Discussion Paper No.222

DOES REGIONAL SIZE MATTER INREGIONALIZATION OF NATIONALINPUT-OUTPUT TABLE BY THE FLQ FORMULA?
-A CASE STUDY OF CHINANobuhiro Okamoto
Professor at the Department ofInternational Relations
Daito Bunka University
April

2014

I

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, Japan

DOES REGIONAL SIZE MATTER IN REGIONALIZATION OF NATIONALINPUT–OUTPUT TABLE BY THE FLQ FORMULA?†- A CASE STUDY OF CHINA NOBUHIRO OKAMOTO
Professor at the Department of International Relations, Daito Bunka University

Abstract
This paper employed the regionalization method of the use of location quotient family such as
Location Quotient (LQ), Cross Industry Quotient (CIQ), Flegg’s Location Quotient (FLQ) and theaugmented FLQ (AFLQ), that take the regional size into consideration, by using the Chinese
national input–output table. The paper examines the accuracy of the output multiplier derived by theestimated regional input–output tables, comparing with the survey-based Provincial input–output
tables. The result shows us that LQ and CIQ of 10 provinces (one third of the total region) is better
than FLQ, and AFLQ gives better estimates in all regions under the appropriate δ value, compared to
LQ and CIQ. However, a reasonable value for δ, which has been reported a relatively stable inprevious research, would be widely distributed for both FLQ and AFLQ for all provinces. Therefore,
the regional size does not matter in regionalization by the FLQ formula based on empirical evidence.

JEL Classification: O53, R10, R15
Keywords: Regionalization, Input–Output analysis, FLQ, Regional size, Regional specialization†

Preliminary version of this paper was presented at the 50th Annual Meeting of the Japan Section of the Regional
Science Association International (JSRSAI) held at Tokushima University in 2013. I would like to thank the panel
members and audience for their comments. This study is funded by the Grants-in-Aid for Science Research (Project
Number: 24530268, Research Leader: Nobuhiro Okamoto).

Corresponding Author. E-mail: okamoton@ic.daito.ac.jp11．INTRODUCTION
The Xi Jinping/Li Keqiang regime in China commenced in 2012. Li Keqiang stressed on
urbanization after being appointed the new Premier of the State Council of the People’s Republic ofChina. In order to analyze the effect of this urbanization on the economy, the input–output model
becomes useful. However, although China began publishing input–output tables at the provincial
level, tables for cities and sub-regions still do not exist. Chinese provinces are considered regions;however, with an average population of about 40 million people and a GDP of about $150 billion,
each province may seem as large as an entire country. If there were input–output models at the levels
ranging from province to city and sub-region, it would greatly help in analyzing regional
development in China.
How would one estimate an input–output model for cities and sub-regions? One effective method
would be to regionalize the currently available provincial input–output table by city and sub-region.
However, it would be difficult to examine the effectiveness of regionalizing the provincial
input–output table without having a survey-based input-output table at the city and sub-regional
level.
Thus, this paper uses the national and provincial input–output tables that are available,
regionalizes the national input–output table to estimate a provincial input–output model, andexamines the effectiveness of the model by comparing it to the actual provincial input–output table.
Specifically, the paper examines the applicability of the FLQ and AFLQ formulas proposed by Flegg
et al. (1995), Flegg and Webber (1997), and Flegg and Webber (2000), that take the “Regional Size”
into consideration.
This paper is organized as follows. After providing an overview of the regionalization methods inthe next section, and the data actually used, I report in Section 3 the results of the regionalization
performed by using the national input–output table of China, and provide a summary at the end.

2．MODEL AND DATA
2.1 Regionalization Methods
A common method of studying regionalization has been to derive the regional input coefficient by
multiplying the national technical coefficient1 with data related to the regional input coefficient.
Therefore, it is expressed as:.
Here,is the input coefficient of region r,is the national technical coefficient (excluding
imported goods), andis the coefficient that reflects the input of the region. However, due to thedifficulty in obtaining the data, it is often assumed thator
. This paper also
maintains the same assumption.
Next, since the regional input coefficient includes goods brought in from other regions, theregional technical coefficient, to show that the region inputs goods only from within, is calculated bymultiplying the regional input coefficient with the regional self-sufficiency rate.

Since it is hard to obtain the regional self-sufficiency rate
, location coefficients (location
quotient (LQ) and its derivative quotients) have been used as substitutes. This is based on the logic
that the region is self-sufficient when the location coefficient is greater than 1, as it implies that theindustry is more concentrated in the region than in the rest of the country. Likewise, it is assumed
that the industry is less concentrated in the region than in the rest of the country when the location
coefficient is less than 1, indicating that the region imports the difference from other regions.
Specifically, location quotient is calculated and regionalization is done by it as follows:1

Miller and Blair (2009) distinguish national input coefficient, which includes imported goods in the national
input-output table, and national technical coefficient, which does not include imported goods. This paper employs
these terms.

2

· · · (1)
Here,
and
refer to gross output data (employment, added value, etc.) for region r andnation n, respectively. The national technical coefficient is slightly adjusted downward based on how
small the location coefficient is, only when the location coefficient is less than 1.
This regionalization is a uniform adjustment that takes only the supply side (the row side) into
consideration. Therefore, the Cross Industry Quotient (CIQ), a method that takes the demand side
sectors (the column side) into consideration, was developed. This method considers the relative
importance of the transaction value between the supply side sector i and the demand side sector j in
the region and nation. The CIQ and its regionalization is written as:· · · (2)This implies that the inputs from sector i to sector j in the region are completely covered by the
supply within the region, when the gross output of sector i in the region relative to the nation isgreater than the gross output of sector j in the region relative to the nation (). Likewise,
when the positioning of sector i is relatively small compared to sector j (), it indicates that
although the inputs of sector j in the region are partially supplied by sector i within the region, therest is purchased from other regions.
Because, and the diagonal cells are, those cells are sometimes adjusted

separately by using the LQ formula (Smith and Morrison (1974), Flegg et al. (1995)).
· · (3-1)· · · (3-2)
However, the CIQ does not take regional size into account. Since it is possible for imports fromother regions to increase when regional size is small, the Flegg’s Location Quotient (FLQ) was
developed (Flegg et al. (1995), Flegg and Webber (1997, 2000)).

Here, because,, regionalization is performed as follows:· · · (4)

Employment is used as a variable that indicates ”Regional size”. When regional size is the sameas the size of the nation, it is depicted as. This is based on the assumption that2

the inflow and import will diminish as regional size increases.
In this model, the size of the parameter δ becomes the focus of argument. Flegg et al. (1995)
2

Miller and Blair (2009) question this logic. In addition, imports tend to increase in China as per capita
GDP—rather than the size of the region—becomes higher (Okamoto, 2013).

3

deems δ = 0.3 to be appropriate. Subsequently, Flegg and Tohmo (2013) examined the case of 20
regions in Finland, indicating that the range of 0.25 ± 0.05 fits well despite regional differences.3
Studies by Bonfiglio and Chelli (2008) and Bonfiglio (2009) that use the Monte Carlo simulation
state that 0.3 ± 0.05 produces a good fit. For an industry-by-industry δ, Kowalewski (2013) showsthat the best fit in the case of Germany is between 0.11 and 0.17. These previous empirical analysis
provide the facts that regional size does matter in the regionalization of national input-output table.
Another augmented version of the FLQ has been proposed by Flegg and Webber (2000) in
response to the argument by McCann and Dewhurst (1998) that purchases within the region would
increase when a sector is clustered in that region (regional specialization). It is assumed that
regionalization reduces the input coefficient in the national table; however, if there is a regional
specialization of a sector, that fact must be incorporated (i.e. the technical coefficient becomes larger
than the national technical coefficient). Thus, the augmented FLQ (AFLQ) was proposed.

· · · (5)represents the regional specialization of sector j. The national technical coefficientis adjusted upward when this density becomes 1 or higher.4
This paper proposes another version of a quotient in the LQ family. As mentioned above,
McCann and Dewhurst (1998) were skeptical of the approach to reduce the technical coefficients
based on regional size, and stressed the need to consider the effect of specialization. Therefore, aspecialized LQ that excludes the size of the region from the AFLQ (referred to as CIQ with
Specialization, or CIQS in this paper) is defined as follows:

Therefore, regionalization is performed as follows:· · · (6-1)· · · (6-2)
In other words, it would increase the technical coefficient of the industries listed with a high LQ
in the regionalized table, based on the CIQ (except for the diagonal cells which are based on the LQ),
and would reflect regional specialization.
2.2 Data
China provides its input–output table at the national and provincial levels, based on thecompetitive import type that includes inflow and import (National Bureau of Statistics, ed. (2011)).
Specifically, the table is presented in the following format.5 It must be observed that the mostdetailed level of sector classification extends to 42 sectors.

3

According to the results in Table 4, 0.35 and 0.15 fit well for the five large regions and two small regions,
respectively.
4
According to Flegg and Tohmo (2013), it is sufficient to use FLQ because the empirical results on AFLQ and FLQ
are almost the same (AFLQ actually has a slightly better result).
5
If region r is replaced with nation n, it translates into a national table.

4

Figure 1
Regions

Configuration of Input–Output Table for Provinces, Cities, and Autonomous: Intermediate goods trade matrix of region r: Column vector of ultimate demands of region r: Column vector of outflow and export of region r (export only in the case of country n): Column vector of inflow and import of region r (import only in the case of country n): Column vector of the gross output of region r: Row vector of value added (prime denotes transpose): Row vector of gross inputs (Transposed gross output column vector)
Here, the goods balance equation in the direction of the row is:· · · (7)i is a column vector with one element as well as a summation vector to calculate the row total.
Here, the intermediate goods input required per unit, or input coefficients A, is calculated by
dividing the intermediate inputs by the gross inputs:,(

is a diagonal matrix in which the vector components are placed on the principal diagonal.)
By plugging this into the balance equation of the input coefficient and the row direction, an
input–output model that uses the well-known Leontief Inverse is derived:· · · (8)· · · (9)It must be noted thatis the Leontief Inverse (so-called output multiplier), which
represents the amount of input goods directly and indirectly required to fulfill the ultimate demand.
However, the problem here is that both the input coefficient and the Leontief Inverse include
inflow and import. In order to regionalize the national input coefficient ( ), the technicalcoefficient must exclude imports ( ). Further, the regional technical coefficient ( ), which is
obtained by regionalizing the national technical coefficient, must exclude inflows and imports and be
distinguished from the regional input coefficient ( ), which includes inflows and imports.
Now, assuming that the inflow and import is determined based on the regional demand, we define
the regional self-sufficiency rate c as follows:· · · (10)The balance equation of the regional goods (Equation 8) using the regional self-sufficiency rate
in Equation 10 is written as below:· · · (11)Alternatively, it is as follows when written in the form of the matrix equation 6:· · · (12)When the input coefficient
the regional (domestic) goods would be:,

is introduced, the input–output model of· · · (13)5· · · (14)Therefore, the national technical coefficient ( ) is defined based on Equations 13 and 14, while
its Leontief Inverse ( ) is defined as in Equation 15 or 16. Meanwhile, the provincial technicalcoefficient ( ) and its Leontief Inverse ( ) are defined as in Equations 17 and 18, respectively:· · · (15)· · · (16)· · · (17)· · · (18)

3．EMPIRICAL ANALYSISThis paper takes China’s national input–output table data ( ) (Equation 15) and regionalizes itusing the FLQ and AFLQ. By comparing the outcome to the actual provincial input–output table( ) (Equation 17), I examine whether the FLQ and AFLQ are effective in the case of China, and inparticular, whether they are more effective than the LQ and CIQ or the CIQS which takes
specialization into consideration. I then consider the size of , which takes focus as the issue in the
FLQ and AFLQ.
3.1 Characteristics of Each Province
Table 1 below summarizes the characteristics of each Chinese province, following Table 1 in
Flegg and Tohmo (2013) which examines regionalization by taking Finland as their model case.6
Table 1 shows regional characteristics in terms of size, using various indicators. As expected,
population size and the number of employed workers are highly correlated (r = 0.99), as is thecorrelation between GDP and gross output (r = 0.99). On the other hand, although they are correlated,
the relationship between the number of employed workers and gross output is weaker (r = 0.71)
compared to other relationships. This is because the availability of capital and the productivity oflabor vary by region. For example, gross output is large (by two to three fold) in Beijing andShanghai even though the number of employed workers is small. It implies that productivity of laboris higher. Furthermore, the size of all coastal regions is larger when perceived in terms of gross
output rather than the number of employed workers, while the size of inland regions is larger when
considering the number of employed workers.
In terms of economic scale (GDP and gross output), the largest region is Guangdong (11.3%
based on GDP), followed by Jiangsu, Shandong, and Zhejiang. While Guangdong is a region that
initiated the Chinese Economic Reform, Jiangsu and Zhejiang are regions that have attracted many
foreign companies by virtue of surrounding Shanghai. Shandong, as with the city of Qingdao, is alsoa region where foreign companies are expanding, in addition to its reputed agricultural productprocessing. The smallest regions are Qinghai and Ningxia (0.3% in GDP), which are underdeveloped
regions among other northwestern regions.
In terms of the land area, the largest is Xinjiang (19.8%), followed by Inner Mongolia, Sichuan,
and Heilongjiang. The smallest regions are Shanghai (0.1%), Tianjin (0.1%), and Beijing (0.2%),
which are municipalities of China.

6

However, the Herfindahl-Hirschman Index mentioned in Table 1 of Flegg and Tohmo (2013) is excluded because it
is not related to the themes in this paper.

6

TABLE 1 Characteristics of Each Province (2007)(Source) Prepared by the author based on China Statistical Yearbook by the National Bureau of
Statistics (2011).
The right side of Table 1 lists the number of sectors with an LQ greater than 1, as well as thenumber of sectors with a column total of provincial technical coefficients greater than the column
total of the national technical coefficient.
There is no particular trend regarding the number of sectors with an LQ greater than 1. The
largest number is 24 for Hubei, followed by 23, 22, and 22 for Anhui, Jilin, and Hunan, respectively.
The regions with the smallest numbers are Jiangsu (12), Shanxi (13), and Shandong (13).
The regions that have a column total of technical coefficient greater than the column total of thenational technical coefficient are Shandong (12), Sichuan (9), Shanxi (8), and Jiangxi (8), while
Tianjin, Hebei, Anhui, Guizhou, and Shaanxi had none. Because LQ-based regionalization reduces
the national technical coefficient, the error due to the regionalization could increase for the provinceswith many sectors, which have a larger technical coefficient than the national technical coefficient.
3.2 Examination of the Accuracy of the FLQ and AFLQThe FLQ and AFLQ-based regionalization areconducted by using the national technicalcoefficient derived from the national input–output table. Its accuracy is then examined by comparing
the output multiplier derived for each region to the output multiplier for each province. I examine the7output multiplier because, like previous studies, the primary purpose of creating a sub-regional
input–output table is to analyze the impact on attracting new industries and formulating development
policies.
Although there are several methods for measuring how far or close the estimated output
multiplier is from the actual output multiplier, the average percentage difference to measure thedifference in output multiplier per one sector—the most frequently used method among theabove-mentioned previous studies—is used here. It is defined by the formula below:
・・・(19)Here,is the estimated (regionalized by using the FLQ) output multiplier of sector j,isthe output multiplier of sector j derived from the actual provincial input–output table, and n, which is42, is the number of sectors.
The characteristics of regionalization based on the FLQ and AFLQ are regional size and the valueof parameter σ. As seen in the discussion on the previous studies, it has been reported that an
appropriate value of σ would lie around 0.2 to 0.3. Therefore, I calculated the average percentage
difference in output multipliers by using the values between 0.05 and 0.325 by the increment of
0.025.
Table 2 shows the results estimated by the LQ, CIQ, and FLQ while Table 3 shows the results
estimated by the CIQS, and AFLQ. We look at Table 2 (FLQ) first.
It is generally known that the LQ-based regionalization overstates the regional multiplier by
understating regional inflow, and that the CIQ slightly improves this condition. The results in Tables
2 and 3 also show that while the LQ-based regionalization overstates provincial output multipliers by
8.2% on average (by 7.8% on a weighted average based on the gross output size), the CIQ-based
regionalization overstates provincial output multipliers by 6.9% (likewise by 5.9% on a weighted
average). The results generated by the FLQ vary by region and σ; however, when an appropriate
value is assigned to σ, the accuracy improves greatly compared to that of the LQ and CIQ. For
example, if we look at the average, the best fit for σ is found between 0.05 and 0.075 where theaverage percentage difference in output multiplier comes down to the 1% level. However, this σvalue is considerably lower compared to what has been suggested in the previous studies. In addition,
the accuracy of this σ value is poor in some regions: the LQ is more accurate than the FLQ in 5 out
of 30 provinces (Jiangxi, Shandong, Henan, Hubei, and Hainan) while the CIQ is more accurate thanthe FLQ in 3 provinces (Shanxi, Heilongjiang, and Sichuan). Under the applicable values of σ, theaccuracy of the CIQ and LQ is better for 2 provinces, Hunan and Chongqing, respectively.7 In thecase of China, the FLQ-generated results are better for 20 provinces, which account for two-thirds ofthe nation. Even within these provinces, the value of σ varies between two groups: the accuracy ismost precise between 0.2 and 0.25 for 6 provinces (Tianjin, Hebei, Jilin, Anhui, Guangdong, and7

However, it has been verified that the FLQ will produce a better result if the value of σ is reduced to about 0.01.

89TABLE 2: Average Percentage Difference from the Actual Provincial Output Multiplier (FLQ)10

TABLE 3: Average Percentage Difference from the Actual Provincial Output Multiplier (AFLQ)

Shaanxi) while it is most precise between 0.05 and 0.125—particularly between 0.075 and 0.1—forthe remaining 14 provinces.
The FLQ would not fit well in some regions, unlike in the previous studies, because the provinceswith highly accurate LQ and CIQ have a national technical coefficient sufficiently reduced by the
CIQ (overstating the interregional trade) (See Equations 1 through 3). We can see this from thenegative values shown under the CIQ. The FLQ ends up further increasing the margin of error
because it estimates interregional trade to be larger as the regional size becomes smaller, comparedto the CIQ-based results (Equation 4).
Next, let us look at the results generated by the CIQS and AFLQ, which take regional specialization
into account (Table 3).
The CIQS improved the accuracy for Shandong, Henan, Hainan, and Sichuan, which did nothave good results based on the FLQ. However, the accuracy declined for Tianjin, Hebei, Jilin, andAnhui, which had overestimated regional inputs based on the LQ. This is a case in which the error
increases because the CIQS increases the technical coefficient.
The AFLQ improved the results better than the FLQ; in fact, the accuracy of the AFLQ improvesin all provinces as long as an appropriate σ is assigned. In terms of average and weighted average,
the accuracy of the AFLQ is best when σ = 0.15. The value of σ is not uniquely determined as it has
a wider distribution compared to the case of the FLQ.
We may ask why the AFLQ provided a better fit than the FLQ. This is because the technicalcoefficient of the sectors with clustered industries (LQ > 1) may have been larger than the national
technical coefficient, as explained in Equation 5, minimizing the overstated interregional trade andrelatively overstating the understated regional input. The AFLQ improved the accuracy of output
multiplier for all 10 provinces that could not be improved by the FLQ; however, as far as σ goes, it is
not possible to assert what value should be used because it varies even more than the FLQ.

4．CONCLUSION
This paper looked at the case of China and examined a series of Flegg LQ-based regionalization
analyses, starting with Flegg et al. (1995).
When the industries in the region are not concentrated as the national average, the LQ-based
regionalization adjusts the technical coefficient downward, based on the assumption that the region
is importing from other regions. Whereas the LQ focuses on the supply capacity of the industry, theCIQ adjusts the technical coefficient by taking into account the demand and supply capacity between
industries. The FLQ adjusts the technical coefficient by considering the “Regional size” andassuming that smaller regions import more, in addition to making the CIQ-based adjustment. The
AFLQ also considers industry’s regional specialization in addition to the regional size.
When China’s national input–output table is regionalized through these coefficient adjustments,
the examination results that emerge are as follows:(1) Unlike previous studies, the accuracy of the FLQ is sometimes not higher than the accuracyof the LQ and CIQ.8(2) Unlike previous studies, the value of δ is considerably lower and widely distributed. 14
provinces fall under the range of 0.05 to 0.125. (values between 0.05 and 0.075 provide a
relative better fit on average).
(3) The AFLQ improves the accuracy of output multipliers and raises the overall value of δ
more than the FLQ does.
The FLQ, which takes regional size into account, fails to estimate for one-third of the provinces,such as Jiangxi, Hunan, and Chongqing. The CIQS, which considers regional specialization, canimprove the estimates for Shandong, Henan, Hainan, and Sichuan, which the FLQ fails to estimate.
However, it generally fails to estimate for provinces such as Tianjin, Hebei, and Jilin. The AFLQ,
which considers regional size and regional specialization, can improve the overall accuracy of theestimation. But the parameter δ is not stable. Based on this empirical evidence, it can be concluded
that the regional size that is taken into consideration in regionalization by the FLQ formula does not
8

Miller and Blair (2009), who examined the LQ, CIQ, FLQ, and AFLQ in a simple case of three sectors by using
China’s regional table, concluded that the FLQ and AFLQ had the worst fit when they had used.

11

matter in the case of China. However I do not deny that the regional size may influence on theregionalization of national input-output table. It is true that we can estimate the regional technicalcoefficient only if the good value of parameter δ can be found. But this is difficult in case of China.
This study revealed another issue pertaining to the question of why the estimated value of the δparameter in the case of China largely differs from the values in the previous studies. It is possible toimagine that there is a problem with the statistical accuracy in preparing the provincial input–output
table, and that other factors such as regional specialization have a stronger effect on the inflow in
China than does regional size. The industry structure created by past industrial policies (e.g. during
the establishment of a full-set industrial structure in line with the self-reliance policy) might haveaffected this because China’s economy is transitional from the plan to the market economy. Eitherway, it is necessary to investigate the determinants of regional inflow in China. These may be left as
future tasks.
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