When will China become a zero-growth economy? An analysis using a Marxian Optimal growth model (1981-2009) Текст научной статьи по специальности «Социальная и экономическая география»

МЕЖДИСЦИПЛИНАРНЫЕ ИССЛЕДОВАНИЯ INTERDISCIPLINARY RESEARCH

Вестник Челябинского государственного университета.

2018. № 8 (418). Экономические науки. Вып. 62. С. 161—168.

УДК 339 ББК 65.9(5 Кит)

DOI 10.24411/1994-2796-2018-10816

WHEN WILL CHINA BECOME A ZERO-GROWTH ECONOMY? AN ANALYSIS USING A MARXIAN OPTIMAL GROWTH MODEL (1981—2009)

Hiroshi Onishi

Keio University, Tokyo, Japan

One of the biggest reasons for China suffering the 2015 stock market crash is overcapacity of production. Overdependency on investment clearly proves that China's economic transition has some way to go, because transformation from a high-growth economy to a medium-growth economy needs a gradual decrease in the share of investment on GDP. To analyze this trend, we introduce an optimal growth model called the Marxian Optimal Growth Model, which explains such a declining trend of the potential growth rate as an inevitable historical law. By estimating two sector production functions of this model using input-output tables, population census data, and some other statistics, this paper projects the optimal "capital — labor" ratio and other some important variables in the future stable state. Furthermore, we also provide a projection of when the Chinese economy will become a zero-growth economy. The results indicate that year to be 2033, at which time China's GDP per capita will be half that of Japan. As a whole, this paper reveals the difficulties China faces in making a soft landing in its efforts to attain medium growth.

Keywords: Middle Income Trap, Medium Growth, Chinese Economy, Marxian Optimal Growth Model, Soft Landing.

China has enjoyed high economic growth for several decades now, making it one of the world's leading economies. However, its long periods of high growth appear to be coming to an end, as evidenced by the Chinese stock market crash in 2015, which has revealed deep-seated structural problems such as its overcapacity of production. Overdependency on investment indicates that China is not transforming its economy successfully; transformation from a high-growth economy to a medium-growth one necessitates a gradual decrease in the share of investment on GDP. To analyze this trend, this paper employs an optimal growth model called the Marxian Optimal Growth Model. This model was first established by Yamashita and Onishi (2002), and later, it was applied to empirical studies of the Japanese, Chinese, and South Korean economies (Tazoe, 2011; Shen, 2011; Yin, 2013).

The model is called a Marxian model as it is based on the labor theory of value, and it was devised to explain the birth, growth, and death of capitalism. Here, the "birth of capitalism" was caused by the Industrial Revolution, while the term "growth" denotes fast-paced economic development and "death" will be realized when its

historical role will be fully achieved. Because capitalism's historical role is economic development, its death signifies the end of economic development. In this sense, the long-term trend of falling economic growth is the most important target to analyze. Thus, this model is an appropriate model for our study.

I begin this paper by explaining the basic structure of this model, and then, I estimate its parameters. Second, using these parameters and other variables, I calculate the target of capital accumulation and identify future stable states for the Chinese economy. Finally, the model is used to project the year in which the Chinese economy will become a zero-growth economy.

Basic Structure

of the Marxian Optimal Growth Model

First, I explain the basic structure of this model, which incorporates the investment goods sector and consumption goods sector. This type of division results from Marx's reproduction scheme and is useful to analyze whether the economy is overly dependent on investment. Indicating the investment goods sector and the consumption goods sector by suffix 1 and

0 renpecnively, 6hi urodoction jeun^tii^ii o= theue 1wo revion ntv Une; iu'lrtrdti^^d ton dnllnn 1 :

A —Annen,

Y — A f°a2 O 2 — 2 2

whrrA Y, K, L, and A mdwvte jdroduction, capital stock, labor inpud wrcd total factor productivity, and

1 cr part viitota1 ; ¡ill oc foi = W2 -c »t ») ond cf» jpuirr oidota1 t^ajtit^ai ntock (rd = K; p +Q +¡¡1; -i^e;ct in the consump-iton uronte ss^i;t;oi,f tdtce two pooduoticnfuncticmc c tin t^^rr^nr^i^^c^nne^lnl^o

Y(—=di{(i f oc wf {(1 f i) aiCl

Y2 —¡d^oitf- {af

(1)

{2)

Here, 5 and 9 are instrumental variables that are controlied to maximize the present valueofthe inter-temporalutilityshown tty thz ncxe obecctive Zunction:

u hj; t-p' izgs2(r )at,

where p is the subjective discount rate, e-pt translates the instantaneous utility into the present value, and this instantaneous utility function for consumptidn is logarithmic.

Therefore, this model is similar to the Ramaey Optimal Growth Model in the sense that repreywntpaive individuals maximize intertemporal utility bychooeing the ratio between Y1 and Y2. However, althougb thp Ramsey Model directly chooses the best savisy ratin on GDP, the Marxian Optimal Growth Model phgppns the best ratio of 5 and 9, thus indirectly determining tSta ratio between Y1 and Y2 in each period. Themodel ie devised as such to express the dynamics of till«;; m aero economy as a result of the division of labor. Because K denotes the production of labor, the ultimate and only factor of production is labor. This idea is expescsed clearly here as it is a model of the labor theory ol'velue.

The calculated growth pattern is shown in Fig. 1 where per capita capital accumulates from eeso to an optimal "capital — labor" ratio, shown as (JeSZ)*. Ie means that the accumulating speed changes from a higher speed to a lower one, and ultimately, it bee comes zero. Japan achieved zero-growth capital cc-cumulation in around 2000, and so did the US, who-e per capita real GDP growth was only 0.7 % from 2000—2010. Therefore, this model can be used to forecast and explain the long-term trend of economies. In the case of China, this long-term trend refers to the transformation toward medium growth, and ultimately, zero growth.

However, the purpose of this paper is not to devise a theory but to predict the growth path of the Chinese

economyas concretely as possible. According to the Marxian Optimal Growth Theory, if we can estimate all the parameters of the two production functions, the subjective discount rate p, and depreciation rate 5,we can calculate the optimal "capital — tabor" tadio, optimal tabor ihare, and share ofcapital staak fdd »he two sctnors in the frCutt ttabla atate using tpe following equations.1

+ A 1

p+s,

a2P jS

s [a2CiS + C2(C + S + (XjS )

- ai+Pi-l

' L 1-a'

l-s* = |Lî-

a2 PjS

L , apfSjii +132 {p + S(l - otj )} K, aS

1 - ^'jKJ V+s

(4)

(5)

Parameter Estimation

of the Two Production Functions

I proceed with the actual parameter estimation of these two production functions. Note that considerable effort was expended toward procuring and arranging the data as the data of capital stock and labor input are not divided into two sectors. Therefore, my first task was to take the capital stock data and labor input data and divide them by industries. cI use the following strategy to estimate these values. I first calculate the ratios of production for investment and consumption in each sector using input— outputtables2. Then,usingtheseratios,Idivideeach industry'scapital stockandlaborinput data between the two sectors.3,4 Finally, summing up each sector's

1 Notethatequation(3)appearsinfootnote5ofChapter 4in0nishi(2015),andadetaileddiscussiononequations (3)-(4) can be found in Onishi and Kanae (2015).

2 The input—output tables of China are published by China's State Statistical Bureau.

31 use each industry's ratio of (intermediate input + invest-ment)toconsumptionastheratioofthetwosectors. Therefore, I neglect the data on international trade and inventory. I add intermediate input data to investment data, as fixed capital is also a part of intermediate goods, and this propor-tionistoolargetoneglectforsomeindustries.Furthermore, another estimation method involves using the inverse ma-trix(I-inputcoefficientmatrix)-1.However,Idonotusethis method because it is too complex to calculate and because equations (1) and (2) already include a part of the matrix calculation even if this matrix has only two sectors.

4 Because the input—output tables of China's System of National Accounts (SNA) exist only for 1987, 1990, 1992, 1995, 1997, 2000, 2002, 2005, 2007, and 2010, the ratios of the two sectors for the other years are estimated by averaging the nearest actual data. For example, the data of 1991 are estimated by averaging the data of 1990 and 1992, and the data of 1993 and 1994 are estimated as a weighted average using the data of 1992 and 1995.

Industrial Revolution -► <-►

0

t

Feudalism Capitalism Socialism/Communism

Fig.l.GrowthPattern Explainedby theManoianOptimalGrowthModel Source:Onishi (2015.P.153).

divided capital stocks ahdlabor mputsgiv(spstw0 serietof (api\al slugk (atainbhthtectossaud two series of labor input data in both sectors respectively.

Nevertheless, the above-mentioned subdivision of capital stock data and labor input data was tedious. Estimating the labor input data is not so difficult as we have access to the population census data, and even if though the census is not conducted every year, I can estimate the labor input d without any data by extrapolating the original data of 1982, 1990, 1995, 2000, and 2010, assuming instant changing rates. Fortunately, the capital stock data from 1980—2009 are partly accessible inMeng (2012), while the missing data were provided tome by Ruoyang Meng, the author of Meng(201S).Ba-ed on the data provided by her, I set the perisd of epti-mation as 1980—2009.

In addition, while nominal data forS^ndT^an be sourced easily from the China Statisaical Yea-book, it is difficult to change them intorealperms, because the price indexes are not pe rfect from 1980 onwards. In the case of investment goods,dataare not available for the fixed capital investmentpride index before 1992. Therefore, I estimate the price indexes of investment goods before 1992 following Meng's (2012) method, using the pries inttex of the industrial sector. Similarly, I estimata the consumption price index before 1985 using workers' cost-of-living index.

Table 1 presents the calculated data used in the estimation of the production functions. The results of the ordinary least squares (OLS) estimations are as follows:

lah|oeSk = -0.27931 + 0.9113// lo ^ Ooj

(-18.7097) (31.3601) R = 0.97229 lo^ j- = -0.08526 + 0.5984181o^ j

(-7.63981) (38.99115) R = 0.98190/

As shown here, I assume constant returns to scale in order to calculate reasonable parameters.1 The estimated t-value and adjusted R-squared are satisfactory, and all the estimated parameters (a1= 0.911, = 0.598, p1= 0.989, and p2= 0.402) lie between 0 and 1. The reason a1 appears to be slightly higher than the ordinary estimators may be attributed to the fact that the share of capital includes intermediate inputs. Furthermore, in thist parameter estimation, the ratio K/L is calculated using the last term of K. This is because K is expressed as end-of-term stock as shown in Table 1. Therefore, all parameter estimations are conducted using data from 1981—2009 instead of data from 1980—2009. Finally, total factor productivities A1 and A2 areestimatedfromtheconstantterms of the

1 I attempt many types of estimations. For example, I drop the assumption about constant returns to scale, and I also adopt a constant speed of technological progress in A1 and A2. However, the former case does not provide reasonable parameters, and I do not use the latter case in this paper because the actual value of K is already understood to include technological progress in price terms.

Table 1

Estimated Real Production, Labor Input, and Capital Stock of Two Sectors (unit: 100 million yuan in 1980 constant price, 10 thousand persons, end-of-term capital stock)

Year Y2 L, L2 Ki K2

1980 1599 3008 27321 22082 2277 1027

1981 1619 3319 28034 22724 2672 1215

1982 1772 3596 28768 23381 3193 1480

1983 2025 3915 29525 24054 3801 1764

1984 2483 4479 30304 24744 4591 2124

1985 3351 5001 31108 25450 5725 2590

1986 3722 5351 31936 26172 7099 3033

1987 4116 5705 32790 26911 8722 3542

1988 5044 6052 34746 26592 10634 4004

1989 5394 5821 36781 26239 11973 4275

1990 5567 6119 38898 25850 13184 4495

1991 6274 7004 38435 26964 14745 4862

1992 7699 8208 38037 28019 17242 5557

1993 11132 9206 39669 27049 20637 6416

1994 13183 8596 41344 26045 23818 7417

1995 15089 10150 43064 25002 26616 8615

1996 15807 11187 43105 25747 28864 10497

1997 15576 11928 43183 26463 30620 12787

1998 15752 12884 44276 26174 35823 13345

1999 16289 14097 45457 25805 41385 13576

2000 16947 15523 46733 25352 47372 13250

2001 19092 16771 46212 25819 47400 18685

2002 21677 18140 45772 26205 48778 25977

2003 26261 19392 47644 24278 50910 33832

2004 31641 21031 49491 22377 53959 43182

2005 34374 23450 51321 20494 58092 54381

2006 39471 26297 51672 20089 79438 51958

2007 45099 29333 52061 19646 106691 47714

2008 53428 32137 53158 18495 126640 55404

2009 61782 35712 54315 17264 156547 67064

Source: as explained in the text.

above equations. That is, A1 is 10-027931 = 0.52564,

and A is 10-'

5 = 0.82175.

Estimation of Subjective Discount Rate and Depreciation Rate

Although I estimate all parameters in the production functions, two more parameters require to be estimated for the calculation of equations (3)—(5). These are the subjective discount rate p and depreciation rate 5.

The depreciation rate 5 is relatively easy to estimate using the data in Meng (2012). Based on her industrially classified estimation of depreciation, I calculate the weighted average of depreciation using Meng's estimation of industrially classified capital

stock for 1995 (the middle year of the estimation period) as the weight. My result indicates that 5 equals 0.17198.

On the other hand, the subjective discount rate is estimated by an application of Piketty's return on capital (r) > growth rate of the economy (g) theory. Strictly speaking, under the assumption of logarithmized instantaneous utility function, r = g + p can be proved theoretically,1 and Piketty also refers to this relationship in his book. Therefore, first, I calculate the average of the operating surplus over K from the input—output tables for 2000,

1 Onishi and Kanae (2015) also proved this equation for the Marxian Optimal Growth Model.

2002, 2005, and 2007. This value equals 0.1772. Then, I take the real-term per capita GDP growth rate from the China Statistical Yearbook (0.1008). Using these values, I calculate the gap between r and g as 0.1772 - 0.1008 = 0.0764. This is the subjective discount rate.

Projection of the Future Stable State

Using the estimated parameters, I calculate the optimal "capital — labor" ratio, optimal labor share, and share of capital stock for the two sectors in the future stable state with equations (3)—(5). The results are as follows.

(1) The optimal "capital — labor" ratio (K/L)* in the future stable state is 293.45 thousand yuan in 1980 constant price. This value is about nine times higher than the actual level in 2009 (31.2 thousand yuan in 1980 constant price). This level of per capita capital also means that total capital stock in the future stable state should be nine times higher than in 2009 if total labor force remains constant.1 However, the current year is 2015, and total GDP in 2015 is about twice as large as that in 2009. In this sense, per capita capital that is nine times higher than in 2009 may translate to per capita capital that is about 4.5 times higher than in 2015. China's urban areas are well-developed in terms of infrastructure, and factories face over-accumulation of capital. However, its rural areas are not as well developed. This result may reflect this situation.

However, although we need much more accumulated capital, too early an accumulation causes problems, because the economic structure cannot change smoothly from accelerated capital accumulation (implying China's overdependency on investment) to the stable state with no net investment. In this sense, such a transition should be taken step by step as shown in Fig. 1. However, at least until 2009, capital accumulation sped up in reality, as shown in Fig. 2. This poses a serious problem for an economy looking to attain zero growth.

Another point that should be discussed here is the problem of individual interests which sometimes oppose social interest. For example, the construction industry is not concerned about the social efficiency of their outputs. Neither does the government bureaucracy, which has a conflict of interest in such

1 Shen (2011) alone calculated the stable state "capital — labor" ratio as 49.335 thousand yuan in 1991 constant price, and it is about twice as high as that in 2005. However, 49.335 yuan in 1991 constant price equals 29.23 thousand yuan in 1980 constant price, the "capital — labor" ratio that must be achieved in 2009 according to the actual data. In this sense, Shen underestimated the stable state "capital — labor" ratio.

cases. Therefore, it is hard to realize an efficient society without fighting against such interest groups and their representatives in the government. If the present anti-corruption movement takes up cudgels against the industrial-bureaucracy complex, China's future depends deeply on the result of this struggle. Thus, political directions and associated struggles are closely connected to economic performance.

(2) The optimal labor share in the investment goods sector (1 - s*) in the future stable state is 0.0919. This figure implies that it will be difficult to transform the Chinese economy from its present serious condition, because the "capital — labor" ratio in 2009 is much higher than our result and continues to rise as shown in Fig. 3. Although the share of investment on GDP shows a slight decline after 2010, it is not enough. Thus, despite President Xi Jinping's strong leadership, China may find it very difficult to transform its economic structure.

(3) The optimal share of capital stock in the investment goods sector (1 — 9*) in the future stable state is 0.6298. Because this figure is close to the actual level in 2009 (0.7001), there will be no difficulty in transforming this part of the economic structure. However, even if it is easy to stop companies from overinvesting, it is not easy to trim the labor force and shift it from the unnecessary sectors to the necessary ones, because of multiple problems such as lack of or differences in employees' professional education, migration, and possible objections from stakeholders. In this sense, this result cannot ease the difficulties China will face in trying to transform its economy.

In addition, the ratios s*/(1 - s*) and 9*/(1 - 9*) indicate the optimal degree of capital intensity and labor intensity respectively. The results imply that only one-tenth of the total labor should be used in the investment goods sector while 63% of the total capital should be used in that sector in the future stable state. Therefore, investment goods production should become more capital-intensive, and on the other hand, consumption goods production should become more labor-intensive. This result may reflect the possible tertiarization of the consumption sector.

When Will the Chinese Economy

Become a Zero-Growth Economy?

The last task of this paper is to project the year the Chinese economy will become a zero-growth economy. Although this type of projection was conducted by Shen (2011), his methodology was rough, and he did not present a theoretical background on this projection. Therefore, I introduce a new methodology to estimate this year (see Fig. 4).

Fig. 2. Marco-level Trends in Capital—Labor Ratio (unit: 10 thousand yuan in 1980 constant price) Source: Explained in the text.

Fig. 3. Trend of Labor Share in the Investment Goods Sector

Source: Explained in this text.

I maketwoassumptions: (1- s*)and(l -y*) willdeceaselinearly andthetotallabor forcewill be constant;. Allhough the forsnes-ssumption can ba psovedmathematically,economscSheoty cosalso identify titrse exureeu ieni as necesshg <ae, ars in o r earlier discussion. If so, under this assump-tion,()-s( tYigft^ia from 76%(n00gd to as/, at thestab(esSatea ant (^S"v^aOhd-U(c^ra

70% to 63%, as shown in Fig. 4. However, because we ato sot hhow tiie final .nsr, (hat is, ah( yeor wh^sdtni( agOSlp—kwin oeash9% tad 6h% res^aeo-t^^^}^, t consluottgn ^^^^ti^^tior^ST^i^c^^r aarta ous assumptions; for example, I check the results for (1 - i) a—d(t — (p)atn% -nd63%,jespoctivel—, in2020,2-yt,0040tandaoot,inordertoppoj(ct

whon nsino-^sn Uesomeozoro-growthectnomy

(Fih. s).

Tltr 3 alcttlations ercett dtrol ehe s 'cnjnital — laboa" rattownll oots—ochShe taogrtvalpei—Sassumethe valuen os— % aeid 63 % fou ld . m and ,s . 9a respectively, in 2030, and it will exceed the target if I assume thesdmevaOues far (l-s)and (1-u)ln 20sh. —here-foru,t ayhtinueoУssktngthestmefor2a3l, 2032, 2sdh, a—tl 0034, until S -ttS Piat t—% "capital — laber" ratio w—s be ctose to re—chm0 its taoget in °033. iysiis ptnjection ls cor—ecO growth w(11

sto)) in about 18 years from now (2015). This projection predates Shen's result (2040). However, the new projection may pe m—re ren^.a giue— thst ws use amoresoplri sOicaseds>Pojrc(ion me1nadnl-gy

1 - 1 - 9

Fig. 4. Estimating When China Will Attain Zero Growth

The above-mentioned resultleadstocertainother implications. Take,forexample,outocolection that the GDP growthrate will follfrom about 7%to zero in the next 18 years, which implies that the potential GDP growth rott will fall by 3.5% eva^yeos.An-other implication irshatthe time difference between Japan and China in terms of zero-growth capital accumulation is obout 40 yeatsS.ajaan's zero^owth started araundrt9e).Furtnarmore, iOthecesulto are correct, today's China should be on par with Japan in the 1970s, a country that suffered the oil shock and consequently transformed itself from a high-growth economy to a medium-growth one. In this sense, today's shock to China should be compared with the Japanese experience of the oil shock; then, it appears that China will suffer another shock 18 years later.1 Moreover, because every zero-growth economy is accompanied by an unstable political situation,2 there is a high possibility that China will also face such a situation.

1 A 40-year delay behind Japan translates to a delay of about 20 years behind South Korea. If so, the present crisis in China can be compared to the hardships faced by Korea in the aftermath of the Asian financial crisis of 1997, which changed the Korean economy from a high-growth economy to a medium-growth economy. This experience is very suggestive for China.

2 Generally, zero-growth destabilizes the political ma-

chinery. See Chapter 2 in Usui and Onishi (2014).

adyitios,we cahmakemwoptojectionsoo GDP andGDt per cayitain 2333.Totai zohPumptlonhOss total investment will reach 58,891 trillion yuan in constant 1980 price, which is about six times larger fhanthet io 2000. IZ srpGPywillsloobe aboutsix times larger than in 2009. Because China's GDP surpassed Japan's GDP in 2010 and became twice as la^essJa^n's in2Cia,CulyakGDPln 303rwill beakyft fivhtimhhAhger hhanihalaZJapan (nrstuh ing zero-growth in Japan), and its GDP per capita will be about half that of Japan.

Some may disagree as to whether China's GDP will be large enough when it reaches six times the GDP of Japan or whether half of GDP per capita is too small. However, the point here is that we have ascertained that China's growth rate is falling and that it has a high possibility of becoming a zero-growth economy. Some years ago, when I shared this notion of mine, that China will eventually become a zero-growth economy, all my Chinese friends disagreed.

China is led by a Marxist party, and Marxists are typically concerned about historical inevitability, including that related to economic trends, which is independent of other interests. China also faces other problems such as resource constraints, environmental issues, a falling trend in its labor force, and population aging. It is important that China recognizes and tackles these issues in tandem with its economic challenges?

References

1. Meng R. The Estimation of Industry-level Capital Input for China. Mita Business Review. The Society of Business and Commerce Keio University, 2012, vol. 55, no. 3, pp. 31—62.

2. Onishi H. Marxian Economics. Tokyo, Keio University Press, 2015. (In Japanese).

3. Onishi H., Kanae R. "Age of Large-Population Countries" and the Marxian Optimal Growth Theory. Mita Journal of Economics. The Keio Economic Society, 2015, vol. 107, no. 3, pp. 139—156. (In Japanese).

4. Onishi H., Kanae R. Piketty's r>g Is Caused by Labor Exploitation. Marxism 21, 2015, vol. 12, no. 3, pp. 319—331.

5. Shen Y. A Marxian Optimal Growth Model of China: 1981—2005. The Economic Review. Kyoto University Economic Society, 2011, vol. 185, no. 2, pp. 83—98. (In Japanese).

6. Tazoe A. Parameter Estimation for the Marxian Optimal Growth Model. The World Review of Political Economy, 2012, vol. 2, no. 4, pp. 635—645.

7. Usui Toshimasa, Onishi H. From Growth State to Matured Society. Kadensha, 2014. (In Japanese).

8. Yamashita Y., Onishi H. Reconstructing Marxism as a Neoclassical Optimal Growth Model. Study on Politics and Economy. Institute of Politics and Economy, 2002, no. 78, pp. 25—33. (In Japanese).

9. Yin P. A Marxian Optimal Growth Model of Korea, mimeo, 2013.

Information about the author

Onishi Hirichi — Professor of Keio University, Faculty of Economics, Professor Emeritus of Kyoto University, Tokyo, Japan. ohnishi@f6.dion.ne.jp

Bulletin of Chelyabinsk State University.

2018. No. 8 (418). Economic Sciences. Iss. 62. Рp. 160—168.