Understanding the inventor team size: A view from “The Rice Theory”

2.1 Rice and wheat culture

Throughout China's history, rice and wheat are the main food crops long time. Wheat first originated in Western Asia and was introduced to the Central Plains via Central Asia in 3000 BC. Wheat entered the Central Plains and became the main crop grown in the Yellow River Basin and nearby areas. Archeologists have discovered many wheat-planting sites, including the Donghui Mountain site in Minle, Gansu, the Zhaojialai site in Wugong, Shaanxi, and the Diaoyutai site in Bo County, Anhui. Since the 4th century AD, ancient Chinese people began to migrate on a large scale to the Yangtze River valley, an area suitable for rice cultivation (Perkins, 1969). In fact, the distinction between rice and wheat culture may have occurred earlier, as cultivation practices of rice in southern China are similar to those of wheat in northern China. The introduction of wheat is a selective one. Meanwhile, the original inhabitants of the middle and lower reaches of the Yangtze River initially chose to domesticate rice, which has many differences in farming practices from wheat. In this way, the differences between rice and wheat cultures in China can date back even 10,000 years to the domestication of the crop by the original inhabitants.

The two main differences between rice and wheat cultivation are irrigation and labor (Liu and Zong, 2018). First, rice is essentially a swamp plant and most of its varieties are grown in standing water, requiring very high levels of irrigation. In contrast, wheat can be grown on dry land and depends only on rainfall to provide enough water. Secondly, rice cultivation is labor concentrated and requires large-scale cooperation. While wheat is mono-annual, rice can be triannual at most, and rice cultivation is at its peak of labor demand at sowing and harvest (Bray, 1986). Rice irrigation consumes 20%–50% of the laborers' working time (Wittfogel, 1957). Agricultural anthropologists studied the labor time of farmers in the premodern history of China and discovered that it took at least twice as long labor hours to grow rice as wheat (Buck, 1938). In the rice and wheat regions, different cultures have taken shape from generation to generation.

Talhelm et al. (2014) proposed “The Rice Theory,” which suggests that growing rice creates a culture that favors holistic thinking. Wheat cultivation, by contrast, creates a culture where individuals are more inclined to be independent of each other. As rice cultivation requires irrigation systems (Talhelm et al., 2014). More labor inputs and coordination between different cultivators are demanded, enhancing the degree of interdependence between people in the area. In contrast, the cultivation of wheat is not overly dependent on large-scale cooperation. The cultivators are free to plan their cultivation, leading to a culture that tends to be individualistic. China falls into northern and southern parts by the Qinling–Huaihe Line, which nearly coincides with the boundary separating the subtropical and temperate regions. So wheat is the main crop in northern China and rice is the main crop in southern China. This geographical boundary is not strictly the dividing line between rice and wheat cultivation regions. Rice can be grown in areas with plenty of water, such as around river floodplains and lakes. But the probability of planting rice across this boundary is significantly reduced. This paper firstly accounts for rice and wheat cultivation area in each region of China at the city level. We then use the ratio of rice-wheat planting area to determine whether it is a rice area.

2.2 Culture and team cooperation

Innovation is the driving force behind the progress of nations and countries. How to make an innovation is one of the topical issues of interest to both Scholars and entrepreneurs. Researchers have validated the relationship between cultural composition and team performance. Scholars have proposed the CEM model (the Categorization–Elaboration Model) to explain the impact of team composition on team performance. The model highlights two different pathways through which an increase in team size affects team performance (Jackson et al., 2003; Milliken & Martins, 1996; O'reilly et al., 1998; Pieterse et al., 2013). An increase in team size enlarges the knowledge pool related to the team's task. Inventors also benefit from cooperation through the information exchange and diversity of perspectives. However, an increase in team size brings problems to team members, like group bias and antagonism which do harm to efficiency. The studies do not seem to reach consistent conclusions on the demographic and cognitive diversity of teams. Some researchers turn to the kinds of contexts in which these diversities have a positive impact. Van Knippenberg et al. find that in knowledge-concentrated environments, conflict from team diversity rather than being harmful enhances the quality of decision-making in complex environments and improves the performance of R&D teams (Pieterse et al., 2013). Roberson highlights how gender diversity can have both positive and negative effects in different contexts. Which factor to dominate rests on the context (Kovenock & Roberson, 2018). Janz et al. studied innovation activities in the context of teamwork. They argued that innovation activities are complex and that R&D activities require more knowledgeable workers to collaborate with different individuals to form a broad knowledge base and analyze problems from multiple perspectives (Janz et al., 1997).

Larger teams reflect the number of resources invested in innovation, which will arouse the subsequent attention given to the innovation and make it easier to realize its promise and value (Breitzman & Thomas, 2015). Studies in specific industries have exhibited that the expansion of a company results in an increase in the efficiency of R&D teams, especially in the pharmaceutical industry. The pharmaceutical invention could benefit from a larger organization. Evidence suggests that confident managers can lead to smaller team size. Managers only prefer to create larger teams when the complementary strengths of members are evident (Hakenes & Katolnik, 2018).

The influence of culture on the inventor teams is highly valued by scholars, as innovation is crucial not only for companies but also for long-term economic growth. Based on the role culture played in team performance, we hope to further examine the differences in inventor teams under diverse cultures. How do the inventors cooperate in knowledge-intensive tasks under rice or wheat culture? And how the inventor team size in rice regions differs from that in wheat regions. The line formed by the Qinling Mountains and Huai River provides a natural experimental basis for the study of this issue. The areas besides this line share similar histories, governments, languages, and religions. Comparisons between different areas within China can help to remove confounding factors that might lead to biased assessments.

It is worth emphasizing that the scale of an inventor team is hard to manipulate in our data. The team size refers to the number of inventors on a patent in this paper. We get the number of inventors from the initial file of the patent application. This information is available once the patent documents have been published or granted. The number of inventors can be the basis for a forward-looking rather than retrospective indicator. It is not an easy indicator to manipulate for two reasons. First. inventors have sufficient motivation to sign on the invention list, and there is no limitation on the number of inventors in patent applications. Second, if the principal or contributing inventor is not on the file list, the patent application will possibly be considered fraudulent, which will result in invalidation. Therefore, the number of inventors is a reasonable reflection of the number of researchers associated with an invention.

4.1 Ordinary least square (OLS) estimation

This paper first makes a simple multiple linear regression model to verify the influence of culture on the inventor team.

()

In the above equation, is the inventor team size of patent i in city j in year t. The number of single inventors accounts for the highest proportion in our sample. The team size has a continuous downward trend year by year. denotes whether the city j was under rice culture regions. We use the ratio of rice to wheat planting area to calculate this variable. We calculate the mean rice and wheat planting area by city from 1989 to 1993. If the ratio of the planting area is larger than 1, then the city j is defined as a rice region. takes the value of 1. Otherwise, the city j is defined as a wheat region and is 0. We focus on coefficients , which represents the difference between rice and wheat regions. denotes the control variables. represents the time-fixed effect and is the random error term.

4.2 IV approach

One may argue that there is endogeneity such as omitted variable bias and reverse causality bias in this study: Are there other unobserved factors that cause people to favor rice cultivation and at the same time favor the formation of small-scale teams? Is cultivating rice makes a bigger inventor team, or that inventors in a bigger group prefer to plant rice? The endogeneity may blur the result of our linear regression analysis. Therefore, to solve this problem, this paper constructs an IV to eliminate endogeneity. We take the suitability of a province's climate to plant rice as our IV. Whether people plant rice or wheat in a given place is primarily determined by the climate condition in that place in premodern time. There is a strong correlation between rice suitability and whether rice grows locally. This long-term climate and soil conditions will not affect the cooperative behavior of the inventor team, making it suitable to be used as an IV. This IV is also applied in the study of “The Rice Theory.” The suitability index provided by FAO is most refined to the provincial level, so this paper verifies the effectiveness of the IV at the provincial level. We examined the correlation between rice suitability and rice cultivating and found that the index can explain 61% of variations in rice cultivating share. In the first stage F test has demonstrated that the index is effective as an IV.

()

In Model (2), is the rice suitability of province j where patent i′s application is located. The value of the rice suitability index varies from 0 to 100 provided by the Food and Agriculture Organization of the United Nations for each province (about 56 km × 56 km). still represents the inventor team size. The rice suitability index stands for the IV of rice regions. controls the time-fixed effect. is the random error term.

4.3 Regression discontinuity design

Regression discontinuity design can act as a “local randomized trial,” which can effectively identify the causal relationship between variables. Rice cultivation is mainly affected by irrigation, which results in the high correlation between the division of rice and wheat areas and the geographical boundary of China. The boundary formed by Qinling Mountains and Huai River is of great significance for the geographical division: First, the subtropical monsoon climate is to the south of the Qinling Mountains, while the temperate monsoon climate is to its north. In addition, the boundary serves as the 0°C isotherm in winter in China as well as the precipitation 800 mm iso-precipitation line. Moreover, the boundary is in the area where the annual accumulated temperature is 4500°C. Therefore, this climate and geographical division make it suitable for planting wheat in North China and rice in South China. The differences in industrial distribution and other aspects are relatively small between the two sides of this boundary. Qinling Mountains, located in 32°N–34°N and 103°E–113°E, are the east–west mountain range across central China. Huai River, located in 31°N–36°N and 112°E–121°E, is one of the main rivers in eastern China. Therefore, the fuzzy RD method can be useful for setting the latitude as the driving variable. We take 33°N as the breakpoint, the areas below 33° N are mostly rice planting areas, and the areas above 33°N are mostly wheat planting areas. Therefore, the probability of being rice planting area crossing the boundary decreases from m to n (1 > m > n > 0) which also makes the design of fuzzy RD conform to the verification of the causal relationship between culture and inventor scale. This part constructs the following model to estimate the impact of culture on the size of inventors.

()

The explained variable still represents the inventor team size of patent i in city j and year t. f (l) is the polynomial smoothing function of latitude L. represents a set of covariates. is the random error term. To verify the team size differences in rice and wheat culture regions, we estimate the local average treatment effect.

()

In Formula (4), represents the change of probability of being rice region across the geographical boundary. represents the change of outcome variables across the boundary. We use the methods of Imbens et al. (Imbens & Lemieux, 2008; Papay et al., 2011) to estimate the causal effects. Here the latitude is regarded as the processing variable of . There will appear a significant discontinuous rise near 33° N. Therefore, the two-stage least squares method (2SLS) can be available for estimating the difference in inventor team size under rice culture and wheat culture. The following two equations show the discontinuity across the geographical boundary:

()

()

We estimate the difference in inventor team size besides 33°N in Equation (5). is the polynomial smoothing function of latitude L. provides the effect of latitude, process variable, on inventor team size. We also estimate the city's probability of being defined as a rice region besides 33°N in Equation (6). From Equations (5) and (6), we verify the difference of inventor team size under rice culture and wheat culture.

()

where , capturing the local average treatment effect of culture on inventor team size.

5.1 OLS estimation

We first examine the OLS results. After controlling the time trend, the average inventor size of invention patents in the rice region was 0.778 smaller than that in the wheat region. Other economic geographic characteristics of the rice and wheat regions may affect the scale of inventor teams. As the economic growth model in classical economics suggests, the number of people engaged in R&D activities increases as the population grows (Cass, 1965; Koopmans, 1965). Particularly in the post-World War II period, the actual number of participants in R&D multiplies in the United States and other OECD countries. In addition, the ability to provide an innovative platform for R&D activities is closely related to its level of economic development. Therefore, it is necessary to control for the size of the population and the level of economic development between regions to avoid their effects on inventor team size. In Table 2, we control for regional population size and level of GDP per capita. The empirical results show that an expansion in total population size will increase the size of invention teams. After controlling for total population and GDP per capita, the difference in inventor size between rice and wheat regions decreases from 0.778 to 0.5. In the geospatial distribution of population, regions with higher population densities tend to have a closer connection. It is easier for people with R&D-related resources and information to get in touch with each other. We, therefore, control for regional population density characteristics by including population density data for each city in China from the China Statistical Yearbook. Column 3 in Table 2 reports the regression results after controlling for population density characteristics. This result demonstrates that increasing the density of researcher distribution has a positive effect on the size of the inventor teams. Fleisher et al. studied the TFP changes in 25 provinces from 1978 to 1993 using economic growth accounting methods. They found that TFP in coastal provinces is twice as high as inland. They attributed the differences between coastal and inland areas to policy and geographic factors (Fleisher & Chen, 1997). In addition, Chen and Feng highlighted the differences in private enterprises across regions in terms of regional differences in protective policies (Chen & Feng, 2000). Considering that regional differences in the business environment, policy bias, and geographic factors may affect the size of inventor teams, we controlled for regional characteristics variables in Column 4. In the empirical study, we divided regions into four parts: eastern regions, central regions, western regions, and northeastern regions. We also considered coastal location to control for geographic factors. Given the large span of China's coastline, the distinction between eastern and western cannot distinguish whether a region is in a coastal location. We also created a dummy variable to reflect whether a region is located in a coastal area. The value of the coastal region was set as 1 and the rest as 0. The results showed that differences in inventor team size still exist significantly between the rice and wheat regions.

Another noteworthy issue is that rice and wheat regions may favor different types of inventions due to industrial structure. Labor and equipment input in producing different types of patents, which may result in size differences between rice and wheat regions. In terms of the division of patent types, the schedule number of Chinese invention patents is identified according to the IPC International Patent Classification Table. One invention patent may have several schedule numbers, but one of them is the main schedule number, which is the one to best represent the classification information of the patent. A complete schedule number is a combination of symbols for the department, major class, minor class, major group, and minor group. We focused on the department of a patent schedule number to distinguish between patents. There are eight main departments. Department A represents patents for the necessities of human life (agriculture, light, and medicine). Department B represents patents for operations and transportation. Department C represents chemical and metallurgical patents. Department D represents patents for textiles and paper. Department E represents patents for fixed buildings (construction and mining). Department F represents patents for mechanical engineering. Department G represents patents for physics and Department H represents patents for electricity. By dividing patents into these 8 departments according to their main schedule number, their average annual patent inventor size was calculated in this paper. Figure 2 shows the average inventor size of the 3 different types of them. The average inventor size of chemical and metallurgical patents was higher compared to the other types of patents. It increased from a size of 3 in 1985 to 4.56 in 2015. The size of the inventor team for operations and transportation patents was in a more stable state. We found that different types of patents could vary in team size in terms of inventor base, due to their complexity and resource requirements in the production process.

It is, therefore, necessary to take into account factors such as the complexity of patent production when examining differences in inventor size. In this paper, we generated seven vectors representing dummy variables in Departments A–G according to the schedule number. That helped us to exclude the effect of the distribution of patent types between regions.

Considering the significant differences in inventor size between patent types, we controlled for the dummy variables of the type in Column 1 in Table 3. After controlling for the type of the patent, the difference in inventor size between the rice and wheat region decreases from 0.532 to 0.509. Among the eight patent types, the average inventor size was lower for patents on human necessities (agriculture, light, and medicine), textiles and paper, and mechanical engineering than for the other categories. This suggested that some of the differences between rice and wheat culture can be explained by the interregional differences in patent structure. This suggested that some of the differences in inventor team size between rice and wheat regions can be explained by differences in patenting preferences between regions.

Invention teams in regions with higher economic transformation efficiency may achieve the same innovation output as larger teams in other regions. Therefore, the size of inventor teams in regions with higher economic transformation efficiency could be smaller. This paper found an index of industrial transformation efficiency. Industrial electricity consumption is related to economic production activities, which can be used to measure the transformation efficiency of a region. Industrial electricity consumption per unit GDP is the total value of regional industrial electricity consumption divided by regional GDP. The smaller value means that the same economic output consumes less power and the economic transformation efficiency is higher. Some may worry that the economic transformation efficiency of a region may affect the organizational form of innovation activities. Regions with higher economic transformation efficiency can form smaller inventor teams. So that the optimal scale of inventor team is smaller than that with lower transformation efficiency. Column 2 in Table 3 shows the results after controlling the industrial electricity consumption per unit GDP. We found the inventor team size of the rice region is 0.505 smaller. The economic transformation efficiency in industrial production does not alter previous estimation results.

The capital city is the political and cultural center of the province and the first-level administrative region in China. Capital cities have some resource advantages and inclinations in the economy, science and education, culture, transportation, and so on. Some may concern that compared to other noncapital cities, there may be some differences in the way inventor teams are organized in provincial capitals. Political factors need to be controlled for when the inventor team size is researched. Two variables were constructed in this paper to control for the effect of political factors: one is , a dummy variable for whether the city j is a provincial capital. The other is , the geographic distance from the city j to the provincial capital. Column 3 in Table 3 shows the regression results after controlling for political and cultural factors of regions. We found that the difference in inventor team size between the rice region and wheat region widens to 0.556, indicating that the difference in inventor team size is more pronounced after deducting influences of political factors. In Column 4, we also controlled for both production transformation efficiency and political factors. Results show that differences still exist between rice culture and wheat culture.

5.2 IV results

In this part, we use IV to further verify the differences in the size of inventor teams between rice culture and wheat culture. The rice suitability given by FAO is used here as an IV to determine rice regions. Precipitation, soil, and topographic conditions significantly affect whether a region grows rice. The suitability index is strongly correlated with rice cultivation, whereas it is not correlated with the cooperative behavior of inventor teams. Rice suitability had yet been proved to be a functional IV for rice regions. We put the suitability for rice cultivation back into the model as the main explanatory variable. The regression results with the inclusion of the IV are presented in Table 4. In Column 1, we controlled for the year fixed effect and took into account the total population size, the level of GDP per capita, and the population density of the area. The coefficient of indicates that the rice area has smaller inventor teams. The scale of the inventor team is 0.791 smaller than that in the wheat regions. The IV results similarly suggest that as the population grows, the number of people engaged in R&D activities increases (Koopmans, 1965), which leads to an increase in the average inventor team size. Regions with higher GDP per capita have smaller average inventor teams out of higher disposable resources per capita. Also, regions with greater population density have larger average inventor teams. In Column 2, we furtherly controlled for the geographic characteristics of patent locations. As in the OLS model, we divided China into four parts according to the eastern, central, western, and northeastern regions. We also distinguished the coastal regions and inland regions according to the coastline. The empirical results indicate that the inventor team size of patents in coastal regions is smaller. After the inclusion of regional geographic characteristics, the difference in inventor team size between rice culture and wheat culture is partially explained by the coastal distribution, eventually narrowing to 0.725. In Column 3, we added the characteristic variable of the patent types. Considering that different categories of invention patents require different amounts of labor input, the difference in inventor team size between the rice culture and wheat culture was reduced to 0.703 after controlling for the patent types. The patent type explained 2.78% of the difference in inventor team size between the rice culture and wheat culture. In Column 4, regional industrial electricity consumption per unit of GDP is further controlled for. The difference remains 0.703 after accounting for economic transformation benefits. In Column 5, we controlled for the political factors. The provincial capital and the geographic distance were added to the regression. Results show that the difference in inventor team size is more pronounced after controlling for relevant political factors. The cultural characteristics of the wheat region make the optimal size of the invention team larger than that of rice culture. In knowledge-intensive activities, inventors under wheat culture form the optimal organization on a larger scale.

5.3 Regression discontinuity

We used a natural experiment to examine differences in the inventor team size under the culture of rice cultivation and wheat cultivation. The division of rice regions and wheat regions is very highly correlated with the geographic line in China, which is formed by Qinling Mountains and the Huai River. This line is of great importance. The line is the 0°C isotherm in winter of China as well as the precipitation 800 mm iso-precipitation line. The climatic and geographic division of the geographic line thus creates climatic conditions suitable for growing rice on the south sides of China and wheat on the north sides. The advantage is that the differences in industrial distribution and other aspects are relatively small beside the line. We restricted the sample to the area on either side of the geographic line to take advantage of this perfect natural geographical experiment. Thus, we could examine the manifestation of cultural differences in scientific cooperation without the influence of extraneous factors. As the cultivation of rice or wheat is mainly influenced by rainfall and irrigation, the probability of cultivating rice decreases significantly from south to north across the geographical line. That permits a natural fuzzy RD design experiment. Cities in the north of 33°N are mostly wheat-growing regions, and the southern part is a mostly rice-growing region.

The geographic distribution makes the cultivation of rice and wheat areas highly correlated with latitude, which acts as a perfect driving variable. As Figure 3 shows, before considering cultivating culture, the size of the inventor team is a continuous variable with latitude. The jump of inventor team size at the boundary appears both in the linear fitting graph and quadratic fitting graph.

Table 5 shows the results of the local polynomial RD. We concentrated the sample in the area between 23°N and 43°N. The estimation of the local average treatment effect is −1.031, indicating there is a significant difference in inventor size between two sides of the Qinling-Huaihe line. There is a significant difference in inventor team size both in the linear fit case and the polynomial fit case with a higher order. The inventor team size is lower on the south side of the Qinling-Huaihe line than that on the north side. In Column 2, a rectangular kernel was used instead of a triangular kernel function. We still found that the estimations are significantly valid, and the inventor team size in the rice region is still significantly 0.527 smaller. In Column 3, covariates were added to the empirical analysis, including population size, GDP per capita level, population density, and regional geographic characteristics. After controlling for these factors, the RD results show that the difference in inventor team size widens further to a level of 2.112. In Column 4, we further controlled for patent type, industrial transformation efficiency, and regional political factors. The results indicate that the average scale of inventor teams in rice regions is 2.017 lower than that in wheat regions. This natural experiment using the Qinling-Huaihe line confirms the significant differences in inventor team size between rice culture and wheat culture.

The change in latitude is considered an IV to deal with the variable , and a significant discontinuity occurs near the 33°N line. We then relaxed the bandwidth selection restriction and applied a two-stage least squares empirical analysis. In the first stage, a significant decrease in the probability of a city defined as a rice region occurs across the 33°N. we found that the probability of a city defined as a rice region is reduced by 0.495 (). In the second stage, the estimated local average treatment effect () is −1.581, suggesting that across the line, cultivation cultural differences lead to a 1.581 reduction in the inventor team size (Table 6).

6.1 The definition of rice region and wheat region

In the empirical analysis, we calculated the historical planting ratio of rice and wheat areas to define whether the city is a rice region. If the area under rice cultivation is larger than that under wheat cultivation in a city, we defined it as rice area. Some may challenge this definition. To eliminate the interference from the definition, we redid the empirical analysis by redefining rice and wheat areas using another two scenarios with rice-to-wheat acreage ratios of 0.8 and 2. Errors due to the definition of rice areas could be checked with this method. Here the cultivated area of rice and wheat is still adjusted as an average of the area from 1989 to 1993.

The results of the empirical analysis after redefining the rice and wheat regions are presented in Table 7. In Columns 1 and 2, a ratio of 0.8 of rice to wheat acreage is chosen as the basis for identification. After controlling for year fixed effects, population size, and GDP per capita, the inventor team size in rice regions is 0.628 lower than that in wheat regions. After adding the patent type, industrial transformation efficiency, and regional political factors, the difference in inventor team size widens to 0.732. In Columns 3 and 4, we present results of a ratio of 1 as the cut-off point for the definition. In Columns 5 and 6, a ratio of 0.8 of rice to wheat acreage is chosen as the basis for identification. We still found that cities with a rice-to-wheat acreage ratio higher than 2 are 0.278 smaller than other cities.

6.2 Percentage of rice cultivation areas

In the previous empirical analysis, this paper used the rice-to-wheat acreage ratio to determine whether it is a rice region. Here, we take the historical rice acreage share as the main explanatory variable to proxy the characteristics of rice culture tendency. We focus on the differences between rice and wheat cultures, the is defined in this section of the validation as the proportion of historical rice acreage in the total historical acreage of these two crops. indicates that the average proportion of rice cultivation area to the total area of the two crops in region j between 1989 and 1993.1

Table 8 shows the results of the analysis using the Percentage of Rice Cultivation areas. In Column 1, we controlled for the economic factors of the location of the patent i, as well as the patent type and time fixed effect. Column 2 further controlled for the population density and GDP per capita. Column 3 further controlled for the political factors of the region, including whether it is a provincial capital city, and the straight-line distance to the provincial capital city. From the regression results in the table, we found that an increase in the proportion of rice cultivation area within a prefecture-level city leads to a decrease in the size of the inventor team. And this difference is significant after controlling for economic, demographic, and political factors, which once again confirms that the inventor team sizes formed under the culture of rice regions are smaller.

Table 8. Robustness check: The percentage of rice cultivation areas

Variables	Dependent variable: Scale
	(1)	(2)	(3)
	−1.192***	−0.867***	−0.972***
	(−181.50)	(−114.40)	(−125.80)
Economic factors	Yes	Yes	Yes
Demographic factors	No	Yes	Yes
Political factors	No	No	Yes
Patent type	Yes	Yes	Yes
Time FE	Yes	Yes	Yes
Constant	4.578***	4.257***	4.758***
	(449.21)	(387.40)	(362.50)
Observations	1,396,102	1,396,102	1,396,102
R2	0.082	0.082	0.082

• Note: T values are in parentheses. is the average proportion of rice cultivation area to the total area of the two crops in region j between 1989 and 1993. ***, **, and * respectively denote significance at the 1%, 5%, and 10% level.

6.3 Institutional patents and individual patents

The number of inventors in an innovation is directly related to whether it is an individual initiative activity or an institutionally supported activity. The initiator of that innovation sets the direction, which will influence the subsequent research. If the innovation is supported by a company or an institution, then at the very beginning, the company could assemble a team to carry out innovative activities in the same direction. That makes institutionally supported patents to be signed by more inventors than individual initiative patents.

We first distinguished whether the innovation is supported by a firm (or an institution). In the patent application documents, we found that if the patents are supported by institutions, then the patents will be directly attributed to them. The patent owners in the application text provide valid information about the patent supporters. On the one hand, the patent is not disclosed at the initial stage of application. If the patent is developed by an individual, it needs time to be transferred to an enterprise. On the other hand, the purpose of applying for a patent is to better protect intellectual property rights. The individual can later transfer the patent to pursue greater personal gains, rather than transfer them before applying at the risk of being stolen. We determined whether it is an institutional patent according to the patent owner information in the text. The documents submitted contain information on the patent owner. We performed textual identification of the patent owner information, distinguishing between the name of an individual and the name of an institution. If there is at least one institution among the patent owners, then we regard the innovation as an institutional patent. We thus distinguished between innovations organized by individuals and those by institutions. The differences in inventor team size after considering the patent owner's type are illustrated in Table 9. We created a variable, , to reflect the type of patent owners. is the interaction term of and . The coefficient before is significantly negative, indicating that the difference in the size of inventor teams is more obvious for institutionally organized innovations. The OLS regression results indicate that the size of inventor teams under institutional support is larger in wheat regions than that in rice regions, compared to the inherent differences between regions. The size of non-institution-supported inventor teams is smaller than that in the wheat region by 0.219. While the size of inventor teams supported by institutions is 0.414 smaller than that in the wheat region. The regression results using rice suitability as IV support the previous findings. We found that differences in inventor team size supported by institutions are bigger between rice culture and wheat culture, with an expansion of 0.7.

Table 9. Robustness check: Institutional patents and individual patents

Variables	Dependent variable: Scale
	(1)	(2)	(3)	(4)	(5)
	OLS	OLS	IV	IV	IV
Rice	−0.363***	−0.219***	−0.455***	−0.305***	−0.359***
	(−29.39)	(−17.29)	(−29.55)	(−18.80)	(−22.03)
	2.187***	2.204***	2.480***	2.485***	2.480***
	(221.80)	(224.50)	(222.40)	(223.20)	(222.80)
	−0.179***	−0.195***	−0.692***	−0.700***	−0.691***
	(−13.59)	(−14.86)	(−42.17)	(−42.57)	(−42.04)
Time FE	Yes	Yes	Yes	Yes	Yes
Patent type	Yes	Yes	Yes	Yes	Yes
Regional characteristics	No	Yes	No	Yes	Yes
Geographic factors	No	Yes	No	No	Yes
Observations	1,396,102	1,396,102	1,396,102	1,396,102	1,396,102
R2	0.122	0.130	0.130	0.134	0.135

• Note: Here patents from schools, hospitals, research institutes, and companies are treated as institutional patents. The institution dummy variable indicates whether the patent-producing subject contains an institution, with the presence of an institution recorded as 1 and 0 otherwise; the interaction term is generated by the rice regional and the institution dummy variable. ***, **, and * respectively denote significance at the 1%, 5%, and 10% level.

6.4 Geographical variables

Based on differences in regional policies and resource endowments, we divide samples into four regions in the empirical research. We also constructed a dummy variable for coastal areas to capture coastal culture. Some scholars point out that coastal residents are more adventurous. In this section, the geographic characteristics are determined using the longitude location of the cities to avoid geographic factors that are missed in the previous research. Column 1 in Table 10 shows the empirical results without controlling for geographic factors. Column 2 shows the empirical results controlling for regional resource endowments and coastal culture. In column 3, we used longitude coordinates to control for geographic factors. In all three cases, the differences in inventor team size between rice culture and wheat culture remain significant. The differences are 0.558 and 0.551 after controlling for geographical factors. This indicates that controlling for geographic factors in different ways does not affect the main findings and that differences between rice culture and wheat culture still exist significantly.

6.5 Removal of special cities

As the capital of China, Beijing is the political and economic center. This may cause the invention teams in Beijing to behave differently from other cities. The total number of patent applications in Beijing has reached 220,893. As invention patents originating from other cities may be applied for in Beijing, that will lead to an upward bias in the number of patent applications in Beijing. This will then affect our examination of the size of inventor teams between rice culture and wheat culture. Similarly, Shanghai is another megacity and economic center in China. The patent application in this city may also be affected by other factors, such as political considerations. Moreover, it is a city with similar significance in the rice region as Beijing in the wheat region.

To circumvent influences from political and other considerations, this paper excluded one comparable city from each of the rice regions and wheat regions, that is, Beijing and Shanghai, from the whole sample. After the exclusion of the abovementioned cities, the rest of the sample is used in empirical research. The results are shown in Table 11. After removing the two special cities of Beijing and Shanghai, the result of general multivariable regression shows that the difference in inventor team size between rice culture and wheat culture remains at −0.551. The result from IV regression also confirms a significant difference in the team size of inventors between rice and wheat regions.

6.6 The tendency of cooperation in rice regions and wheat regions

The size of the inventor teams in rice regions and wheat regions can be treated as the optimal size formed by different cultures. Based on the analysis of “The Rice Theory,” people under the influence of rice culture prefer cooperation. Due to the labor-intensive farming method, people in the rice culture region are more dependent on each other and historically develop a highly coordinated social organization system. Hence, people under the influence of rice culture will be more inclined to cooperate in innovation. This higher degree of coordination in the rice region allows the production of new technologies even based on a smaller inventor team. To verify this conjecture, this paper examines whether the inventors cooperate in each of the regions.

In this paper, invention patents are divided into two types: cooperative patents and independent patents, based on the number of inventors of the invention. is a dummy variable to indicate whether the patent is cooperatively developed. If patent i in city j and in year t is developed by a team with more than one inventor, then will be recorded as 1, otherwise 0. A simple multivariable linear regression model is used to examine the cooperation in the R&D behavior of rice and wheat regions. Table 12 reports the cooperative tendency of regions in R&D activities. Control variables are consistent with those in the main regression. Particularly, in the first column, time-fixed effects and patent type are controlled for. The rest of the columns add part of the following control variables: regional industrial characteristics, political factors, and geographic factors.

Table 12. Tendency of cooperation in rice and wheat region

Variables	Dependent variable: Scale
	(1)	(2)	(3)	(4)
	0.0724***	0.0733***	0.0755***	0.0773***
	(75.40)	(75.62)	(77.16)	(77.78)
Time FE	Yes	Yes	Yes	Yes
Patent type	Yes	Yes	Yes	Yes
Industrial characteristics	No	Yes	No	Yes
Political factors	No	No	Yes	Yes
Constant	0.278***	0.290***	0.322***	0.348***
	(18.72)	(19.42)	(19.94)	(21.27)
Observations	1,396,973	1,396,973	1,396,973	1,396,973
R2	0.056	0.056	0.056	0.057

• Note: The dependent variable is a dummy variable for whether to conduct cooperative R&D. For the patents of cooperative R&D, it is recorded as 1, and the patents of independent R&D are recorded as 0. ***, **, and * are respectively significant at the level of 1%, 5%, and 10%.

The empirical results suggest that the cooperation tendency in the rice regions is significantly different from wheat regions. The proportion of cooperative invention patents in the rice region is 7.73% higher. Culture itself contains complex and profound meanings. We believe that it is also a complex influencing mechanism for the formation of the inventor team. To understand the mechanism of how culture affects people's cooperative behavior in innovative activities, more data and evidence are needed. Given the existence of team differences between rice culture and wheat culture, this paper attempts to explain it from the perspective of “The Rice Theory.” We regard the size of the inventor team as the optimal team size formed under different cultures. The results of this paper show that the proportion of cooperative invention patents in the rice region is higher, but the inventor team size is smaller. Therefore, this paper tends to believe that people under the influence of rice culture are more inclined to trust each other and have a higher tendency to cooperate. As people have formed a higher degree of trust which is beneficial for teamwork, the optimal size of the inventor team is smaller. We also highlight that more data and evidence are needed to test whether cooperation in the rice region is more effective. It is of significant difference to research the quality of innovative output under the rice culture and the wheat culture.

6.7 Migration between regions

Migration may bias the results of inventor size differences under different cultivation cultures. The limitation is that we can only observe the address of where the invention patent application is located from the data. We cannot obtain information about the location of the inventor's birthplace. The migration between rice and wheat regions may make the size differences of inventor teams deviate from their true level. To eliminate the effect of this factor as much as possible, we controlled for the percentage of foreign population in each region and uses the overall percent of foreigners to control for the characteristics of regional population mobility. We selected four years of census sample data, 2000, 2005, 2010, and 2015. Within the sample, we got the data on the foreign population of each region. denotes the share of the foreign population in the total population of the region in the survey years.

Table 13 shows the results of the empirical analysis after considering population mobility. Column 1 presents the results of adding a control variable, the share of the foreign population, by simply controlling for economic and demographic characteristics. Column 2 shows the results of the analysis without controlling for the share of the foreign population in the sample. Column 3 shows the results of the analysis after controlling for the share of the foreign population. We found that there was still a significant difference in inventor size between the rice and wheat regions within the sample data. And this difference remained significant after accounting for the percentage of foreign population in the region, decreasing from 0.825 to 0.807. the difference in inventor team size is narrowed after considering the migration factor.

Table 13. Robustness check: Considering migration between regions

Variables	Dependent variable: Scale
	(1)	(2)	(3)
Rice	−0.814***	−0.825***	−0.807***
	(−82.66)	(−79.17)	(−77.06)
	−1.055***		−0.831***
	(−22.51)		(−16.42)
Economic factors	Yes	Yes	Yes
Demographic factors	Yes	Yes	Yes
Political factors	No	Yes	Yes
Patent type	No	Yes	Yes
Time FE	Yes	Yes	Yes
Constant	4.654***	4.846***	5.068***
	(240.5)	(222.5)	(197.8)
Observations	329,969	329,969	329,969
R2	0.062	0.071	0.072

• Note: T values are in parentheses. denotes the share of the foreign population in the total population of the region in the survey years. ***, **, and * respectively denote significance at the 1%, 5%, and 10% level.