Is the world flat? Economic consequences of geographic information in financial reports

Abstract

This study examines whether investors are concerned about textual geographic information in annual reports. Based on a sample of China’s listed firms, we report the following findings: First, the more low marketisation districts (LMDs) appear in the annual reports, the higher the market return will be. Second, the result is more pronounced in non-state companies. Third, the frequency of LMDs is positively related with Tobin Q and CEO’s compensation. Fourth, we are unable to detect any relation between the frequency of high marketisation districts (HMDs) and firm characteristics including short term market reaction, Tobin Q and CEO’s compensation. Lastly, frequencies of both LMDs and HMDs are positively related with corporate innovation measured by patents. Taken together, the results show that a company can succeed in a developing area by filling the void of infrastructure. The strategy of expanding business in developing areas does not impair long term innovative activities.

Keywords:

• Economic consequences
• geographic structure
• marketisation level
• textual analysis

1. Introduction

As the best-selling book, “The world is flat: a brief history of the twenty-first century” (Friedman, 2005) predicts, with the development of computer and logistics technology, the impact of geography on people’s lives will be mitigated. However, in research areas such as economics and management, the topic of geographic factors remains interesting. For example, Morris (2011) posits that the geographic factor and its interaction with society is the most important determinant of the domination of the west over the east. In accounting and finance literature, Garcia & Norli (2012) find that the abnormal return following dispersed firms in future is much lower than that of the local firms due to high recognition, indicating that even in the US market where regional institutional differences are relatively small, investors are still concerned about geographic information.

Apart from geographic dispersion, investors in China may also take the marketisation level of districts where a company operates into consideration when making investment decisions. This issue is important because the international capital not only grows in developed countries but also flows to emerging markets in recent years. Khann et al. (2010) show that international companies can succeed in developing countries by filling the void of institutional infrastructure of low marketisation districts (hereinafter, LMDs). For example, a company will cooperate with local government to improve the efficiency of property protection when it decides to invest in a district with poor property protection. This logic is also reflected in China’s Western Development Policy. Therefore, there is much tension in the choice between developed and developing areas for companies in China. On one hand, some companies may try to expand their businesses in high marketisation districts (hereinafter, HMDs), for example, SANY, XCMG and Zoomlion acquiring companies in HMDs to get further growth.¹ On the other hand, companies such as Wahaha and Jingdong keep investing in LMDs.² Whether the stock market may react to these two strategies remains unknown.

We are motivated to investigate the economic consequences of the choices of Chinese listed companies to expand into LMDs or HMDs since it is important in both theoretical and practical aspects. According to theory of transaction costs, it is suggested that firms should expand into HMDs because the transaction cost in HMDs is lower. For example, Acemoglu et al. (2012) show that a nation’s failure is driven by high transaction costs and poor institutional infrastructure. On the contrary, Khanna et al. (2010) suggest firms expand in an emerging market for higher returns based on the assumption that firms can fill the void of institutional infrastructure in LMDs. These two theoretical analyses show opposite predictions and could be explored by an empirical test. Prior literature also indicates that there are successful cases for firms who expand themselves into either HMDs or LMDs. For example, firms such as Starbucks applies a market penetration strategy which takes the sequence from HMDs to LMDs while a firm such as the Hangzhou Wahaha Group chooses to set factories in LMDs in the first stage. Therefore, it is meaningful to empirically test this issue in a large sample.

Following Garcia & Norli (2012), we extract the frequency of provincial and urban names appearing in Chinese listed firms’ annual reports. We then merge the geographic data with the marketisation index of Fan et al. (2009) and Fan et al. (2016). Our key independent variables, LOW and HIGH, measure firms’ expansion into LMDs and HMDs respectively. Compared with the US, there is greater difference among provinces in China. For example, Rithmire (2014) shows that the Chinese local governments behave quite differently even in enforcement of the same policy released by the central government.

The results are as follows: First, the more low marketisation districts (LMDs) appear in the annual reports, the higher the market return will be. Second, the result is more pronounced in non-state companies. Third, the frequency of LMDs is positively related to Tobin Q and CEO’s compensation. Fourth, there is no relation between frequency of HMDs and firm characteristics including short term market reaction, Tobin Q and CEO’s compensation. Finally, both frequencies of LMDs and HMDs are positively related with corporate innovation measured by patents.

Our study makes several contributions to the literature of geographic information in financial reports. First, we show that the Chinese market reacts positively for firms expanding into LMDs, which provides additional evidence explaining why more capital is flowing to emerging markets. Second, while there is both theoretical and practical support for firms entering into either HMDs or LMDs, we show evidence of positive economic consequences of LMDs in this paper. Third, the issue of geographic determinants in corporate decision-making has attracted much attention in recent years, especially in China. For example, Xia et al. (2011) investigated the relationship between firms’ trans-provincial investment and their political connections; Sun and Liu (2014) examined why companies hire nonlocal independent directors. Yu et al. (2017) find that the geographical proximity between the chairman and the CEO has a negative impact on internal control quality. This paper enriches existing literature by providing evidence of geographic information on corporate valuation. Finally, in addition to literature such as Zhao (2014), Xie and Lin (2015) showing that soft information such as textual tone in Chinese financial reports has significant economic consequences, this paper shows that geographic information is another valuable item of soft information for the Chinese investors.

The remainder of the paper proceeds as follows. Section 2 discusses the institutional background and hypotheses, followed by research design in section 3. We report the empirical results in section 4. Section 6 presents the conclusion.

2. Literature, institutional background, and hypothesis development

Our tests are conducted based on the three advantages of China’s stock market. In the first place, Gertler (2003) posits that the transfer of tacit knowledge to another location is a valuable activity for companies. Therefore, geographic information will be important for investors since it reflects the tacit knowledge held by the firm. Secondly, there is a great difference among China’s local governments (Fan et al., 2009; Fan et al., 2016), which indicates that a company should learn to interact with another local government if it wants to expand its business into a new province. Therefore, the geographic information is more sensitive to Chinese investors than that of the investors in the US. Thirdly, China’s development of text-mining techniques make it easier for investors to capture and evaluate the geographic information in financial reports. Taken together, we conjecture that the investors will be interested in geographic information in the Chinese financial report.

2.1. The specific operation knowledge in a certain region

Gertler (2003) contends that it is costly for a company to transfer its tacit knowledge to another region even if there are abundant resources. In his findings, many Germany companies have faced great failures when they try to transfer their original production technology to branches in America. Landier et al. (2009) find that geographically dispersed companies are less likely to fire employees in their company’s registration area because these employees hold valuable tacit knowledge which cannot be easily transferred. Hence, due to the existence of tacit knowledge which is valuable but specific for a certain region, the geographic information is rather important for the management and investors. Consistent with this conjecture, prior research shows that companies’ geographic information is of significant economic consequences. For example, geographic information is shown to be an important driver of the precision and coverage of analysts’ forecast (Malloy, 2005; O’Brien and Tan, 2015). There is evidence showing that even with the assistance of modern communication technology and vocational training, an audit firm could not keep a unified quality standard among all its offices around the country. In the US market, an auditor is perceived to provide high-quality services only when s/he is the industrial expert at both national and city level (Ferguson et al., 2003; Francis et al., 2005; Reichelt & Wang, 2010). In addition, Dicken (2010) argues that international companies can bargain for better treatment in certain community by threatening to close operation divisions, which suggests that it is a kind of valuable resource for a company to be operating in a certain region.

2.2. The institutional background in China

2.2.1. Regional competition

To attract investments, intense competition arises among Chinese regions. Zhang (2009) shows that such regional competition has formed companies’ different investment environments. For example, the prices of production factors are low in some provinces, while a company may enjoy the benefit of low transaction costs in other provinces. Therefore, it is a strategic process for a company to choose the location to run its business. Xia et al. (2011) find that with the assistance of political connections, Chinese listed firms are likely to achieve their motivations of trans-provincial investment, indicating that firms may also invest in LMDs if the interaction between the local government and the company could improve the investment environment in LMDs.

2.2.2. Marketisation level and regionalism politics

As is shown by previous studies (Jin et al., 2010; Xin & Tan, 2009; Li et al., 2013), the Chinese Marketisation Index has strong explanatory power on Chinese provincial institutional differences. Moreover, the theory of regionalism in politics indicates that institutional differences will greatly shape local governments’ behaviour in the development of the economy. For example, despite private property rights having been approved by the central government, the local governments make various explanations of private property and treat private enterprises in diversified ways. Since the behaviour of local governments is one of the most important factors on the development of the economy and corporate operations in China (Zhou, 2007; Zhang & Gao, 2007; Li et al., 2013; Chen & Lu, 2014; Tan et al., 2015) the choice of HMDs and LMDs could be a strategic issue for the management.

The following two cases show that the local governments have significant regional impact on corporate decision making. The first case shows that local governments have discretion in explaining the central policy. Recently, as is required by the Chinese central government, officials in local government should be very careful about the potential corruption of their family members. According to this policy, Shanghai municipal government published a policy which forbids the family members of their officials to take any business in Shanghai. Obviously, this local regulation draws more attention to geographic information about companies in Shanghai.

Another case shows that the local governments will support local industrial development in various ways. Thun (2006) investigates the development strategies of automobile industry in three Chinese large cities, namely Beijing, Shanghai and Guangzhou. He finds that unlike Beijing and Guangzhou’s government decentralisation policy delegating more decision-making power to companies, the government of Shanghai chooses to set SAIC motor as a bureaucratic structure. As a result, upstream and downstream of automobile industries in Shanghai are better developed than that in Beijing and Guangzhou.

2.2.3. A case for Chinese-based textual analysis on geographic information

The case of Shanghai Chlor-Alkali Chemical Co (hereinafter, SCAC) shows how a company expands into LMDs. In the annual report of year 2016, SCAC presented its expansion plan to enter Inner Mongolia. As a result, we find that the regional name “Inner Mongolia” appear frequently in many parts of the annual report such as MD&A, notes of financial statement, information of the management and so on. Specifically, the textual information shows that SCAC will cooperate with local companies such as Junzheng Co in Inner Mongolia to take advantages of resources and labour cost. Meanwhile, the local infrastructure in Inner Mongolia will also be improved because of the technology and managerial system offered by SCAC.

2.3. Motivations for expansion to HMDs

We focus on the marketisation level rather than other region level characteristics for the two mainly reasons. First, compared to other characteristics such as culture and religion, the marketisation has more direct impact on local economy development and corporate operations. In fact, the frequency of use of marketisation level is much higher than other characteristics in Chinese top economic and management journals. Second, the marketisation index for Chinese provinces is shown to be universally accepted according to prior studies, which makes our study more feasible.

Neo-institutional economics theory suggests that transaction cost is an important factor in shaping corporate investments. In order to promote economic development for certain areas, it is necessary to keep the transaction cost at a lower level so as to attract more capital. Recently, the economy of Northeast of China has suffered continuous decline. One of the articles cited from the The Economist Journal argues that one of the important reasons for the decline of the Northeast economy is that “many people still do not understand or believe the role of the market”, which is consistent with the theory of transaction cost. ³

Acemoglu et al. (2012) posit that low marketisation level and poor institutional infrastructure play a quite important role in failures of nations. Due to poor property protection, companies in LMDs may choose to transfer their operation into HMDs where transaction cost is low. As is shown in crisis of Northeast China, many listed companies escaped by M&A. Another consistent case is the Starbucks’ strategy of entering the Chinese market. Starbucks opened its first three stores in Beijing, Shanghai and Shenzhen during 1999-2002, and until 2011, it opened its first stores in Kunming, Hefei, Shijiazhuang, Zhengzhou, and Harbin. Since 2012, Starbucks has expanded its businesses to more developing areas in China. Following the sequence from HMDs to LMDs, Starbuck’s market penetration strategy plays a quite important role for its sound development in China. Therefore, the market should react positively for firm’s expansion into HMDs for low transaction cost. Thus, we provide the transaction cost hypothesis as is followed.

H1: Market reaction is positively related to the frequency of HMDs (transaction cost effect.)

2.4. Motivations for expansion to LMDs

The rapid development of an emerging market seems to be a strong negative example which shows companies can get even larger growth in LMDs where the transaction cost is high. Obviously, LMDs are well known for being void of institutional infrastructures, which is shown by the lack of formal property protection, financial intermediaries, or basic infrastructure (Khanna et al., 2010). However, firms who can fill such a void are expected to earn excess returns. A typical example of firms filling a void of infrastructure is Hong Kong Li & Fung, who build an intermediaries system based on information extracted from the network of companies in the Asian market, which can be used to overcome the lack of information intermediaries.

Expansion to LMDs may reflect a company’s ability to overcome the shortage of poor infrastructure conditions, which is very similar to China’s cadre training system. The cadre training system of Chinese officials encourages training exercises at grass-roots level. Many officers are required to go to poor areas to understand the grassroots, which is conducive to their ability to work under difficult conditions. The successful LMD work experience indicates the officials have the ability to work under pressure and fill the void of institutional infrastructure.

Local governments in LMDs may also improve the infrastructure conditions so as to attract new investments. For example, six provinces of southwest China established the Inter-provincial Economic Association for the sake of economic development in 1984. The following year, the Association organised an international trade fair to provide information services to companies. (Zhen, 2013). Thus, we provide the following void-filling hypothesis.

H2: Market reaction is positively related to the frequency of LMDs (void-filling effect.)

3. Research design

3.1. Model

To investigate the economic consequences of geographic information, we first exam the association between short-term market reaction and the frequency of LMDs (or HMDs). We then test the impact of this geographic factor on long-term corporate outcomes such as Tobin Q, innovation, and CEO compensation so as to help to understand why investors react in this way.

We use the following model (1) to examine the association between market return and the geographic information in Hypothesis (1) and (2):(1) $${\text{CAR}}_{[-\text{t},\text{t]}}=\alpha +{\beta }_1\times \text{LMD}+{\beta }_2\times \text{HMD}+\text{Control Variables}$$(1)

test the impact of geographic factor on long-term corporate outcomes such as Tobin Q, innovation, and CEO compensation, we use model (2) as follows:(2) $${\text{Tobin Q}}_{\text{t}+1}/{\text{Patent}}_{\text{t}+1}/{\text{CEO Compensation}}_t=\alpha +{\beta }_1\times \text{LMD}+{\beta }_2\times \text{HMD}+\text{Control Variables}$$(2)

The coefficients β ₁ and β ₂ are the focus of our interest in this test. The transaction cost effect will be proved if β ₂ is positive and significant. The void-filling effect will be confirmed if β ₁ is positive and significant.

3.2. Measures

3.2.1. Geographic strategy

We use LMD to measure void-filling strategy. The detailed steps for getting LOW’s estimation are as follows. First, we count the frequency of all Chinese provinces (or cities) appear in each year’s annual report. Second, we replace city’s frequency by the province which it belongs and get the quantified geographic information at province level. Third, based on the marketisation index disclosed in Wang et al. (2016 in Chinese), we classify each province as either LMD or HMD by yearly median value of all provinces. Finally, we calculate the value of LMD by following equation (i.e. LMD=Ln (1+frequency of LMDs)). Similarly, HMD is calculated as following equation (i.e. HIGH=Ln (1+ frequency of HMDs)) to measure transaction cost strategy.

3.2.2. Dependent variables

The dependent variable CAR _[−t,t] in model 1 is cumulative abnormal return over [−t,t] around the announcement date of the annual report. Daily abnormal return is estimated by CAPM and β is predicted on the 120 trading days prior to event date. Consistent with previous research, an observation will be deleted if its yearly trading days is less than 60 or its β is negative. Dependent variables used in model 2 are defined as follows. TQ _t+1 and TQ _t are Tobin Q in t+1 and t respectively. PAT1 _t+1 equals the natural logarithm of 1 plus the number of all patents applied by company i in t+1. PAT2 _t+1 equals the natural logarithm of 1 plus the number invention patents applied by company i in t+1. GPAY _t is calculated by the following equation:

$${\text{GPAY}}_{\text{t}}=Log\left(\text{CEO compensation in}\text{t}\right)-Log\left(\text{CEO compensation in}\text{t}-1\right)$$

DPAY _t is a dummy variable equals 1 if a CEO has received more than 50% increase of pay in this year and 0 otherwise. Please note that CEO compensation is available at the Chinese Stock Market Research Database (hereinafter, CSMAR) since year 2005, the sample period of the regressions on GPAY _t and DPAY _t is after 2006.

3.2.3. Moderating variables

To test moderating effect of model 1, we use four moderating variables as follows. STATE is a dummy variable equals 1 if a company is state-owned and 0 otherwise. Second, POL is a dummy variable which equals 1 if a CEO is politically connected with the government and 0 otherwise. Third, if a company is registered in one of the HMDs, then variable DMKT takes a value of 1 and 0 otherwise. The last moderating variable RSQ is stock synchronicity in t.

3.2.4. Control variables

UE is unexpected earnings measured by earnings changes between year t and year t − 1 divided by firm’s year-end market value in t − 1. DIV is number of industry segments a company has. OP is a dummy variable equals 1 if a company received a modified audit opinion. ST equals to 1 if a company receives special treatment due to continuous losses and 0 otherwise. Following Chen et al. (2010), we define industrial policy variable, SUPP, which equals 1 if a company belongs to one of the industries supported by central government in the 5-year plan. DE is debt to asset ratio. SIZE measures the company size which takes the value of the natural logarithm of total asset in t. INDEP is the proportion of independent directors in board. RDTA equals the amount of R&D expenditures in year t divided by total asset in t − 1. In Table 1, we put a brief description of all variables used in this paper.

Table 1. Variable definitions.

Variable	Definition
CAR[−t,t]	Cumulative abnormal return over [−t,t] around the announcement of the annual report(%)
DIV	Number of industry segments
LOW	Log of 1 plus frequency of LMDs, a district is treated as LMD if its marketisation index is lower than the yearly median of all the districts
HIGH	Log of 1 plus frequency of HMDs, a district is treated as HMD if its marketisation index is higher than the yearly median of all the districts
UE	Unexpected earnings, the change of earnings in t and earnings in t − 1 over outstanding shares
STATE	1 if a company is State-Owned and 0 otherwise
POL	1 if a CEO is politically connected with the government
DMKT	1 if the headquarter of a company is located at one of the HMDs, and 0 otherwise
OP	1 if a company receives a modified audit opinion and, 0 otherwise
ST	1 if a company receives a special treatment due to suffering losses in t and t − 1, and 0 otherwise
SUPP	1 if a company’s industry is supported by the government in the 5-year plan, and 0 otherwise
DE	debt to asset ratio
SIZE	The natural logarithm of total assets in t
INDEP	The proportion of independent directors to all members in board
RDTA	R&D expenditures in t over total assets in t − 1
TQ t+1	Tobin Q in t+1
TQ t	Tobin Q in t
TQ t−1	Tobin Q in t − 1
PAT1	Log of 1 plus number of all patents in t+1
PAT2	Log of 1 plus number of invention patents in t+1
SUBSTA t+1	Government subsidy income in t+1 over total assets in t
SUBSTA t	Government subsidy income in t over total assets in t−1
GPAY	Log (CEO compensation in t)-log(CEO compensation in t−1)
DPAY	1 if growth ratio of CEO compensation is higher than 0.5; and 0 otherwise
CEODUAL	1 if CEO also serves as the chairman of the board; and 0 otherwise
DROA	ROA in t minus ROA in t−1
LIAGE	Log of CEO age
FEMALE	1 if a company hires a female CEO; and 0 otherwise
OVERSEA	1 if the CEO has oversea experience; and 0 otherwise
ACA	1 if the CEO has academic experience; and 0 otherwise
AGE	Log of company age

3.3. Sample selection and the summary statistics

We use a sample of non-financial listed firms in Chinese A-stock market from 2001 to 2012. Our initial sample size is 17,825 which contains sufficient accounting variables for both current and prior years. Based on the work of Garcia & Norli (2012), we drop those observations whose pdf annual reports are not machine-readable or contains no provincial/urban names. After deleting samples due to their lack of either dependent, moderating or control variables, the baseline sample consists of 11,930 firm-year observations from 2001 to 2012. The financial data, stock price and return data, and corporate characteristic of listed Chinese firms from are obtained from the CSMAR database. The descriptive statistics are presented in Table 1 and all continuous variables are winsorized at 1% level by year to reduce the influence of outliers.

As is shown in Table 2, the mean and the median of variables LMD are about 3.5, indicating that firms disclose 27 LMDs on average. Similarly, the mean and the median of HMD are about 5.5 indicating that firms disclose 330 HMDs on average. The dummy variable STATE has a mean of 0.63, showing that 63% of our sample are SOEs. DIV has a median as 2 and maximum of 5, suggesting that most firms diversified their businesses.

Table 2. Descriptive statistics.

Variable	N	Minimun	Maximum	Std	Mean	Median
CAR[−1,1]	11930	−19.688	34.867	5.599	−0.351	−0.706
CAR[−5,5]	11930	−36.019	64.954	9.562	0.243	−0.400
CAR[−15,15]	11930	−41.982	101.475	13.157	0.745	−0.119
DIV	11930	1.000	5.000	1.164	2.155	2.000
LMD	11930	0.000	6.750	1.733	3.495	3.434
HMD	11930	2.197	7.380	0.869	5.628	5.826
UE	11930	−0.531	0.396	0.066	−0.004	0.002
STATE	11930	0.000	1.000	0.483	0.629	1.000
POL	11930	0.000	1.000	0.379	0.174	0.000
DMKT	11930	0.000	1.000	0.500	0.504	1.000
OP	11930	0.000	1.000	0.236	0.059	0.000
ST	11930	0.000	1.000	0.173	0.031	0.000
SUPP	11930	0.000	1.000	0.328	0.123	0.000
DE	11930	0.042	2.002	0.220	0.497	0.502
SIZE	11930	18.764	28.088	1.235	21.563	21.397
INDEP	11930	0.000	0.714	0.089	0.339	0.333
RDTA	11930	0.000	0.111	0.014	0.006	0.000
TQ t+1	11930	0.118	13.827	1.593	1.699	1.214
TQ t	11930	0.115	12.809	1.562	1.735	1.280
TQ t−1	11930	0.146	14.364	1.627	1.872	1.420
PAT1	11930	0.000	6.792	1.586	1.334	0.693
PAT2	11930	0.000	5.740	1.219	0.838	0.000
SUBSTA t+1	11930	0.000	0.119	0.009	0.005	0.001
SUBSTA t	11930	0.000	0.079	0.009	0.004	0.001

Note: All variables are as defined in Table 1.

4. Results

4.1. The economic consequences of geographic strategy

The result of model 1 in Table 3 shows that the coefficients of LMD are significantly positive in all three regressions while there is no significance result for HMD, indicating that the stock market has given positive reaction to those firms who expand their operation into LMDs, which is consistent with the hypothesis of filling the void of institutional infrastructure. Compared to firms who expand their businesses in HMDs, Chinese investors prefer those firms who try to explore growth opportunities in LMDs.

Table 3. Economic consequences of geographic information in annual reports

VARIABLES	(1)	(2)	(3)
	CAR[−1,1]	CAR[−5,5]	CAR[−15,15]
UE	0.400	3.160*	2.218
	(0.401)	(1.744)	(0.888)
LMD	0.068*	0.114**	0.157**
	(1.860)	(1.961)	(1.965)
HMD	0.085	0.056	0.055
	(1.148)	(0.486)	(0.353)
DIV	0.032	0.101	0.120
	(0.681)	(1.209)	(1.094)
STATE	−0.054	−0.396*	−0.514*
	(−0.434)	(−1.942)	(−1.866)
POL	−0.101	−0.251	−0.320
	(−0.743)	(−1.081)	(−1.035)
DMKT	0.062	0.126	0.131
	(0.500)	(0.622)	(0.492)
OP	−0.419	−1.460***	−1.668***
	(−1.480)	(−3.061)	(−2.646)
ST	−3.388***	−5.698***	−4.895***
	(−8.312)	(−7.943)	(−5.250)
SUPP	0.540**	0.670*	0.431
	(2.268)	(1.895)	(0.896)
DE	0.387	1.066*	1.541*
	(1.240)	(1.852)	(1.960)
SIZE	0.062	−0.016	−0.310**
	(1.234)	(−0.180)	(−2.528)
CONSTANT	−2.671**	0.144	5.936**
	(−2.437)	(0.077)	(2.345)
Industry FE	Yes	Yes	Yes
Year FE	Yes	Yes	Yes
Observations	11,930	11,930	11,930
Adjusted R-squared	0.022	0.045	0.056

Notes: This table presents the regression results of the following model: CAR _[−t,t] = a + b*LOW + c*HIGH + d* controls; All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

4.2. The impact of geographic strategy on long term corporate outcomes

In this section, we first examine the impact of geographic strategy on Tobin Q in both current year and following year. Besides those control variables mentioned above, we also control for the prior year’s Tobin’s Q in t/t − 1 to capture the change effect of geographic strategy. The results in Table 4 show that the coefficients of LMD are significantly positive in column (1) and (2) while there is no significant result for HMD. These results indicate that while operations in LMDs greatly increase a firm’s long-term valuation, expansion in HMDs may has no impact.

Table 4. Geographic information and Tobin’s Q.

VARIABLES	(1)	(2)
	TQt	TQt+1
TQt		0.642***
		(38.462)
LMD	0.025***	0.015**
	(4.158)	(2.475)
HMD	0.011	0.004
	(0.832)	(0.277)
DIV	−0.029***	−0.025***
	(−3.756)	(−3.279)
TQt−1	0.560***
	(39.609)
STATE	0.019	−0.071***
	(0.849)	(−3.363)
POL	0.055**	0.004
	(2.206)	(0.187)
DMKT	0.074***	0.084***
	(3.182)	(3.725)
INDEP	0.200	0.151
	(1.284)	(1.062)
ROA	1.896***	0.584**
	(6.341)	(2.387)
ST	0.473***	0.248***
	(6.398)	(2.838)
SUPP	0.066	0.150***
	(1.161)	(2.680)
DE	−0.256***	−0.036
	(−3.145)	(−0.373)
SIZE	−0.274***	−0.220***
	(−16.876)	(−15.547)
Constant	6.109***	4.758***
	(18.155)	(16.001)
Industry FE	Yes	Yes
Year FE	Yes	Yes
Observations	11,930	11,930
Adjusted R−squared	0.655	0.641

Notes: This table presents the regression results of the following model: TQ_t & TQ_t+1 = a + b*LOW + C*HIGH+d* controls; All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

4.3. The influence of geographic strategy on corporate innovation

Due to the lack of competition in LMDs, companies who expand their operation into those areas may dominate the local market and have less incentive to invest in R&D. Thus we present the influence of geographic strategy on corporate innovation in Table 5. As the results show, both LMD and HMD have significantly positive coefficients, indicating that firms opening business in LMDs still retain their efforts with innovative activities.

Table 5. Geographic information and corporate innovation

VARIABLES	Total patents	Invention patents
	PAT1	PAT2
LMD	0.033**	0.028**
	(2.381)	(2.571)
HMD	0.150***	0.091***
	(5.330)	(4.174)
DIV	0.035*	0.028*
	(1.888)	(1.941)
STATE	−0.018	0.040
	(−0.387)	(1.130)
RDTA	24.798***	21.687***
	(15.301)	(15.363)
POL	−0.005	0.036
	(−0.085)	(0.806)
DMKT	0.295***	0.223***
	(6.178)	(5.893)
INDEP	0.835***	0.639***
	(3.414)	(3.140)
OP	−0.150***	−0.052
	(−2.599)	(−1.180)
ROA	0.586**	0.314
	(2.337)	(1.520)
ST	0.114*	0.089*
	(1.706)	(1.759)
SUPP	0.077	0.210***
	(0.937)	(2.835)
DE	−0.236**	−0.136*
	(−2.504)	(−1.859)
SIZE	0.362***	0.293***
	(13.809)	(12.880)
Constant	−8.215***	−6.832***
	(−15.355)	(−14.660)
Industry FE	Yes	Yes
Year FE	Yes	Yes
Observations	11,930	11,930
Adjusted R-squared	0.464	0.411

Notes: This table presents the regression results of the following model: PAT1 & PAT2= a + b*LMD + C*HMD+d* controls; All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

4.4. The influence of geographic strategy on CEO compensation

If strategy of LMDs or HMDs increases shareholders’ value, it is expected that the boards would encourage such investment by rewarding those CEOs who achieve such expansions. Therefore we investigate the impact of geographic strategy on CEO compensation and the results are presented in Table 6. As Table 6 shows, either using continuous or dummy variable as dependent variable, the coefficient of LMD is significantly positive while that of HIGH has no significant result, which indicates those CEOs are rewarded for their successful strategy of LMDs.

Table 6. Geographic information and CEO compensation.

VARIABLES	(1)	(2)
	GPAY	DPAY
	OLS	Logistic
LMD	0.006*	0.051**
	(1.945)	(0.022)
HMD	−0.002	−0.029
	(−0.277)	(0.047)
DIV	−0.003	−0.024
	(−0.745)	(0.029)
STATE	0.000	−0.008
	(0.020)	(0.073)
INDEP	0.160**	0.634
	(2.066)	(0.495)
CEODUAL	0.025*	0.058
	(1.907)	(0.090)
DROA	0.600***	1.845***
	(6.309)	(0.388)
LIAGE	0.066*	−0.361
	(1.741)	(0.258)
FEMALE	0.004	−0.083
	(0.187)	(0.142)
OVERSEA	−0.010	−0.220
	(−0.369)	(0.211)
POL	−0.012	−0.012
	(−0.967)	(0.089)
ACA	−0.018	−0.118
	(−0.805)	(0.154)
SUPP	0.013	−0.046
	(0.712)	(0.144)
DE	−0.053**	−0.075
	(−2.057)	(0.148)
SIZE	−0.003	−0.011
	(−0.566)	(0.031)
AGE	0.014	0.131
	(0.962)	(0.099)
Constant	−0.143	−0.828
	(−0.808)	(1.279)
Industry FE	Yes	Yes
Year FE	Yes	Yes
Observations	7,177	7,177
Adjusted R-squared	0.029
Pseudo R-squared		0.033

Notes: This table presents the regression results of the following model: GPAY1 & DPAY= a + b*LOW + C*HIGH + d* controls; All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

4.5. Additional tests and robust check

4.5.1. 2sls regression and endogeneity

A concern for our empirical findings is self selection. It may be that certain unobserved variables affect both LMD and dependent variables. A common approach to address this issue is using instrumental variables in a 2sls regression. Therefore, we identify five instrumental variables which would have an impact on annual report disclosure but do not affect long-term corporate characteristics. The first one is RME_LVD, which measures the text similarity of Management’s Discussion and Analysis (MD&A) between the target and the other companies in the current year. ⁴ The second variable RLVD measures the text similarity between the current year’s MD&A and that of last year. ⁵ The third variable RSQ_1 is defined as the firm’s stock price synchronicity in t − 1. The fourth variable GROUP is a dummy variable which equals 1 when the Chairman of the board or CEO has work experience in a Group Company and 0 otherwise. The last variable DGO is also a dummy variable which equals 1 if the chairman or CEO has trans-provincial work experience and 0 otherwise.

Panel A of Table 7 presents the first stage results of 2sls. As is shown in panel A, there exists great difference in explanatory power of these five instrumental variables. The coefficient of RSQ_1 is significantly negative when taking LMD as first stage’s dependent variable, which indicates that firms whose information quality is low may have less incentive to expand themselves into LMDs. The results of DGO variable indicate that a company would be more likely to expand into LMDs but not HMDs when her Chairman or CEO has trans-provincial work experience, since its coefficient is significantly positive in regressions on LMD but has no significance result when HMD is used as dependent variable. Last but not least, when a firm’s MD&A in t contains less information compared to that of year t − 1 (namely, RLVD is higher), it would be harder for a firm to expand into HMDs.

Table 7. Results of 2sls regressions

Panel A. Results of instrumental variables in the first stage
	TQt&TQt+1		PAT1&PAT2		GPAY
	LMD	HMD	LMD	HMD	LMD	HMD
RME_LVD	−0.010	0.002	−0.010	0.003	0.000	−0.003
	(−1.380)	(0.604)	(−1.464)	(0.810)	(0.030)	(−0.677)
RLVD	−0.010	−0.008**	−0.010	−0.008**	0.004	−0.014***
	(−1.614)	(−2.571)	(−1.593)	(−2.514)	(0.474)	(−3.433)
RSQ_1	−0.120***	−0.029*	−0.146***	−0.020	−0.167***	−0.015
	(−3.475)	(−1.823)	(−4.338)	(−1.293)	(−4.317)	(−0.844)
GROUP	−0.094	0.017	−0.094	0.022	−0.046	0.005
	(−1.442)	(0.563)	(−1.441)	(0.734)	(−0.575)	(0.139)
DGD	0.144**	0.045	0.147**	0.044	0.154*	0.016
	(2.158)	(1.458)	(2.205)	(1.398)	(1.872)	(0.438)

Panel B. Results of geographic variables in the second stage
	LMD	HMD
TQ t	0.427***	−0.029
	(3.104)	(−0.109)
TQ t+1	0.392***	0.301
	(3.045)	(1.214)
PAT1	0.328**	1.484**
	(2.143)	(2.575)
PAT2	0.351***	1.133**
	(2.750)	(2.515)
GPAY	0.135**	0.134
	(2.523)	(1.098)

Notes: Panel A table presents the results of instrumental variables in the first stage. RME_LVD: We rank the mean value of the Levenshtein edit distance between MD&A of firm i and MD&A of the other firms in 10 groups and RME_LVD is the group number. RLVD: We rank the Levenshtein edit distance between MD&A in t and MD&A in t−1 and RLVD is the group number. RSQ _t−1 is stock price synchronicity in t−1. Group is equal to 1 if the CEO or the Chairman has job experience in group companies and 0 otherwise. DGD is equal to 1 if the CEO or the Chairman has job experience in at least 2 provinces and 0 otherwise. Control variables are omitted for simplicity. All the other variables are as defined in Appendix 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

Notes: Panel B table presents the results of geographic variables in the second stage. Control variables are omitted for simplicity. All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

Panel B of Table 7 shows the results of second stage of 2sls regressions, the results of control variables are not shown for simplicity. The results are as same as those in Table 4 ^{Table 5}–6, showing that after taking into consideration of these instrumental variables, the coefficient of LMD is still significantly positive in all regressions and that of HMD are not significant unless patents are used as dependent variables. These results indicate that endogeneity is not a concern when assessing the reliability of our findings.

4.5.2. Moderating factors of geographic strategy

This section examines how the relation between market return and strategy is affected by moderating variables including ownership, political connection, and stock price synchronicity. The results of the moderating effect may help us to better understand how the geographic strategy works. The first moderator we choose is STATE, a dummy variable equal to 1 if a company is owned by state equity. Prior literature shows that there is great difference between SOEs and non-SOEs in decision-making (Zeng & Chen, 2006; Wei & Liu, 2007; Xue & Bai, 2008; Yu et al., 2010). To test the moderating effect of STATE, we add two additional interaction items including STATE*LMD and STATE*HMD in model 1. We predict that while SOEs can enjoy institution bonus due to their political connection in LMDs, they may have to face more pressure when expanding into HMDs since the competing there is stronger and the market is more transparent. Meanwhile, non-SOEs may have more incentive to fill the void of infrastructure when choosing to enter into LMDs. Therefore, it is expected to find more significant economic consequences of non-SOEs choosing to expand into LMDs than that of SOEs choosing to expand into HMDs, predicting a negative sign for coefficient of STATE*LMD and a positive sign for coefficient of STATE*HMD.

As is shown in Table 8, the coefficient of STATE*LMD is one-tailed significantly negative when using CAR_[−1,1] as dependent variable and two-tailed significantly negative when using CAR_[−15,15] as dependent variable. We also test model 1 in SOE and non-SOE subsamples respectfully and find that the coefficient of LMD is only significantly positive in non-SOE subsample. These results are consistent with our prediction that there is greater positive market reaction for non-SOEs expanding into LMDs. In terms of the results, one may argue that since SOEs have more resources than non-SOEs, they should have greater ability in filling the void of institutional infrastructure when expanding into LMDs. To exclude this conjecture, we present two reasons why the market does not react positively when SOEs expand into LMDs. Firstly, SOEs have multiple goals including corporate value and social responsibility, the goal of expanding into LMDs for future success may not be their first-order consideration. For example, many SOEs prefer growing at their original place to increase local employment rate. It is obviously that the top managers of SOEs who are in favor of local economy are more likely to be promoted. Secondly, while SOEs have a greater ability to fill the void of infrastructure in LMDs, their expanding activities may already be caught by the stock market and therefore it does not surprise investors when the annual report is released. For example, from the case raised in 2.2.3, we find that this SOE chose a way of joint venture to expand into LMDs and the venture’s setting news had already been published before the disclosure of the annual report. On the contrary, it is unexpected for investors to witness non-SOEs’ expansion into LMDs if they believe that it is hard for non-state-owned companies to get succeed in LMDs.

Table 8. Moderating effect in economic consequences of geographic information

VARIABLES	(1)	(2)	(3)
	CAR[−1,1]	CAR[−5,5]	CAR[−15,15]
1. LMD*STATE	−0.0997	−0.0902	−0.234*
	(−1.552)	(−0.861)	(−1.641)
2. LMD*POL	−0.0126	0.0693	0.137
	(−0.163)	(0.523)	(0.764)
3. LMD*DMKT	0.0208	−0.0622	−0.119
	(0.291)	(−0.520)	(−0.739)
4. LMD*RSQ	−0.0785*	−0.0837	−0.0559
	(−1.865)	(−1.048)	(−0.495)

Notes: This table presents the regression results of the following model: CAR[−1,1]= a + b*LOW + C*VAR*LOW + d* VAR + e*controls; Control variables are omitted for simplicity. All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

We also examine the moderating effect of a CEO’s political connection. We expect political connection to be in favour of companies’ operation in LMDs, however, the results do not support this prediction as the coefficient of POL*LMD is not significant in Table 8.

Our third moderating variable is DMKT which measures the marketisation level of a firm’s registration location. Since international companies are attaining further success by expanding from developed countries to developing countries, we expect the higher the marketisation level for the registration place, the better the market will react for their expansion into LMDs. However, the results in Table 8 show that there is no significance for the coefficient of DMKT*LMD.

Finally, we use the firm’s stock price synchronicity in year t as a moderating variable to test model 1. We predict that if a company has high stock synchronicity (which means the company has disclosed less firm specific information), the positive market reaction of LMD will be impaired because the investors cannot extract enough inside information to evaluate potential value of businesses in LMDs. Therefore, the expected sign of coefficient of RSQ*LMD is negative. The results partly support our expectation as the coefficient is significantly negative when using CAR_[−1,1] as dependent variable.

4.5.3. The economic significance of geographic information

To test the economic significance of geographic information, we define a dummy variable DLOW which equals 1 if the value of LOW if higher than the median value of the whole sample to deal with this issue. We then replace LOW by DLOW in the estimation of model 1 based on Non-SOE sample and find that coefficient of DLOW is still significantly positive. Above all, the absolute value of the coefficient indicates there is economic significance of geographic information. Specifically, the coefficient of DLOW is 0.4 when CAR_[−1,1] is used as dependent variable, indicating that a portfolio based on median of geographic information would bring 0.4% abnormal returns in the short period of [−1, +1]. Similarly, geographic information will bring 0.5% and 1.2% abnormal returns in the periods of [−5, +5] and [−15, +15].

4.5.4. Alternative explanation of government subsidies

Another explanation of our research is that a company may expand into LMDs just because of the subsidies provided by local governments and hence the stock market would react positively. As is shown in Bu et al. (2017), a company can obtain local government subsidies more easily by making an equity investment in the local government region. In order to eliminate the concern of government subsidies explanation, we test model 1 and replace the original dependent variable with the government subsidies for next year (namely, the variable SUBSTA_t+1). The results presented in Table 9 show that neither LMD nor HMD make a significant impact on the amount of received government subsidies, suggesting that there is no evidence supporting the government subsidies explanation. Meanwhile, firms with bad performance such as poor ROA and being ST attract more subsidies, which is consistent with findings in previous research.

Table 9. Geographical bias and government subsidies

VARIABLES	SUBSTAt+1
LMD	−0.000
	(−0.577)
HMD	0.000
	(1.120)
SUBSTAt	0.525***
	(16.744)
DIV	−0.000
	(−0.797)
STATE	0.000
	(1.354)
RDTA	0.039***
	(3.730)
POL	−0.000
	(−0.159)
DMKT	0.000
	(0.738)
INDEP	−0.000
	(−0.456)
OP	−0.000
	(−0.046)
ROA	−0.005***
	(−3.403)
ST	0.001**
	(1.969)
SUPP	0.002***
	(2.911)
DE	0.001**
	(2.175)
SIZE	−0.000***
	(−5.261)
Constant	0.011***
	(5.094)
Industry FE	Yes
Year FE	Yes
Observations	11,930
Adjusted R−squared	0.325

Notes: This table presents the regression results of the following model: SUBSTAt+1= a + b*LOW + C*HIGH +d* controls; All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

4.5.5. Alternative explanation of enter barriers into HMDs

If companies founded in LMDs cannot freely expand themselves into HMDs due to the existence of market entry barriers in these areas, then our main findings may indicate something other than filling the void of institutional infrastructure. To exclude this explanation, we conduct the following tests to show that enter barriers do not matter. First, firms have a strong incentive to expand into HMDs for a greater market as well as better infrastructure of innovation. Infrastructures such as information system and modern logistics technology in HMDs are attractive for capital. Second, based on the statistic of sample, there is some evidence supporting our argument. The mean value of HMD in the sample of firms founded in LMDs is 5.0, which is very close to that in sample of firms founded in HMDs, indicating that firms founded in LMDs do expand into HMDs. At last, one may argue that firms in LMDs will be afraid of losing local government subsidies when expanding to HMDs. We also conduct additional tests to deal with this concern. As is shown in section 4.5.4, the coefficient of HMD is not significant in regression on government subsidies. Further test shows that this coefficient keeps no significance when we use subsample of firms founded in LMDs, indicating that the concern of losing original government subsidies will not impede firms’ decision of expanding into HMDs.

4.5.6. Alternative explanation of labor costs

The stock market would react positively for those firms expanding into LMDs only because firms can take advantage of low labour cost in these areas. We present three reasons why low labour cost is not fundamental to our main results. First, it is not necessary that the labour cost in LMDs be lower than that of the HMDs. Due to the high transaction cost such as cost of enforcement of labour contracts in LMDs, the total employment costs (especially the contract cost) may not be substantially lower in these areas. Second, if the low labour cost explanation dominates, it would be expected that both SOEs and non-SOEs operating in LMDs can take this advantage and therefore the coefficient of LMD in regressions for SOE samples should also be significantly positive, which is opposite to the findings we present in section 4.5.2. Third, if the level of marketisation really implies labour cost, it would be expected that those firms who were founded in HMDs may benefit more for expanding into LMDs compare to their counterparts, which indicates the coefficient of DMKT*LMD in table 7 would be significantly positive. However, as is shown in section 4.5.2, this prediction is not confirmed. Taken together, labour cost cannot explain our results.

4.5.7. Alternative measure of cumulative abnormal returns

To check the robustness of our results, we calculate abnormal return in a different way as an additional test. Instead of using CAPM to estimate abnormal return, we now use the daily stock return (A) which take consideration of reinvestment of cash dividends and the daily market return (B) which is based on the weighted average value of tradable stocks to estimate the daily abnormal return which equals (A – B). After changing the estimation method, we find that the coefficient of LMD is still significantly positive, suggesting that replacement of cumulative abnormal returns for model 1 does not change the results of model 1.

4.5.8. Test of geographic segment report

This paper investigates the economic consequences of geographic information of expanding operations into LMDs or HMDs which is disclosed in the text of the annual report, there may be a concern that such information would already be included in the firm’s geographic segment report. In order to test whether there is additional information content apart from geographic segment report, we take the following approach. First, we read each firm year’s segment report and find that there is only 10% of the whole sample disclosing geographic information at province or city level, which indicates that solely by reading segment reports, investors could not catch full geographic information of firms’ operations in LMDs and HMDs. We then define an additional dummy variable, DGEO which equals 1 if a firm’s segment report discloses geographic information at province or city level and 0 otherwise and control for this variable in the model. The new results are as shown in Table 10. After adding the variable of segment report, there is no substantial difference for the results of model 1 and the coefficient of LMD is still significantly positive, suggesting that there is additional geographic information in text of annual report.

Table 10. Robust test on disclosure of geographic segments

VARIABLES	(1)	(2)	(3)
	CAR[−1,1]	CAR[−5,5]	CAR[−15,15]
UE	0.400	3.167*	2.227
	(0.401)	(1.747)	(0.892)
LMD	0.068*	0.123**	0.167**
	(1.873)	(2.108)	(2.096)
HMD	0.086	0.069	0.071
	(1.155)	(0.596)	(0.451)
DIV	0.032	0.106	0.126
	(0.689)	(1.271)	(1.148)
STATE	−0.054	−0.401**	−0.519*
	(−0.437)	(−1.970)	(−1.891)
POL	−0.101	−0.257	−0.327
	(−0.745)	(−1.107)	(−1.058)
DMKT	0.062	0.130	0.136
	(0.503)	(0.643)	(0.511)
OP	−0.420	−1.476***	−1.688***
	(−1.483)	(−3.104)	(−2.682)
ST	−3.388***	−5.700***	−4.897***
	(−8.312)	(−7.952)	(−5.261)
DGEO	−0.030	−0.410	−0.484
	(−0.187)	(−1.467)	(−1.239)
SUPP	0.539**	0.655*	0.412
	(2.263)	(1.853)	(0.858)
DE	0.388	1.083*	1.561**
	(1.243)	(1.882)	(1.986)
SIZE	0.061	−0.023	−0.318***
	(1.221)	(−0.252)	(−2.585)
Constant	−2.664**	0.240	6.050**
	(−2.429)	(0.128)	(2.390)
Industry FE	Yes	Yes	Yes
Year FE	Yes	Yes	Yes
Observations	11,930	11,930	11,930
Adjusted R-squared	0.022	0.045	0.056

Notes: This table presents the regression results of the following model: CAR _[−t,t] = a + b*LOW + C*HIGH+d* controls; DGEO is equal to 1 if a company disclose geographic segments at province level or city level and 0 otherwise. All variables are as defined in Table 1. *, **, and *** represents statistical significance at 10%, 5%, and 1% level, respectively. Standard errors are clustered at firm level.

5. Conclusion

This paper investigates the economic consequences of textual geographic information of Chinese listed firms.The result is contrary to the suggestion of Friedman (2005), who posits that the impact of geography is mitigating and the world is flat. We find that the market positively reacts to disclosure of LMDs in annual reports. The results are more pronounced in non-SOE companies, suggesting that the investors believe that non-SOEs are more capable in fulfilling the void of institutional infrastructure in LMDs. We also find that the frequency of LMDs is positively related with Tobin Q and CEO’s compensation. Meanwhile, we are unable to detect any relation between the frequency of high marketisation districts (HMDs) and firm characteristics including short term market reaction, Tobin’s Q and CEO’s compensation. Finally, the frequencies of both LMDs and HMDs are positively related with corporate innovation measured by patents. Taken together, the results are consistent with the conjecture that companies can succeed in LMDs even though the marketisation level is low and transaction costs are high. The main limitation of our study is that due to the lack of public information about companies’ interaction with the institutional infrastructure in LMDs. We see that there is an institutional void, because aspects of infrastructure such as property protection or information mediation are poor, but we cannot conduct a direct test on how firms fill the detailed institutional void in LMDs by firm-level archival data.

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgements

We acknowledge financial support from the National Natural Science Foundation of China (grant numbers: 71632006 and 2015110598) and the MOE Project of Key Research Institute of Humanities and Social Science in University (grant numbers: 16JJD790038).

Notes

¹ See http://stock.hexun.com/2012/syzgbg, http://news.hexun.com/2012-04-21/140641547.html and http://stock.hexun.com/2015-06-03/176419797.html respectively.

² See http://business.sohu.com/20130718/n381941237.shtml and http://finance.ifeng.com/a/20180117/15931455_0.shtml.

³ https://www.economist.com/china/2014/12/30/back-in-the-cold

⁴ The similarity between two texts is measured by the Levenshtein-edit-distance of these two texts divided by the longer length of texts. This value ranges from 0 to 1, and the higher it takes, the more similar the objective texts are. According to previous research, we rank all sample’s similarity value into ten groups and use the group number as the value of RME_LVD.

⁵ Like the estimation of RME_LVD, we also rank all sample’s similarity value into ten groups and use the group number as the value of RLVD.