A substantial body of literature explains heterogeneity in the spatial distribution of economic activity (e.g. Marshall, 1890; Jacobs, 1969; Krugman, 1991; Henderson, 2003 ). The idea of the sources of geographic concentration of firms goes way back to Marshall’s (1890) pioneering work. Marshall argued that geographical concentration leads to firm productivity through input sharing, labour market pooling, and knowledge spillovers. These sources are external to individual firms and benefits pertinent to firms within the same industry known as localization economies. Duranton and Puga (2004) study classify the micro-foundations for agglomeration economies via sharing, matching, and learning². Jacobs (1969) argues that a diversity of regional economic activity nurtures innovation and growth in inter-industry rather than intra-industry spillovers. This indicates that a firm benefits from being located near other firms of other industries known as urbanization economies³. In explaining the uneven spatial distribution of economic activity, urban economics and new economic geography dominate recent research in economics (Brakman et al., 2009) . A critical difference between these two approaches is that NEG highlights the role of spatial linkages. In urban economics, cities or regions are like freely floating islands, which imply not considering spatial interdependencies between regions⁴. Krugman (1991) laid the foundation of “New Economic geography” (hereafter, NEG) and created a spatial economic model to understand the mechanism of firm localization and put stress on the role of “second nature geography” (location of economic agents, i.e., workers and firms relative to one another in space).

In contrast, previous neoclassical explanations for uneven economic activity distribution across space emphasize “first-nature geography” (resource endowments, topology, and the physical geography of climate). The main building blocks of NEG are product differentiation modelled through various assumptions, increasing returns to scale, reducing transport costs, and creating pecuniary externalities in agents’ location choices (Redding, 2010) . When these three building blocks are combined with interregional factor (labour) mobility, they give rise to cumulative causation forces and lead to the spatial concentration of economic activity⁵. Krugman’s model is based on Dixit & Stiglitz (1977) model of imperfect competition and increasing returns to scale. However, the importance of increasing returns to scale came from the Starrett (1978) “Spatial Impossibility Theorem”⁶. In Krugman’s model, the firms specialize and concentrate at a particular location if there are strong internal economies of scale and low transportation costs. There are likely many reasons for the geographical concentration of industries, but two key factors influencing it are natural advantages and localized knowledge spillovers (Ellison & Glaeser, 1997) ⁷.

The agglomeration of firms occurs due to various sources of agglomeration economies, localization economies, urbanization economies, natural advantages, market access, lower transportation costs, and other factors. Helsely and Strange (1990) showed that the searching costs of firms with differentiated labour demands and workers with differentiated skills are reduced when firms are geographically concentrated. Audretsch and Feldman (1996) find that knowledge-intensive industries are generally more agglomerated than traditional industries, implying the importance of knowledge spillovers. Ellison & Glaeser (1997) find that industries that are not localized have a lower level of productivity. Puga (2010) study reveals that the production is more clustered geographically even after controlling for comparative advantages, spatial patterns in wages and rents, and systematic variations in productivity within the urban environment. Also, the geographical concentration of activities has a positive impact on productivity. Over the last two decades, the most advanced firm and establishment-level datasets emerged that help study agglomeration economies and productivity spillovers within cities. A group of research focuses on distance-based continuous measures of geographical concentration ( Duranton and Overman (2005) , Marcon and Puech (2010) ) for industries’ agglomeration causal effect on productivity (Melo et al., 2009; Graham et al., 2010; Combes & Gobillon, 2015) , and for dynamic outlooks that include firms entry and exit (Dumais et al., 2002; Glaeser et al., 2015) . Besides, Mudambi and Swift (2012) , Beugelsdijk and Mudambi (2014) , and Lorenzen and Mudambi (2013) have done extensive research on the geographical dimension of FDI and modes of entry of MNEs into the host country’s regional location. These studies trace the origins of research on geographic clusters and identify the seminal contributions focusing on the role of MNEs, connectivity of firms of different clusters through knowledge, R&D, innovation of new technology, etc. For instance, in India, Behera (2017) examine the productivity spillovers from FDI at the regional level using 22 manufacturing industries. He finds that firms’ absorptive capacity with market concentration acts as a crucial conduit for innovation, enhancing the total factor productivity. Similarly, Behera et al. (2012) and Behera (2015a, 2015b) find that R&D and technology import intensity enhances the productivity of Indian manufacturing industries.

In the Indian context, various studies explore the appropriate determinants of firm locational choice and firm productivity. Mitra (1999) uses firm-level data to evaluate the significance of agglomeration economies in two manufacturing industries by applying a statistical stochastic frontier model. The study reveals substantial evidence of a positive association between technical efficiency and city size. But, after a certain threshold level, the size of the city works as diseconomies of scale. Lall et al. (2003) find that industrial diversity (urbanization economies) has a significant cost-reducing effect on firms that lead to industrial clustering in metropolitan areas in India. Chakravorty et al. (2005) studied eight industrial sectors in three Indian metropolises (Mumbai, Kolkata, and Chennai) to determine whether localization economies play a substantial role in cluster formation. The results suggest that urbanization economies are more important for a firm’s business location than localization economies. Lall and Mengistae (2005) study of manufacturing plant levels from India’s major industrial centres shows significant productivity gaps across cities due to differences in agglomeration economies, market access and the local business environment. Sridhar and Wan (2010) study reveal that more labour-intensive firms tend to refrain from locating in large cities of India. However, firms established in the post-reform period tend to locate in large cities.

Moreover, the availability of inputs positively impacts firm location in India. Mukim (2015) analyze coagglomeration patterns between formal and informal manufacturing enterprises in India. The study finds that buyer-seller linkages and technology spillovers are the most significant factors that explain formal-informal manufacturing enterprises’ coagglomeration. Desmet et al. (2015) focus on India’s spatial development, particularly in the service sector. The study reveals that high-density clusters of economic activity continue to be India’s engines of growth. Besides, given the role played by Information and Communication Technology (ICT), the study finds that agglomeration forces in service sectors still dominate dispersion forces in high-density areas. Ghani et al. (2016) studied the spatial pattern of manufacturing and service industries in India from 2001 to 2010. The main finding of their study is summarized as follows. First, the organized manufacturing sector moves away from urban cores to the rural periphery while services move towards the urban centres. Second, manufacturing industries have a stronger inclination to locate closer to larger cities in an urban area as compared to the service activity. Third, human capital matters for services while infrastructure for manufacturing output.

The measurement of geographical concentration is one of the primary difficulties in agglomeration literature. Many scholars (Krugman, 1991; Audretsch and Feldman, 1996; Brülhart, 2001) have tried to measure the degree of geographical concentration using a series of global indices such as the Locational Gini coefficient and Herfindahl Index⁸. However, the Gini index is insensitive to the spatial concentration of firms within the industry. This shortcoming is overcome by the Ellison-Glaeser index (1997) (hereafter EG index), which contains the Herfindahl index to measure plant-level employment concentration in the industry. A plethora of literature (Dumais et al., 2002; Braunerhjelm & Johansson, 2003; Devereux et al., 2004; Lu & Tao, 2009) measures geographical concentration through the EG index (1997) is applied broadly across different countries. Rosenthal and Strange (2001) use the EG index (1997) and find that labour market pooling significantly impacts industry agglomeration at all geographical scales.

The EG index (1997) has its benefits and practical applicability. However, it suffered from a “checkerboard problem” and “modifiable areal unit problem” (MAUP) (Arbia, 2001; Duranton and Overman, 2005) ⁹. The MAUP problem occurs when there are pre-defined boundaries, and the researcher has to work with these units, which leads to bias in the measurement of geographical concentration¹⁰. However, the checkerboard problem implies that the geographic position of regions or region-relatedness is not considered while computing industries’ geographical concentration. Ideally, the geographic concentration needs to be measured using distance-based continuous measures following Ripley (1977) , Duranton and Overman (2005) , and Marcon and Puech (2003, 2010) , relying on the point pattern spatial data that requires location for each plant.

Nevertheless, scholars often only have access to spatially aggregated areal data and thus cannot apply the distance-based continuous measures. However, to overcome the checkerboard problem in areal data, Guimarães et al. (2011) extend the Ellison-Glaeser index (1997) by incorporating spatial dependence among regions. Their application of the spatially weighted EG index in the US context shows that it captures neighbourhood effects while quantifying geographical concentration. Behrens & Bougna (2015) study the locational patterns of manufacturing industries in Canada by applying the unweighted EG index and spatially weighted EG index. Their results reveal that Spearman’s rank correlation between weighted and unweighted EG indices was around 96%. It indicates that the geographical concentrations were not extending “too much” across different regions in Canada. Similarly, Dauth et al. (2018) also applied the EG index and spatially weighted EG index in Germany from 1980 to 2010 to examine the long-run geographical concentration of manufacturing, service, and knowledge-intensive industries at the county level. In a similar line, Crafts & Klein (2021) study also applied a spatially weighted EG index to examine the geographical concentration of US manufacturing industries between 1880 and 2007.

In the Indian context, Lall et al. (2004) studied how agglomeration economies contribute to economic productivity by measuring the geographical concentration of only formal manufacturing firms using the Gini Index and Ellison-Glaeser index (1997). They use Annual Survey of Industries (ASI) data for the 1994-1995 period at the NIC two-digit level. The result suggests that improved market access significantly determines firm-level productivity. Lall & Chakravorty (2005) evaluated the relationship between industrial spatial location and spatial income equality by measuring the magnitude of industrial concentration using the Gini Index. Their study conducted empirical analysis for only eight manufacturing industries using the ASI database’s plant-level data for 1998-1999¹¹. Fernandes and Sharma (2012) examine the impact of industrial reforms on the geographic concentration of manufacturing industries measured by the Ellison-Glaeser index (1997) using plant-level data from ASI over the period 1980-1999. Kathuria (2016) used plant-level data for 1997-1998 to examine the geographical concentration of organized manufacturing firms in 21 Indian states using the Ellison-Glaeser index (1997). Nevertheless, to our best understanding, none of the previous literature examines the spatial dimension of neighbourhood effects factor for the geographical concentration of 71 manufacturing and 120 service industries at a district level in India. Therefore, this paper bridges the research gap in the agglomeration literature by estimating the effect of neighbourhood factors on the spatial concentration of three highly concentrated manufacturing and service industries in India using two spatial structures.

The measurement of geographical concentration is one of the primary difficulties in agglomeration literature. Many scholars have tried to compute the degree of geographical concentration using a series of global indices such as the Locational Gini coefficient and Herfindahl Index (Brülhart, 2001; De Dominicis et al., 2013) . The fundamental problem with the Gini index is that it is insensitive to the spatial concentration of firms within the industry (Guimarães et al., 2007) . The limitations in the Gini index are overcome by the Ellison-Glaeser (EG) index (1997), as it contains the Herfindahl index to measure plant-level employment concentration in the industry. It derives from a location choice model, assuming that firms choose their location as if dartboards were thrown at a map (Dauth et al., 2018) . The index for an industry (i) in a country with M regions (indexed by m) is defined as follows:

γ i = G i − H i ( 1 − X ′ X ) ( 1 − H i ) ( 1 − X ′ X ) (1)

where G i represents an index of geographical concentration, defined as G i = ( S − X ) ′ ( S − X ) , the vector S ′ = [ s 1 , s 2 , ⋯ , s M ] represents the share of industry i employment across geographical regions m and X ′ = [ x 1 , x 2 , ⋯ , x M ] represent a vector of aggregate employment shares across geographical regions m.

Arbia (2001) and Lafourcade & Mion (2007) recognized traditional measures of geographical concentration (locational Gini coefficient and unweighted EG index) but did not take into account the spatial dependence factors. As spillover effects do not recognize any areal boundaries, so ideally, this issue has to be addressed (Guillain & Le Gallo, 2010) . We cannot calculate Duranton and Overman’s (2005) or Billings and Johnson’s (2016) geographical concentration index because these indices require the address of each establishment to calculate the distance between them. This distance data requirement is not available in the case of India. However, Guimarães et al. (2011) extend the original EG index (1997), which includes neighbourhood effects through a spatial weight matrix to capture the neighbourhood effects. The spatially weighted Ellison-Glaeser index is suitable for countries where precise information about a firm’s location is unavailable. The spatially weighted version of the Ellison-Glaeser index is calculated as follows:

γ i s w = G i S − H i ( 1 − X ′ Ψ X ) ( 1 − H i ) ( 1 − X ′ Ψ X ) (2)

where G i S = ( S − X ) ′ Ψ ( S − X ) represent the spatially weighted version of the geographical concentration index ( G i ) and Ψ is a spatial weight matrix ( Ψ = W + I ) . For Ψ = I , the index collapses to the standard EG measure. W is a first-order queen contiguity rule created by assuming the convention that ω r s = 1 when r and s are neighbours and that ω r s = 0 otherwise. Each row in the binary contiguity matrix is divided by row sum to get a row standardized weight matrix ω r s which is as follows:

ω r s = ω r s ∑ s ω r s (3)

For empirical analysis, the study uses the latest Sixth Economic Census (EC) data of 2013-2014 compiled by the Central Statistics Office, Ministry of Statistics and Programme Implementation (MOSPI)¹². The EC (2013) data enumerated all establishments engaged in various agricultural and non-agricultural activities, excluding crop production, plantation, public administration, defence, and compulsory social security (Central Statistics Office, 2013) ¹³. Some studies (Unni & Raveendran, 2006; Manna, 2010) pointed out that EC data suffer from the under-coverage of minor establishments (i.e. number of own account establishments) compared with estimates based on follow-up surveys. Despite this caveat, EC is not censored by size or constrained to include only the formal or informal sector and thus the only Indian dataset that permits estimation of the complete establishment size distribution—across all sizes and types of establishments (Amirapu and Gechter, 2020) . The Economic census (EC) dataset is more reliable micro-unit establishment data available in the Indian context to examine the geographical concentration of manufacturing and service industries. The dataset covers 71 manufacturing and 120 service sector industries, followed by NIC-2008 at a 3-digit level.

Table 1 summarizes employment and establishment data for India’s manufacturing and service industries. It shows that 10.3 million manufacturing establishments employ 30.1 million workers and 33.6 million service establishments employ 73.8 million workers. The manufacturing and service sectors comprise 43.9 million establishments that employ 103.9 million workers. We need to calculate the spatial weight matrix to capture the neighbourhood effect. We require data on India’s district boundaries to construct a spatial weight matrix¹⁴. Our study considers two spatial structures to understand the role of neighbourhood effects. First, the spatial structure measures industries’ geographical concentration using data aggregated at the district level by covering 636 districts across 34 states and union territories of India. Second, the spatial structure measures an industry’s geographical concentration within every 29 contiguous states of India using district-level data. We apply the queen contiguity spatial weight matrix for both spatial structures to capture the neighbourhood effect¹⁵.

Source: Author’s computation using India’s Economic Census (2013) data. Notes: Economic census (2013) provides data for 34 states and union territories which comprises 642 districts, out of which we have taken data for 636 districts. We have excluded six districts due to neighbours’ data non-availability. The six districts consist of Shahdara and South-East (New Delhi); Nicobar, North & Middle Andaman and South Andaman (Andaman and Nicobar Islands); and Lakshadweep.

Our empirical interest is to evaluate the geographical concentration of manufacturing and service industries using Ellison-Glaeser (EG) indices at a district level in India. Table 2 reports the estimated weighted and unweighted EG index values for the top three highly concentrated manufacturing and service industries. According to both EG indices, the manufacture of glass and glass products (NIC-231), sports goods (NIC-323) and air and spacecraft and related machinery (NIC-303) are three highly concentrated manufacturing industries. Similarly, software publishing (NIC-582), leasing of nonfinancial intangible assets (NIC-774) and landscape care and maintenance service activities (NIC-813) are three highly concentrated service industries. The weighted and unweighted EG index estimated values for highly concentrated manufacturing and service industries seem similar. This indicates that the neighbourhood effect cannot be adequately captured across these manufacturing and service industries while we estimate spatial concentration in the aggregate data. Therefore, this suggests that the neighbourhood effect is overshadowed when estimating geographical concentration across the district level in India while considering an aggregate of 636 districts covering all states in India. Therefore, to examine the role of neighbourhood effects, we conduct a more robust check by considering another spatial structure to analyze the spatial concentration of industries within the Indian states and union territories.

Our subsequent empirical analysis uses district-level data to measure an industry’s geographical concentration within India’s 29 contiguous states and union territories. Table 3 shows the estimated weighted and unweighted EG index

Source: Author’s computations. Notes: NIC represents National Industrial Classification at a 3-digit level. EG represents the Ellison-Glaeser index, and EGSPAT represents the spatially weighted EG index. The significance of the EG and EGSPAT index is measured at the 5 percent significance level (Guimarães et al., 2011) . *Denotes the estimated values are statistically significant at 5 percent level.

Source: Author’s computations. Notes: EG and EGSPAT represents the unweighted and spatially weighted Ellison-Glaeser index. *Denotes the estimated values are statistically significant at 5 percent level.

values for a few selected states within the three most highly concentrated manufacturing industries. Himachal Pradesh secured the eighth rank for glass and glass products (NIC-231) when we measured geographical concentration using the unweighted EG index. In contrast, it secured the fourth rank using the spatially weighted Ellison-Glaeser (EGSPAT) index. However, it reveals a difference in industry ranking within a state while measuring geographical concentration. Also, Andhra Pradesh secured thirteen positions using the unweighted EG index and the sixth position using the EGSPAT index. It exhibits that two EG indices give different results within an industry for a particular Indian state.

Similarly, for the sports goods (NIC-323) industry, Meghalaya secured the first rank when applying the unweighted EG index, while it secured the third rank using the EGSPAT index. For Haryana and Rajasthan, EG indices estimated values are different, but hierarchy-wise, both secure the same position. It implies no substantial deviation in a state while using EG and EGSPAT indexes for a particular industry. For the air, spacecraft, and related machinery (NIC-303) industry, Jharkhand secured the seventh position using the EG index and the ninth position using the EGSPAT index. It secured the ninth rank in Kerala using the EG index while securing the seventh position following the EGSPAT index. Within Telangana, the air and spacecraft and related machinery (NIC-303) industry secured the second rank according to EG and EGSPAT index. However, the estimated values seem different for both indices. Nevertheless, the estimated results in Table 3 show that neighbourhood effects seem evident within the three highly concentrated manufacturing industries across Indian states using the district-level data.

Further, Spearman’s rank correlation needs to be computed to detect the highly concentrated manufacturing industries where deviation in EG indices seems higher for particular states. Table 4 shows Spearman’s rank correlation for three highly concentrated manufacturing industries. It shows that glass and glass products (NIC-231), sports goods (NIC-323), and air and spacecraft and related machinery (NIC-303) industry have a high-rank correlation of 93.6%, 98.56% and 97.20%, respectively¹⁶. This indicates that glass and glass products (NIC-231) show a high deviation in ranking for a particular state and union territories compared to other highly concentrated manufacturing industries.

Nevertheless, using the district-level data, we estimate the geographical concentration of three highly concentrated service industries within 29 contiguous states and union territories. Table 5 shows the estimated results of three highly concentrated service industries. In the case of the software publishing (NIC-582) industry, Punjab has secured the third position using the EGSPAT index and the fourth position using the unweighted EG index. Similarly, in the case of the other two states (Haryana and Orissa), results reveal a negligible difference in ranking. Besides, it seems that the estimated values of both indices are similar for the leasing of nonfinancial intangible assets (NIC-774) industry across the selected states in India.

Next, we estimate Spearsman’s rank correlation between the two indices across three highly concentrated service industries in India. Spearsman’s rank correlation

Source: Author’s computations.

Source: Author’s computations.

results reported in Table 4 show that in the case of software publishing (NIC-582) and the leasing of nonfinancial intangible assets (NIC-774), the estimated rank correlation is 99.38% and 98.80%, respectively. However, for landscape care and maintenance service activities (NIC-813), the estimated rank correlation is 91.42%, indicating more deviation while estimating both indexes for spatial concentration. Table 5 shows that Delhi has secured the tenth and sixth positions using the EG and EGSPAT index for the landscape care and maintenance service activities (NIC-813) industry. In contrast, the estimated values validate a significant difference in the other states, like Uttarakhand and Bihar. Further, empirical results suggest that the spatial dimension is well captured using the spatially weighted Ellison-Glaeser index across the three highly concentrated service industries. Nevertheless, to get the relationship and the deviation between these two indices, our subsequent empirical interest is to plot a regression line between these two indexes.

The results reported in Table 3 and Table 5 exhibit a substantial deviation between the EG indexes in India’s highly concentrated manufacturing and service industries. However, we plot this relationship using a familiar regression line to get more robust evidence of the relationship between the two indexes. Figures 1(a)-(f) depicts the fitted line between EG indices for the top three highly concentrated manufacturing and services industries. The x-axis represents the EG index, while the y-axis represents the spatially weighted EG index. Moreover, for the glass and glass products (NIC-231) industry, the estimated regression coefficient between spatially weighted vs unweighted EG index is close to 1 (0.996 ≈ 1), and it is significantly different from zero (see Figure 1(a))¹⁷. It suggests that one unit change in the unweighted factor has increased the spatial weight factor close to 1 unit. Besides, blue dots depict that for some Indian states, the EGSPAT index is greater or less than the EG index. It validates that states have secured a different position in terms of spatial concentration while we use the spatially weighted EG index. Although as regression indicates, on average, the spatially weighted index is more or less similar to its counterpart.

Similarly, Figures 1(b)-(f) plots the fitted line between EG indices for the other five highly concentrated industries. Figure 1(a), Figure 1(d) and Figure 1(e) displays that the spatially weighted index is more or less similar to its counterpart on average. Figure 1(b) depicts that, on average, the spatially weighted index is less than the unweighted EG index by 21 percent for the sports goods (NIC-323) industry. It indicates that our estimated results do not align with what Duranton and Overman (2005) find in their study by criticizing the unweighted EG index. The unweighted EG index is criticized for the checkerboard problem, leading to downwardly biased estimated values.

However, in the case of sports goods, the spatially weighted EG index is lower than the unweighted EG index. However, Figure 1(c) and Figure 1(f) suggests that the spatially weighted index is higher than the unweighted EG index by 9 and 10 percent for air and spacecraft and related machinery (NIC-303) and landscape care and maintenance service activities (NIC-813) industry. In other words, results exhibit that a one-unit change in the unweighted factor has increased the spatial weight factor by more than 1 unit. Figure 1 suggests that the

spatially weighted EG index is substantial while quantifying geographical concentration for a particular state across the highly concentrated manufacturing and service industries except for the sports goods (NIC-323) industry.