1. Accounting for China’s Productivity Performance across Regions in an Industry Origin Framework
Zhan Li
Institute of Economic Research
Hitotsubashi University, Tokyo
Prepared for the Fifth World KLEMS Conference
Harvard University, June 5th, 2018

2. 1. Introduction
Under the institution of “regional decentralized authoritarian” regime (Xu, 2011), competitions among growth-motivated local governments have in a large part accounted for the spectacular economic growth of China during past nearly four decades. Local governments tend to adopt industry policy to instruct the flow of factor inputs among industries to stimulate regional economic growth.
Instead of market mechanism, such governmental interventions tend to introduce misallocation of resources among industries and further affect the regional distribution of development and productivity growth of industry.
Thus, the regional effects cannot be ignored to comprehensively understand the Chinese growth model. However, the existing KLEMS type studies have mainly focused on industries with little regional dimension.

3. Take a step forward from the work of Wu (2016) who investigated the productivity growth of Chinese economy based on 37 sectors at national level, the purpose of this study is to explore how regional distribution of sectors affect both the economic growth and productivity growth in China.
To conduct this study, two issues have to be resolved: one is methodology used to analyze regional effects and the other is data.
As for methodology, we adopt aggregate production possibility frontier (APPF) framework and further incorporates Domar aggregation scheme by adding regional dimension.
As for data, we construct regional data that covers 31 regions and further each region consists of 37 sectors over the period of

4. 2. APPF Framework Including Regions
The gross output of an industry 𝑖 is a function of capital, labor, intermediate inputs and technology, indexed by time 𝑇, that is
(1) 𝑌 𝑖 = 𝑓 𝑖 ( 𝐾 𝑖 , 𝐿 𝑖 , 𝑋 𝑖 ,𝑇)
Under the assumptions of firms are price-taker in factor markets, full input utilization, and constant returns to scale, the growth of output can be expressed as the cost-share weighted growth of all inputs and technological change:
(2) ∆𝑙𝑛 𝑌 𝑖 = 𝑣 𝑖 𝐾 ∆𝑙𝑛 𝐾 𝑖 + 𝑣 𝑖 𝐿 ∆𝑙𝑛 𝐿 𝑖 + 𝑣 𝑖 𝑋 ∆𝑙𝑛 𝑋 𝑖 + 𝑣 𝑖 𝑇
where 𝑣 𝑖 𝐾 = 𝑃 𝑖 𝐾 𝐾 𝑖 𝑃 𝑖 𝑌 𝑌 𝑖 , 𝑣 𝑖 𝐿 = 𝑃 𝑖 𝐿 𝐿 𝑖 𝑃 𝑖 𝑌 𝑌 𝑖 , and 𝑣 𝑖 𝑋 = 𝑃 𝑖 𝑋 𝑋 𝑖 𝑃 𝑖 𝑌 𝑌 𝑖
And
𝑣 𝑖𝑡 𝐾 = 𝑣 𝑖𝑡−1 𝐾 + 𝑣 𝑖𝑡 𝐾 2 , 𝑣 𝑖𝑡 𝐿 = 𝑣 𝑖𝑡−1 𝐿 + 𝑣 𝑖𝑡 𝐿 2 , and 𝑣 𝑖𝑡 𝑋 = 𝑣 𝑖𝑡−1 𝑋 + 𝑣 𝑖𝑡 𝑋 2 , and 𝑣 𝑖 𝐾 + 𝑣 𝑖 𝐿 + 𝑣 𝑖 𝑋 =1

5. Since aggregation is a value-added concept, Equation 2 can be written as:
(3) ∆𝑙𝑛 𝑌 𝑖 = 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝑉 𝑖 + 𝑣 𝑖 𝑋 ∆𝑙𝑛 𝑋 𝑖
where 𝑉 𝑖 is the real value-added of industry 𝑖 and 𝑣 𝑖 𝑉 is the two- period average of nominal share of value-added in industry gross output.
Combing Equations 2 and 3, we can obtain an expression for the sources of industry value-added growth:
(4) ∆𝑙𝑛 𝑉 𝑖 = 𝑣 𝑖 𝐾 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝐾 𝑖 + 𝑣 𝑖 𝐿 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝐿 𝑖 𝑣 𝑖 𝑉 𝑣 𝑖 𝑇

6. The aggregate growth rate of value added is the weighted sum of growth rate of value added across industries:
(5) ∆𝑙𝑛𝑉= 𝑖 𝑤 𝑖 ∆𝑙𝑛 𝑉 𝑖
where 𝑤 𝑖 = 𝑃 𝑖 𝑉 𝑉 𝑖 𝑖 𝑃 𝑖 𝑉 𝑉 𝑖 , and 𝑤 𝑖 = 𝑤 𝑖𝑡−1 + 𝑤 𝑖𝑡 2

7. Combining Equations 4 and 5, we introduce Domar weights (Domar 1961), i.e. a ratio of each industry’s share in total value added to the proportion of the industry’s value added in its gross output and yield a new expression of aggregate value added growth by weighted contribution of industry capital, labor and TFP growth:
(6) ∆𝑙𝑛𝑉= 𝑖 𝑤 𝑖 ∆𝑙𝑛 𝑉 𝑖 = 𝑖 𝑤 𝑖 𝑣 𝑖 𝐾 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝐾 𝑖 + 𝑣 𝑖 𝐿 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝐿 𝑖 𝑣 𝑖 𝑉 𝑣 𝑖 𝑇
where 𝑤 𝑖 is the size of industry 𝑖 value added in aggregate value added, 𝑣 𝑖 𝐾 and 𝑣 𝑖 𝐿 are the shares of factor income in the gross output of industry 𝑖, 𝑣 𝑖 𝑉 is the share of value added in gross output of industry 𝑖.

8. The aggregate growth rate of TFP is defined as:
(7) 𝑣 𝑇 =∆𝑙𝑛𝑉− 𝑣 𝐾 ∆𝑙𝑛𝐾− 𝑣 𝐿 ∆𝑙𝑛𝐿
Combining Equations 6 and 7, we get Domar-weighted TFP growth and reallocation effects of K and L:
(8) 𝑣 𝑇 = 𝑖 𝑤 𝑖 𝑣 𝑖 𝑉 𝑣 𝑖 𝑇
+ 𝑖 𝑤 𝑖 𝑣 𝑖 𝐾 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝐾 𝑖 − 𝑣 𝐾 ∆𝑙𝑛𝐾
+ 𝑖 𝑤 𝑖 𝑣 𝑖 𝐿 𝑣 𝑖 𝑉 ∆𝑙𝑛 𝐿 𝑖 − 𝑣 𝐿 ∆𝑙𝑛𝐿

9. Since each industry 𝑖 has a regional (𝑗) distribution, Equation 6 can be further extended to regional level:
(9) ∆𝑙𝑛𝑉= 𝑖 𝑤 𝑖 ∆𝑙𝑛 𝑉 𝑖 = 𝑖 𝑤 𝑖 ∙ 𝑗 𝑤 𝑖𝑗 ∆𝑙𝑛 𝑉 𝑖𝑗
= 𝑖 𝑗 𝑤 𝑖 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝐾 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐾 𝑖𝑗 + 𝑣 𝑖𝑗 𝐿 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐿 𝑖𝑗 𝑣 𝑖𝑗 𝑉 𝑣 𝑖𝑗 𝑇

10. By also extending Equation 8 to regional level, we can get:
(10) 𝑣 𝑇 = 𝑖 𝑗 𝑤 𝑖 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝑉 𝑣 𝑖𝑗 𝑇
+ 𝑖 𝑗 𝑤 𝑖 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝐾 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐾 𝑖𝑗 − 𝑣 𝐾 ∆𝑙𝑛𝐾
+ 𝑖 𝑗 𝑤 𝑖 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝐿 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐿 𝑖𝑗 − 𝑣 𝐿 ∆𝑙𝑛𝐿

11. In parallel, the aggregate economic growth can be also written as the weighted sum of growth rates across regions:
(11) ∆𝑙𝑛𝑉= 𝑗 𝑤 𝑗 ∆𝑙𝑛 𝑉 𝑗 = 𝑗 𝑤 𝑗 𝑣 𝑗 𝐾 𝑣 𝑗 𝑉 ∆𝑙𝑛 𝐾 𝑗 + 𝑣 𝑗 𝐿 𝑣 𝑗 𝑉 ∆𝑙𝑛 𝐿 𝑗 𝑣 𝑗 𝑉 𝑣 𝑗 𝑇
where 𝑤 𝑗 is the size of region 𝑗 value added in aggregate value added, 𝑣 𝑗 𝐾 and 𝑣 𝑗 𝐿 are the shares of factor income in the gross output of region 𝑗 , 𝑣 𝑗 𝑉 is the share of value added in gross output of region 𝑗.

12. Equation 8 becomes:
(12) 𝑣 𝑇 = 𝑗 𝑤 𝑗 𝑣 𝑗 𝑉 𝑣 𝑗 𝑇
+ 𝑗 𝑤 𝑗 𝑣 𝑗 𝐾 𝑣 𝑗 𝑉 ∆𝑙𝑛 𝐾 𝑗 − 𝑣 𝐾 ∆𝑙𝑛𝐾
+ 𝑗 𝑤 𝑗 𝑣 𝑗 𝐿 𝑣 𝑗 𝑉 ∆𝑙𝑛 𝐿 𝑗 − 𝑣 𝐿 ∆𝑙𝑛𝐿

13. Since each region consists of 37 industries, we can get the following expression by extending Equation 11 to industry level:
(13) ∆𝑙𝑛𝑉= 𝑗 𝑤 𝑗 ∆𝑙𝑛 𝑉 𝑗 = 𝑗 𝑤 𝑗 ∙ 𝑖 𝑤 𝑖𝑗 ∆𝑙𝑛 𝑉 𝑖𝑗
= 𝑖 𝑗 𝑤 𝑗 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝐾 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐾 𝑖𝑗 + 𝑣 𝑖𝑗 𝐿 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐿 𝑖𝑗 𝑣 𝑖𝑗 𝑉 𝑣 𝑖𝑗 𝑇
Finally, the aggregate TFP is:
(14) 𝑣 𝑇 = 𝑖 𝑗 𝑤 𝑗 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝑉 𝑣 𝑖𝑗 𝑇
+ 𝑖 𝑗 𝑤 𝑗 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝐾 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐾 𝑖𝑗 − 𝑣 𝐾 ∆𝑙𝑛𝐾
+ 𝑖 𝑗 𝑤 𝑗 𝑤 𝑖𝑗 𝑣 𝑖𝑗 𝐿 𝑣 𝑖𝑗 𝑉 ∆𝑙𝑛 𝐿 𝑖𝑗 − 𝑣 𝐿 ∆𝑙𝑛𝐿

14. 3. Data Construction by Sector and Region
Regional Output Data
1. Regional nominal accounts…
Problems in official statistics: 1) coverage: “above designated size” industrial enterprises only, no data for “below designated size” ones; 2) inconsistent industry classification along the time; 3) discrepancy between national total and regional accounts due to various reasons, such as double accounting, statistical system, and so on.
Solution: 1) regional input-output tables are adopted and values of three broad sectors (primary, secondary and tertiary) from Regional Yearbooks are used as regional control totals; 2) discrepancy is redistributed to regions based on the structure of newly constructed regional data.

15. 2. Regional price indices…
Basically, regional sector-specific PPIs are used for industrial sectors, and relevant components of regional CPI are used for non-industrial sectors.
Regional Capital Input
Problems in official statistics: 1) no data of capital stock with SNA standard; 2) investment data mix up with various types of assets ; 3) lack of data on investment price indices and depreciation rates at sectoral level.
Solution: 1) book value of stock is adopted to derive investment flow further with two adjustments: one is to remove investment in residential structures, the other is to add back investments not covered by official statistics; 2) sector-specific types of assets, depreciation rate and investment price indices of regions are mainly based on national data.

16. Regional Labor Input
Problems in official statistics: 1) inconsistency of employment data along time; 2) no data of hours worked for sectors; 3) no cross- classified data for employment and compensation, only available data of average wage by sectors.
Solution: 1) using marginal matrices of employment from regional Population Census to construct full-dimensioned employment matrices; 2) compensation matrices are constructed by applying the ratio of compensation of each attribute to sectoral average wage at national level to regions.

17. 4. Growth Rates (%)

18. TFP Growth of Region (%)

21. Industry®ion Perspective National TFP Growth (%)
Aggregate TFP
0.74
2.28
0.10
0.96
1. Domar-weighted TFP
0.47
1.76
-0.30
0.58
2. Reallocation of K
-0.10
-1.04
-0.14
-0.37
3. Reallocation of L
0.36
1.57
0.55
0.75

24. Annual Growth Rates of Reallocation Effects,1992=100

25. 5. Conclusions
1. The capital and intermediate inputs are still the main growth sources of both regional and national economy.
2. TFP growth performance demonstrates obvious disparity among regions. The national TFP achieves moderate growth after Xiaoping Deng's southern tour speech in 1992, peaks in WTO period ( ), and declines dramatically during post-Crisis period. On average, the annual growth rate of national TFP is 0.96% during , contributing around 10% to gross value added in China.
3. From industry perspective, the closer to final consumption, the better TFP growth, such as ICT sector, Manufacturing of Machinery and Equipment, and so on.
4. From regional perspective, TFP growth in coastal regions is better than that in central and western regions.

26. 5. Both reallocation effects of capital and labor are significant in China. Since capital is heavily affected by administrative planning rather than market mechanism, its reallocation effect is negative at both regional and national levels. The positive reallocation effect of labor is benefited from relaxation of various restrictions on labor mobility, which tends to be market-oriented.
6. Adding region in the framework improves both reallocation effects of capital and labor, which represents that the barriers for preventing factors of production from flowing across regions will not be conducive to factor allocations. Taking China as a united market and allowing factors of production to flow freely across sectors and regions will promote the overall economic growth.

27. Main References
Jorgenson, Dale W., Mun S. Ho and Kevin Stiroh “Information Technology and the American Growth Resurgence.” Productivity (volume 3), The MIT Press, Cambridge, London
Wu, Harry X “Sustainability of China’s Growth Model: A Productivity Perspective.” China & World Economy, Vol. 24, No. 5, pp
Xu, Chenggang “The Fundamental Institutions of China’s Reforms and Development.” Journal of Economic Literature, Vol. 49, No. 4, pp

28. Thank you !