
IROGR
0.157973
0.437441
0.361131
0.7222
IROGUR
-1.957175
0.865256
-2.261962
0.0363
C
18.15472
11.69324
1.552583
0.1370
T
-0.653593
0.525435
-1.243908
0.2287
IROI
1.023501
0.938719
1.090317
0.2892
IROG
0.176344
0.507849
0.347237
0.7322
10
Here IROSOI is the difference between the increase rate of heavy industry and that of light industry, and
INDOSOI is the investment index of heavy industry to that of light industry. For example, if the increasing rate of
investment in heavy industry is 13 percent, while that of light industry is 10 percent, then IROSOI comes out to be
3 percent. At the same time, the index of heavy industry is 113, and that of light industry is 110. The INDOSOI
then can be obtained as (113/110)*100.
- 10 -
③
④
IROIR
-2.498528
1.011140
-2.471000
0.0231
IROGUR
-1.892885
0.827140
-2.288470
0.0337
C
5.702848
6.125797
0.930956
0.3630
IROI
0.543146
0.867238
0.626294
0.5382
IROG
0.109480
0.511860
0.213886
0.8328
IROIR
-1.614210
0.728798
-2.214894
0.0385
IROGUR
-1.503892
0.776153
-1.937623
0.0669
IROIR
-0.618492
0.277814
-2.226279
0.0361
IROGUR
-0.693544
0.391983
-1.769320
0.0901
0.100452
8.061153
8.304928
0.123446
7.935021
8.032531
AIC
SC
0.080278
7.720250
8.061535
0.128278
7.640717
7.933247
0.083410
7.662200
7.905975
0.155119
7.516045
7.662310
Table7. Regressions with INDOSOI as Explained Variable
model
Exponent
Coefficients
variables
①
②
③
④
Standard
t-Statistics
Probability
Adjusted
R2
errors
C
116.9328
10.37607
11.26946
0.0000
T
-0.590275
0.469816
-1.256396
0.2250
IROI
0.804446
0.795362
1.011422
0.3252
IROG
0.203446
0.455028
0.447105
0.6601
IROIR
-2.095733
0.851760
-2.460475
0.0242
IROGR
0.032583
0.355400
0.091680
0.9280
IROGUR
-1.499022
0.702980
-2.132382
0.0470
C
117.2643
9.468193
12.38508
0.0000
T
-0.606089
0.425453
-1.424572
0.1705
IROI
0.818363
0.760095
1.076658
0.2951
IROG
0.187929
0.411213
0.457012
0.6528
IROIR
-2.108121
0.818736
-2.574848
0.0186
IROGUR
-1.485762
0.669748
-2.218389
0.0389
C
105.7175
5.018004
21.06763
0.0000
IROI
0.372920
0.710406
0.524939
0.6054
IROG
0.125925
0.419295
0.300325
0.7670
IROIR
-1.288077
0.597002
-2.157577
0.0433
IROGUR
-1.125042
0.635793
-1.769509
0.0921
C
107.0321
4.099153
26.11079
0.0000
IROIR
-1.098367
0.455650
-2.410551
0.0247
IROGUR
-0.874542
0.404592
-2.161542
0.0418
R2,
Based on the factors of Adjusted
AIC, SC etc, model④ in table6 and model④ in table7
can be selected as the final regression equations.
IROSOIt  -0.62ROIR t -0.69IROGUR t
(6)
INDOSOIt  107.03-1.10IROIR t -0.89IROGUR t
(7)
The following can be inferred from the above equation (5), (6) and (7): (1) Both the increase
of income level and expansion of income disparity in urban area would cut down the marginal
propensity to consume (and average propensity to consume), raise the relative investment share
- 11 -
and accumulation speed of heavy industry, and lead to the investment structure favoring heavy
industry. (2) The increase of rural income level would not reduce the marginal propensity to
consume since it is still on a low level. As a result, the aggregate consumption demand would be
improved, and so would the relative (investment) share and accumulation speed of light industry.
(3) Since the consumption of rural residents is mainly agricultural products due to the fairly low
level of their income. The disparity inside rural area has little effect on investment structure. (4)
With the acceleration of urbanization, the high-level income groups of the rural residents become
urban residents gradually, this may widen the income disparity between urban and rural area. At
the same time these people would change their life-style and consumption structure. They may
consume more commodities and thus improve the relative (investment) share and accumulation
speed of light industry.
V Concluding Remarks
According to the empirical studies in part II, III and IV, we can draw the following
conclusions.
First, the income level of urban residents has positive effects on investment of the two
industries, while the influence on heavy industry is more significant than that of light industry. As
for the income disparity of urban residents, it has negative impacts on the investment of light
industry and positive impacts on that of heavy industry.
Second, both the increase of urban income level and the expansion of urban income disparity
would lead to the investment structure favoring heavy industry.
Third, the increase of rural income level may improve the relative (investment) share and
accumulation speed of light industry, which may curb the trend of favoring heavy industry.
Fourth, the rural income disparity has little effect on the capital accumulation and investment
structure.
Fifth, the process of urbanization may also curb the trend of favoring heavy industry.
References:
Anonymous (1998a): “Income distribution, Capital Accumulation and Growth”, Challenge.
Armonk, Vol.41, Iss.2, p61.
Anonymous (1998b): “Growth and distribution in the classical and Keynesian traditions”,
Challenge. Armonk, Vol.41, Iss.2, p76.
Kuznets, Simon (1955): “Economic Growth and Income Inequality”, The American Economic
Review, Vol.45, No.1, pp1~28.
Arthur. Lewis (1989): “On Dual Economy” , Chinese Edition, Beijing Economic Institute Press.
Rostow (2001): “The stages of Economic Growth: A Non-Communist Manifesto” (Chinese
Edition), Chinese Social Sciences Press.
Li Zinai and Ye Azhong (2000): “Senior Econometrics”, Tsinghua University Press.
Karl Marx (1975): “On Capital” (Chinese Edition) Vol.2, Renmin Press, 1975.
Wang Tongsan (2004): “Income Distribution And Economic Structure Adjustment”, Academic
Journal of Graduate School, CASS, No.2 (In Chinese).
Wang Tongsan and Zhang Tao (2003): “Paying Attention to Promoting Economic Structure
Adjustment From the Perspective of Income Distribution”, Quantitative and Technical Economics,
- 12 -
Vol.20, No.12, PP5~8, (In Chinese).
Simon. Kuznets (1989): “Modern Economic Growth”, Chinese Edition, Beijing Economic
Institute Press.
Appendix: Co-integration test and ECM for logarithm series
Table A1. Co-integration analyses for logarithm series
Explained
Exponent
Coefficients
Standard
t-Statistics
Probability
variables
LNINVOL
C
4.298544
-1.768272
-7.600992
0.0915
T
0.050889
-0.678944
-0.034551
0.5046
LNINCOU
0.764262
0.964649
0.737245
0.3457
LNGOU
0.658995
-0.647339
-0.426593
0.5244
LNINVOH
0.349536
3.109656
1.086935
0.0053
C
-5.197079
2.407406
-2.158788
0.0420
LNINCOU
0.277313
0.349467
0.793530
0.4359
LNGOU
-0.676671
0.539711
-1.253765
0.2231
LNINVOH
1.111386
0.343390
3.236516
0.0038
LNINCOU
0.113081
0.367226
0.307932
0.7609
LNGOU
0.383454
0.241066
1.590659
0.1253
LNINVOH
0.778498
0.330333
2.356704
0.0273
C
3.622966
2.245063
1.613748
0.1215
T
-0.000249
0.026576
-0.009352
0.9926
LNINCOU
0.455976
0.391007
1.166159
0.2566
LNGOU
0.999442
0.265787
3.760316
0.0012
LNINVOL
0.290073
0.093281
3.109656
0.0053
C
3.641077
1.109715
3.281091
0.0034
LNINCOU
0.452626
0.153274
2.953044
0.0074
LNGOU
0.997752
0.190400
5.240297
0.0000
LNINVOL
0.290229
0.089673
3.236516
0.0038
LNINCOU
0.866107
0.104136
8.317101
0.0000
LNGOU
0.449765
0.109122
4.121689
0.0004
LNINVOL
0.249853
0.106018
2.356704
0.0273
LNINVOL
LNINVOH
LNINVOH
LNINVOH
AIC
SC
0.953012
-0.686260
-0.444319
0.954164
-0.741470
-0.547917
0.946869
-0.626258
-0.481093
0.986377
-2.007244
-1.765302
0.986996
-2.084163
-1.890609
0.981474
-1.762750
-1.617585
R2
variables
LNINVOL
Adjusted
errors
Notes: “LN” before the variables means the logarithm series for corresponding variables, the others are the same
with what’s in table3.
lnINVOLt  -5.20  0.28lnINCOU t -0.68lnGOUt  1.11lnINVOHt
lnINVOH t  3.64  0.45lnINCOU t  1.00lnGOU t  0.29ln INVOLt
(A1)
(A2)
Table A2. Regression for difference and residual (ECM for equation (A1) and (A2))
Explained
Exponent
Coefficients
Standard
t-Statistics
Probability
Adjusted
AIC
SC
-1.524635
-1.232104
R2
variables
variables
errors
DLNINVOL
C
0.050523
0.058562
0.862727
0.3990
T
-0.003075
0.002975
-1.033667
0.3143
- 13 -
0.596399
DLNINVOL
DLNINVOL
DLNINVOL
DLNINVOL
DLNINVOH
DLNINVOH
DLNINVOH
DLNINCOU
-0.069346
0.597731
-0.116015
0.9089
DLNGOU
-0.232438
0.473997
-0.490378
0.6295
DLNINVOH
1.302013
0.264247
4.927259
0.0001
RESID(-1)
-0.450511
0.160784
-2.801956
0.0114
C
0.010847
0.044304
0.244822
0.8091
DLNINCOU
-0.040672
0.598108
-0.068001
0.9465
DLNGOU
-0.174559
0.471483
-0.370234
0.7151
DLNINVOH
1.223567
0.253547
4.825791
0.0001
RESID(-1)
-0.426697
0.159397
-2.676938
0.0145
DLNINCOU
0.075411
0.356319
0.211639
0.8344
DLNGOU
-0.129453
0.424170
-0.305191
0.7632
DLNINVOH
1.219380
0.247243
4.931906
0.0001
RESID(-1)
-0.416267
0.150121
-2.772869
0.0114
DLNGOU
-0.146881
0.406966
-0.360917
0.7216
DLNINVOH
1.252251
0.188149
6.655634
0.0000
RESID(-1)
-0.427615
0.137141
-3.118074
0.0050
DLNINVOH
1.208449
0.141030
8.568731
0.0000
RESID(-1)
-0.422879
0.133906
-3.158039
0.0044
C
-0.024405
0.033129
-0.736679
0.4703
T
0.002234
0.001703
1.311559
0.2053
DLNINCOU
0.291089
0.330588
0.880519
0.3896
DLNGOU
0.796640
0.260199
3.061656
0.0064
DLNINVOL
0.322944
0.091455
3.531176
0.0022
RESID(-1)
-0.513505
0.173427
-2.960927
0.0080
C
0.003260
0.026002
0.125379
0.9015
DLNINCOU
0.326646
0.335354
0.974034
0.3417
DLNGOU
0.814530
0.264478
3.079764
0.0059
DLNINVOL
0.329181
0.092961
3.541064
0.0021
RESID(-1)
-0.527846
0.176171
-2.996217
0.0071
DLNINCOU
0.360145
0.197868
1.820128
0.0830
DLNGOU
0.828647
0.233640
3.546677
0.0019
DLNINVOL
0.328270
0.090479
3.628144
0.0016
RESID(-1)
-0.529928
0.171227
-3.094883
0.0055
0.595017
-1.549924
-1.306149
0.613146
-1.626931
-1.431911
0.629943
-1.704801
-1.558536
0.643936
-1.778897
-1.681387
0.676347
-2.560228
-2.267698
0.664693
-2.553559
-2.309784
0.680409
-2.632773
-2.437753
Notes: RESID(-1) is the one period lag series of corresponding residuals.
lnINVOL t  1.21 ln INVOH t 0.42(lnINVOL t-1  5.20  0.28lnINCOU t-1  0.68lnGOU t-1  1.11lnINVOH t-1 ) (A3)
 ln INVOH t  0.36ln INCOU t  0.83ln GOU t  0.33lnINVOL t 0.53(lnINVOH t-1  3.64  0.45lnINCOU t-1  1.00lnGOU t-1  0.29 ln INVOLt-1 ) (A4)
- 14 -