1 Introduction

Knowledge has become the major capital for national and regional competitiveness in the knowledge-based societies, and knowledge-intensive business services (KIBS) industries have become one of the main drivers in the modern economy. KIBS are considered one of the main characteristics of the knowledge economy over recent decades (Ciriaci and Palma 2016).

Macroeconomic research has identified KIBS as one of the fastest growing sectors in terms of adding value to the output of industries as well as job creation and trade value in the economy (see, e.g., Bain and Company 2012; BIZ 2010; Eurostat 2013; Fersht et al. 2011; Mieres et al. 2012; NSF 2012; Wirtz et al. 2015). For example, KIBS have been among the most dynamic segments of the service sector in European countries since the mid-1980s and are one of the most rapidly growing sectors of the EU economy (Strambach 2008). European Commission (2012) reports that there are approximately 18.8 million employees in KIBS in Europe, or 11% of overall employment. The employment in KIBS grew by an average 2.3% in the period between 2006 and 2011 compared to the growth of the overall economy by 1.5%.

Not only in the EU economy, but KIBS also contribute to innovation and economic development across different regional and national contexts (see, e.g., Freel 2016). A vast body of research suggests that KIBS play an important role in the innovation and economic development across the world (see, e.g., Andersson and Hellerstedt 2009; Czarnitzky and Spielkamp 2000; Hansen 1993; Marshall et al. 1987; Miles et al. 1995; Miles 2003; Muller and Zenker 2001). For example, Duranton and Puga (2004) illustrate that KIBS can be a main driver for urban agglomeration economies with labor market interactions. This is because KIBS are particularly representative of the knowledge-based economy, since knowledge constitutes both their main input and output, and they are both processors and producers of knowledge (see, e.g., Antonelli 1998; Gallouj 2002; Herstad and Ebersberger 2014).

While authors have recognized the importance of KIBS in our knowledge-based era and have studied the relationship between KIBS and economic development, most studies have examined the role of KIBS in European countries. For instance, Muller and Doloreux (2007) point out that 54 out of 68 articles (about 80%) are researched in Europe, and only four articles are studied in North America. In addition, the distribution of authors of the reviewed articles shows that KIBS research is mainly concentrated in the disciplines of economics (39%), management and business administration (38%) and, to a lesser extent, geography and regional planning (11%). In other words, while the role of KIBS has substantially increased in the modern economy, the spatial patterns and economic effects of KIBS in the USA remain largely unexamined, bringing the necessity of studies on KIBS in the context of the USA.

Therefore, this study highlights the spatial patterns and effects of KIBS on the urban economy at the US Metropolitan Statistical Areas (MSAs) in 2015 given that KIBS are located primarily in MSAs (see, e.g., Shearmur and Doloreux 2008). To the best of my knowledge, this article is the first study examining how KIBS are distributed across the US MSAs by each KIBS field and play an important role in economic development at the MSAs level based on empirical analysis by employing a cluster quotient (CQ) index and a simultaneous equations model. To be specific, this study proposes a new CQ to highlight the spatial patterns of KIBS clusters given that the traditional location quotient (LQ) index, which is often used to measure the magnitude of clusters in prior research, has a serious issue because it cannot reflect the agglomeration of industries, which is directly related to the definition of clusters (see the CQ part for the detailed explanation). Also, this study employs a Seemingly Unrelated Regression (SUR) model to estimate the mutual relationship between KIBS and the urban economy given that they interact with each other (see, e.g., Andersson and Hellerstedt 2009; Antonelli 1998; Bain and Company 2012; BIZ 2010; Gallouj 2002; González Mieres et al. 2012; Hansen 1993; Herstad and Ebersberger 2014; Marshall et al. 1987; NSF 2012; Wirtz et al. 2015). To be specific, in order to estimate the effect of KIBS on the urban economy and vice versa, authors should develop a set of equations. While other regression models, such as Ordinary Least Square (OLS), may contain a number of linear equations, it is unrealistic to expect that the equation errors are not correlated. This is because a set of equations has contemporaneous cross-equation error correlation. For example, the error terms in each regression equation are correlated. In contrast, the SUR model allows scholars to reflect the error terms correlated into the model with unbiased estimators for the parameters by joint analysis of the set of regression equations unlike equation-by-equation analysis in other models. Therefore, the SUR model allows us to estimate the effect of KIBS on the urban economy or vice versa by gaining efficiency in estimation based on information combined on different equations (see the SUR part for the detailed explanation). The findings from the CQ index and SUR model would play an important role in understanding the spatial patterns and effects of KIBS in our knowledge-based societies and contribute to the KIBS literature. The data used in this article were collected from the US Census Bureau, Bureau of Economic Analysis, United States Patent and Trademark Office, and American FactFinder.

1.1 The characteristics of KIBS

Since the mid-1990s, many scholars have significantly paid attention to KIBS because KIBS are growing much faster than manufacturing and other service industries and play an important role in innovation systems and support economic development at regional and national levels (see, e.g., Aharoni and Nachum 2000; Javalgi and Grossman 2014; Muller and Zenker 2001; Peneder et al. 2003). According to Miles (2005), KIBS have some important characteristics as follows: (1) they rely heavily on professional knowledge: they either are themselves primary sources of information and knowledge, or use their knowledge to produce intermediary services for their clients’ production; (2) they are of competitive importance and supplied primarily to business. Some of these are traditional professional services—others are new technology-based services. KIBS are highly innovative and facilitate innovation in other industrial sectors and thus contribute to economic growth. This is because they are very information technology-intensive industries and thus play a crucial role in the diffusion of knowledge and technology (see, e.g., Antonelli 1998; Herstad and Ebersberger 2015; Katsoulacos and Tsounis 2000; Miozzo and Grimshaw 2005). In this background, among a variety of industrial fields, KIBS can be one of the most growing industries in our contemporary societies. The industries themselves not only have strong potential for regional growth, but also exert a positive impact on other industries’ productivity such as manufacturing or other service industries (see, e.g., Ciriaci et al. 2015; Corrocher and Cusmano 2014; Muller and Zenker 2001; Pina and Tether 2016; Shearmur and Doloreux 2008, 2019). For instance, Muller and Zenker (2001) reveal that KIBS show a considerable growth and innovation potential and promote economic development at both regional and national levels based on 1,144 KIBS between 1995 and 1997. Corrocher and Cusmano (2014) exhibit that KIBS are key players in innovation systems and development based on a set of 220 European regions, particularly in advanced regions. Ciriaci et al. (2015) show that KIBS have a significant innovation impact on not only the knowledge based on fields but also the manufacturing fields by analyzing 18 manufacturing sectors in four European countries (France, Germany, Italy, and the UK) between the mid-1990 s and the mid-2000s. Shearmur and Doloreux (2008) demonstrate that the distribution of KIBS over geographic regions is connected with regional economic structure by analyzing 152 urban agglomerations and 230 rural areas in Canada between 1991 and 2001. Shearmur and Doloreux (2013) find evidence that KIBS are related to the geographic pattern of innovation based on a survey of 1122 KIBS firms in Quebec, Canada. Jacobs et al. (2013) show that the location of new entries of KIBS plays an important role in a regionalized service economy by analyzing the case in the Northwing of the Dutch Randstad. Meliciani and Savona (2014) show that the location of valued-added and knowledge-intensive activities fosters regional development in large metropolitan areas by analyzing across EU-27 regions over the period 1999–2003.

Given that there is no standard definition of KIBS, researchers have tried to define KIBS sectors and examine the role of KIBS (Tether and Hipp 2002). For example, Eurofound explains that KIBS are companies that provide inputs—based heavily on advanced technological or professional knowledge—to the business processes of other organizations. The KIBS sector includes a range of activities such as computer services, research and development (R&D) services, legal, accountancy and management services, architecture, engineering and technical services, advertising and market research, among others.Footnote 1 Hertog (2000) defines KIBS as firms that rely heavily on professional knowledge, i.e., knowledge or expertise connected to a specific discipline or functional domain to provide intermediate products and services that are knowledge based. Miles et al. (1995) explain KIBS as services that involve economic activities, which are intended to result in the creation, accumulation, or dissemination of knowledge. Toivonen (2006) suggests KIBS as expert companies that provide services to other companies and organizations. As prior research indicates, there is no single definition of KIBS (Wood 2002).

This study defines KIBS as industrial fields relying heavily on the high intensity of knowledge to produce products and services. KIBS include business services (e.g., accounting, finance, insurance, and legal), technical services [e.g., technology, telecommunications, and research and development (R&D)], and educational services. This study categorizes KIBS based on prior literature using North American Industry Classification System (NAICS) as follows: telecommunications, finance, insurance, legal, accounting, technology, R&D, and education (see Appendix Table 5).

1.2 The geographic distribution of knowledge economy in the USA

In order to understand the spatial patterns of KIBS in the context of knowledge economy, it is worth exploring the geographic distribution of knowledge economy in the USA. While scholars have barely highlighted KIBS in the context of US MSAs based on empirical analysis, there are many articles on the knowledge economy at the US states level, such as regional innovation systems, innovative clusters, and innovation ecosystems (see, e.g., Acs et al. 2002; Almeida and Kogut 1999; Amin and Cohendet 1999; Audretsch and Feldman 1996; Baptista and Swann 1998; Baptista 2000; Cooke and Morgan 1999; Feldman and Florida 1994; Gertler 2003; Leamer and Storper 2014; Levy and Murnane 2005; Lundvall et al. 2002; Maskell 2001; Nelson 1993; Sonn and Storper 2008). Varga et al. (2005) highlight that whereas there are no significant results for Midwest, Northeast, and the West, there is a significantly negative result of the South region for regional innovation systems by running pooled time series cross-sectional regressions based on 429 observations. Porter (2001) shows that the highest per capita patent-producing region (Boise City, ID) produces almost nine times the number patterns per person of the median region, and the top 10 patenting regions account for 51% of the nation’s patents. Porter et al. (2001) demonstrate that California plays an important role in patenting activity as the information technology cluster and California and New Jersey are the major centers in pharmaceutical/biotechnology clusters.

Many other authors also show that the knowledge economy is largely concentrated in some regions in the USA based on empirical analysis. For instance, Feldman and Florida (1994) show that the geographic distribution of innovations is heavily concentrated in some states; 11 states, such as New York, California, New Jersey, and Massachusetts, consist of 81 percent of the 4200 innovations. Audretsch and Feldman (1996) exhibit that the distribution of knowledge economy is heavily concentrated in California, followed by New York, New Jersey, and Massachusetts. In contrast, Midwestern states, such as North Dakota, South Dakota, Montana, and Wyoming, demonstrate underdeveloped knowledge economy. Acs et al. (2002) find that 10 states are innovative clusters given that 80% of the total US activity is for innovation and 70% for patents, respectively: California, New Jersey, New York, Pennsylvania, Illinois, Ohio, Texas, Michigan, Massachusetts, and Connecticut.

The empirical evidence shows that the knowledge economy is highly clustered in some regions. It can apply to the distribution of KIBS given that they are based on the knowledge economy. In this background, this study explores the geographic distribution of KIBS across the US MSAs by employing a new CQ index in the next section.

1.3 The differences between a traditional LQ and a new CQ

Clusters are defined as geographic concentrations of interconnected businesses, suppliers, and associated institutions in a particular field (Porter 1990). To be specific, a cluster can be explained as a group of interconnected industries gather together in a specific region to share their ideas, produce products, increase the productivity with other companies, and interact with other industries. Therefore, the agglomeration of industries plays an important role in developing clusters.

However, most prior studies have employed a location quotient (LQ) index to highlight industrial clusters in regions, which cannot consider the agglomeration of industries (see, e.g., Austrian 2000; Billings and Johnson 2012; Carroll et al. 2008; Fallick et al. 2006; Fernhaber et al. 2008; O’Donoghue and Gleave 2004; Woodward and Guimarães 2009; Zook 2000). For example, Henderson and Ono (2008) highlight location patterns of manufacturing by analyzing County Business Patterns based on the LQ. The LQ index is calculated as follows:

$$LQ_{ij} = \frac{{\frac{{e_{ij} }}{{e_{j} }}}}{{\frac{{E_{i} }}{E}}}$$
(1)

where LQij = location quotient, i = industries, e = employment, j = MSAs, and E = employment in all MSAs.

As we can see the equation above, while LQ may be a valuable way of quantifying the number of workers or the size of industries in the region, it has a serious problem to measure the magnitude of clusters. This is because it relies only on the number of workers. In contrast, a new CQ proposed by this article considers both the number of industries and workers as follows:

$$CQ_{ij} = \frac{{\left( {IQ_{ij} + EQ_{ij} } \right)}}{2} = \frac{1}{2}\left( {\frac{{\frac{{i_{ij} }}{{i_{j} }}}}{{\frac{{I_{i} }}{I}}} + \frac{{\frac{{e_{ij} }}{{e_{j} }}}}{{\frac{{E_{i} }}{E}}}} \right)$$
(2)

where CQij = cluster quotient, IQij = Industry Quotient, EQij = Employment Quotient, i = industries, e = employment, j = MSAs, I = industries in all MSAs, and E = employment in all MSAs. In the index, a CQ greater than 1 indicates that the region has a greater share of the cluster than the case in the reference area. If a CQ is equal to 1, then the region has the same share of the cluster as it does in the reference area.

Equation 2 indicates that the CQ index is a better method than the LQ index given that the CQ enhances conceptual and methodological strength by considering the agglomeration of industries that is the definition of clusters. In order to highlight the flows of LQ, let us assume that there are two regions: the former region has one firm hiring 1000 workers, and the latter region has 100 firms hiring 1000 workers. The LQ calculates their cluster value as the same even though it does not make any sense for the same value given that one firm cannot make the cluster effect and is not the same with 100 firms for the cluster. In contrast, the CQ calculates the different number of firms between one and 100, reflecting the number of firms in the region into its index. The CQ index also includes the number of workers given that it shows the size and economic impact of the industries in the region. For instance, it is easy to understand that 10 firms hiring 10,000 workers have a more cluster effect than 10 firms hiring 10 workers. Therefore, the CQ index considers both the number of industries and workers into its value.

One may be still curious about the differences in LQ and CQ, the flaws of LQ, and results of measuring clusters by LQ and CQ. This study empirically provides them by analyzing the spatial patterns of KIBS clusters drew by the indices based on all US MSAs in 2015. First, Table 1 demonstrates that the spatial patterns of KIBS clusters calculated by the LQ and CQ are quite different. None of the MSAs between LQ and CQ have the same ranking within top 20th (see the EQ value given that LQ and EQ are calculated by the same equation). To be specific, California, MD, which placed first in LQ, ranked second in CQ. In contrast, Washington, DC, took first place in CQ even though it ranked second in LQ. It is reasonable to interpret that Washington, DC, has a more developed cluster than California, MD, given that the agglomeration of industries (IQ) of Washington, DC, ranked second, even though that of California, MD, ranked 14th. Not only that five out of top 20 MSAs in CQ, such as San Jose, CA; Colorado Springs, CO; Raleigh, NC; Atlanta, GA; and Salt Lake City, UT, are excluded in the LQ even though they have the high agglomeration of industries. The findings show that some important KIBS clusters cannot be measured by the LQ index. In other words, the LQ index overestimates, underestimates, and misses some important clusters, and scholars may totally misunderstand the magnitude of clusters when they apply the LQ to measure the degree of clusters given that the LQ does not reflect the agglomeration of industries that is the definition of clusters. The results empirically exhibit the differences between LQ and CQ, show the flaws of LQ, and support that the CQ index would be a better index over the LQ index. Therefore, this study highlights the spatial patterns of KIBS clusters across all US MSAs in 2015 based on the new CQ index in the next section.

Table 1 Top 20 MSAs of IQ, EQ, and CQ
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1.4 The spatial patterns of KIBS clusters

Scholars have showed that KIBS cluster in large MSAs owing to benefits of the agglomeration, such as input sharing, a specialized labor force, and knowledge spillovers (see, e.g., Jacobs et al. 2013; Keeble and Nachum 2002; Muller and Doloreux 2009; Shearmur and Alvergne 2002; Shearmur and Doloreux 2008). This study shows the spatial patterns of Industry Quotient (IQ), Employment Quotient (EQ), and cluster quotient (CQ) across US MSAs in 2015. Table 1 indicates that high IQ MSAs and high EQ MSAs show different spatial patterns across US MSAs. For instance, Boulder, CO, ranked first in IQ, whereas it ranked sixth in EQ. California, MD, which ranked first in EQ, placed 14th in IQ. The biggest difference between IQ and EQ is that high IQ MSAs are more concentrated in the West and South region, whereas high EQ MSAs are more clustered in the Midwest and Northeast region, meaning that industry-centered regions and worker-centered regions are differentiated across the US MSAs (see Figs. 1, 2). This result also highlights that the LQ (LQ is calculated by the same methodology with the EQ) cannot reflect the developed IQ MSAs in the West and South region, causing a serious problem as a cluster index. For instance, 11 out of top 20 MSAs in IQ, such as San Jose, CA, Cheyenne, WY, and San Diego, CA, are ruled out in EQ.

Fig. 1
figure 1

Value of Industry Quotient across US MSAs in 2015

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Fig. 2
figure 2

Value of Employment Quotient across US MSAs in 2015

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When looking into the CQ index, Washington, DC, ranked first with a value of 1.64, followed by California, MD (1.56), Boulder, CO (1.50), Huntsville, AL (1.43), and Boston, MA (1.31). CQ has high values in the Northeast region, especially nearby Washington, DC. Also, MSAs in Colorado, such as Boulder (1.50), Denver (1.28), and Colorado Springs (1.18), and MSAs in California, such as San Francisco (1.28) and San Jose (1.22), show a high CQ value (see Table 2; Figs. 3, 4).

Table 2 Top 20 MSAs by KIBS fields
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Fig. 3
figure 3

Value of cluster quotient across US MSAs in 2015

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Fig. 4
figure 4

Value of cluster quotient by each field across US MSAs (Telecommunications, finance, insurance, legal, accounting, technology, R&D, and education)

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This study advances some implications for urban planners and governments based on the results of CQ. First, this study empirically shows that LQ and CQ illustrate different spatial patterns of clusters across US MSAs, and the LQ index can underestimate, overestimate, and exclude important clusters, meaning that urban planners and policy practitioners should reconsider the results of clusters, which are based on the LQ index, in the prior papers. The CQ index allows them to measure the magnitude of clusters more accurately by reflecting both the agglomeration of industries and workers. Second, this article practically highlights that the spatial patterns of IQ and EQ are different across US MSAs, meaning that urban planners and governments need to develop different policies based on their purpose. For example, high IQ MSAs have a large number of firms, meaning that the regions may have many start-up companies and a variety of industrial environments in the industry field. In this case, governments can aim to develop cluster effects and industrial networks to promote the industry field. In contrast, high EQ MSAs have a great number of workers, implying that the regions have significant job effects and major companies. In this background, governments can develop strategies based on the industry field to increase employment creation and economic development. Third, the CQ index can be utilized in any industry field as well as the KIBS field in this study because of generality. Governments and policymakers can readily compute the magnitude of clusters for other industries when they have the information on the industry’s share of regional employment and firms with its share of national employment and firms.

1.5 The effect of KIBS on economic development

This study employs a Seemingly Unrelated Regression model (SUR) to reflect the interaction between KIBS and the urban economy in the real world. SUR, proposed by Arnold Zellner (1962), is a generalization of a linear regression model that consists of some regression equations and has been widely adopted by many authors (Carlson 1978; Kakwani 1967; Kmenta and Gilbert 1968; Moon and Perron 2008; Srivastava and Dwivedi 1979; Srivastava and Giles 1987; Wilde et al. 1999). The SUR model comprises some individual relationships from the fact that their disturbances are correlated (Hyungsik and Perron 2006). The correlation among the equation disturbances could come from industries and the urban economy given that they interact with each other. The SUR model provides a natural application for explaining the relationship between industries and the urban economy in different cities, metropolitan areas, states, and countries because the diverse entities tend to be associated with other entities. The SUR model shows the variation in not just one dependent variable, but that of a set of dependent variables (Zellner 2006). In other words, in the SUR model, each equation has its own dependent variable and different sets of exogenous independent variables. Each equation has a valid linear regression on its own and can be estimated, respectively, which is why the model is called Seemingly Unrelated (Greene 2012). Scholars have employed the SUR model for two reasons. The former is to gain efficiency in calculation by gathering information from different equations. The latter is to impose and/or check restrictions that involve parameters (Fiebig 2001; Srivastava and Giles 1987; Zellner 1962). The SUR model allows us to solve the problem of the error terms correlated between KIBS and the urban economy. It is a better model than the OLS model when the error terms are correlated because the OLS model brings a biased result, but the SUR model can consider feedback loops in the equations. For example, Zellner (1962) highlights that SUR is efficient over separate equation by equation when the correlation between disturbances is high and independent variables are uncorrelated in two-stage approach. He shows that definite gains are obtained for all samples when |ρ| ˃0.3 where ρ is the contemporaneous correlation for the disturbances in the equations. Yahya et al. (2008) show that SUR estimators are consistently more efficient than the OLS in all cases considered in their simulation studies, especially when the predictors have Gaussian distribution. He shows that definite gains are obtained when |ρ| ˃ 0.333. Alaba et al. (2010) also insist that the standard errors of the SUR estimator are consistently lower than the OLS estimator. Thus, the SUR performs better than OLS when the errors are correlated between the equations. Many scholars have proved that SUR is the better model than OLS when |ρ| ≥ 0.3 and for at least sample size of 23 for cross-sectional data (see, e.g., Kmenta and Gilbert 1968; Kunitomo 1977; Mehta and Swamy 1976; Telser 1964; Zellner 1962). This study compares the results between OLS and SUR to verify the relationship between KIBS and the urban economy. The basic SUR model consists of multiple regression equations as follows:

$$ym = \, Xm\beta m \, + \, \varepsilon m$$
(3)

The equation can be written in matrix form:

$$\left[ {\begin{array}{*{20}c} {y_{1} } \\ {\begin{array}{*{20}c} \cdot \\ \cdot \\ \end{array} } \\ {y_{m} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {x_{1} } & {} & {} \\ {} & \ddots & {} \\ {} & {} & {x_{m} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\beta_{1} } \\ {\begin{array}{*{20}c} \cdot \\ \cdot \\ \end{array} } \\ {\beta_{m} } \\ \end{array} } \right] + \left[ {\begin{array}{*{20}c} {\varepsilon_{1} } \\ {\begin{array}{*{20}c} \cdot \\ \cdot \\ \end{array} } \\ {\varepsilon_{m} } \\ \end{array} } \right] = X\beta + \varepsilon$$
(4)
$$\in = \left[ {\varepsilon_{1}^{\prime } ,\varepsilon_{2}^{\prime } , \ldots \varepsilon_{m}^{\prime } } \right]^{\prime } E\left[ \varepsilon \right] = 0$$
(5)
$$E = \left[ {\varepsilon \varepsilon^{\prime } } \right] = V = \left[ {\begin{array}{*{20}c} {\sigma_{11} I} & \cdots & {\sigma_{1m} I} \\ \vdots & \ddots & \vdots \\ {\sigma_{m1} I} & \cdots & {\sigma_{mm} I} \\ \end{array} } \right]$$
(6)

When there are M regression equations, the expected value of disturbance terms is zero like Eq. 5, but the value of covariance across disturbance terms is not zero like Eq. 6. In the SUR model, Cov(εi, εj) = σij; then, variance covariance matrix of ε can be easily shown as follows:

$$\varOmega = \left[ {\begin{array}{*{20}c} {\sigma_{11} } & \cdots & {\sigma_{1m} } \\ \vdots & \ddots & \vdots \\ {\sigma_{m1} } & \cdots & {\sigma_{mm} } \\ \end{array} } \right]$$
(7)

The covariance matrix of the stacked error terms can be equal to:

$$V = \sum \otimes In$$
(8)

where In is the N-dimensional identity matrix and ⊗ denotes the matrix Kronecker product. This study highlights the relationship between KIBS as well as KIBS clusters and the urban economy, and the SUR model in this study consists of two equations as follows:

KIBS2015 (or CQ2015) = f (the GDP2012, population, the specialization of knowledge-based industries, the diversity of knowledge-based industries, education achievement (the proportion of the bachelor’s degree above), regional innovation systems (patents), Internet Information Technology (IIT) (NAICS: 519130)).

The GDP2015 = f (KIBS2012 (or CQ2012), labor stock (the number of workers), capital stock (real personal income), an industrial environment (the number of all industries), demographic variables (the proportion of whites, blacks, Asians, and foreigners), education achievement).

This study sets a time lag (3 years) between KIBS (or CQ) and the GDP to solve the simultaneity problem. This method helps the author correctly calculate the causal link between KIBS and the urban economy. In this study, the first equation demonstrates the effect of the GDP on KIBS (or CQ). The number of KIBS (or the CQ value) is the dependent variable, and this study adds seven explanatory variables: first, a population in the region can be one of the important factors for the number of KIBS (or CQ) given that a larger population of the region can have a bigger market for the industries, and KIBS prefer to locate in the region. For instance, Shearmur and Doloreux (2008) highlight that KIBS increase their presence in larger cities because the labor market, synergies, and spillover effects. Andersson and Hellerstedt (2009) show that 78 percent of KIBS start-ups are stimulated by the simultaneous presence of a large market. Shearmur (2010) reveals that KIBS locate in places where many clients and markets can be found. This is because development of new products is also based on interpretations of market trends (Isaksen 2004). Shearmur and Doloreux (2019) find that KIBS are clustered in metropolitan areas to increase the likelihood of having recourse to KIBS intermediation services for the innovation activity.

Next, the specializationFootnote 2 and the diversityFootnote 3 of knowledge-based industries (KBI)Footnote 4 (see Appendix Table 6) are included as explanatory variables because the diffusion and the growth of KIBS are deeply affected by the parallel diffusion and implementation of the new knowledge and information (Antonelli 1998). The core competence common to all KIBS is the integration of various forms of knowledge given that they rely highly on knowledge to produce their products (Consoli and Elche-Hortelano 2010). KIBS rely on qualified professionals, which are experts in specific technical disciplines or functional domains, and supply information, knowledge or other knowledge-based services (Scarso and Bolisani 2010). In the KIBS sectors, competitive success comes directly from continuous technological innovations, where a single organization cannot successfully innovate in isolation; therefore, KIBS should be dependent on external relationships and networks in order to complement its knowledge domains and then develop better and faster innovations (Martín-de Castro 2015). KIBS have been found in the knowledge-based regions, because of their role as a driver of the development of the knowledge-based economy (Smedlund and Toivonen 2007). In this sense, KBI can play an important role in the industrial environment for KIBS.

Human capital can be one of the important factors for the location of KIBS since human capital has been increasingly emphasized in industrial development (Cover et al. 2011; Glaeser and Shapiro 2003; Jones 2014; Langdon et al. 2011; Shapiro 2006; Simon and Nardinelli 2002). KIBS rely heavily on the knowledge, creativity, and innovative ideas of their knowledge workers (see, e.g., Bessant 2003; Kheng et al. 2013). KIBS should hire well-educated workers with management organization, information systems, legal affairs, market research, technical testing, and much more (Tomlinson and Miles 1999). Knowledge workers contribute to promoting the specialization and diversification of knowledge products for KIBS (Strambach 2010). For instance, Yeoh and Mahmood (2013) find that knowledge workers play an important role in the development of KIBS based on 310 questionnaires. In this sense, education achievement can be used to analyze spatial patterns of KIBS (Growe 2016).

This study assumes that regional innovation systems hold a specific position for KIBS since they act as an external knowledge source and contribute to KIBS and KIBS are highly related to internal innovations and economic performance and growth (Muller and Zenker 2001). For instance, Strambach (2001) highlights that KIBS should establish themselves in the innovative regions to ensure their survival with new products. Innovative networks in the regions play an important role in KIBS as carriers of knowledge and intermediates for their products (Hipp 1999). In this background, regional innovation systems can be the great attraction for KIBS. This article uses the number of patents in regions as a proxy variable of the regional innovation systems. According to the existing literature, patents are a commonly used measure of the innovative intensity of firms and industries (Acs et al. 2002; Ahuja 2000; Bottazzi and Peri 2003; Fritsch and Slavtchev 2011; Jaffe 1989; Singh 2008; Stuart 2000; Whittington et al. 2009).

Next, information technology is intimately connected to development of KIBS (Antonelli 2000). It contributes to growth and competitiveness of KIBS (Hipp 2000). Not only localized knowledge, but also information inputs and high-quality information infrastructure are explanations for the spatial concentration of KIBS (Simmie and Strambach 2006). Information technology has fundamentally promoted the opportunities to effectively combine internal and external knowledge for KIBS (Smedlund and Toivonen 2007). Information technology is an important determinant of specialization in KIBS (Meliciani and Savona 2014). Therefore, information technology can be one of the important factors for the locations of KIBS (Zieba 2013). This study especially highlights the role of Internet Information Technology (IIT) given that many KIBS products, such as online games, software, programs, rely highly on the Internet environments.

In the second equation, the GDP is the dependent variable as a proxy variable for the urban economy because it represents the productivity of economic activities. This study employs the Cobb–Douglas function to estimate the productivity of KIBS (or CQ). The Cobb–Douglas function has been widely employed for large-scale studies (such as MSAs, states, and countries), which estimates between the effect of input and the change of output consistent with this study (see, e.g., Balistreri et al. 2003; Blundell and Bond 2000; ECFIN 2006; Garcia-Mila et al. 1993; Stern 2000). For example, Garcia-Mila et al. (1993) analyze the effect of public capital at the state level in the USA, using a panel data set from 1970 to 1983. Stern (2000) explores the causal relationship of the GDP and energy use in the USA in the post-war period by employing four different Cobb–Douglas models. Balistreri et al. (2003) support the Cobb–Douglas function in the context of the USA by analyzing 28 industries that cover the entire economy in the USA. Blundell and Bond (2000) analyze 509 R&D-performing US manufacturing companies in 8 years based on the Cobb–Douglas function. ECFIN (2006) employs the Cobb–Douglas function to calculate potential growth and output gaps estimates for EU member states and the USA.

Lastly, this study sets some control variables, which can affect the productivity of the regions, such as an industrial environment (the number of all industries), population composition (the proportion of whites, blacks, Asians, and foreign-born people), and educational achievement (the number of people who have bachelor’s degree above). For example, industries have been one of the main drivers for economic growth (see, e.g., Florida 2003; Hall 2000; Scott 2004), population composition is associated with the regional income (see, e.g., Bailey 1959; Price-Spratlen and Guest 2002; Reardon and Bischoff 2011), and human capital is one of the important resources for economic growth in our knowledge-based era (see, e.g., Benhabib and Spiegel 1994; Florida 2014; Gennaioli et al. 2012).

This study explores the differences in results between OLS and SUR by suggesting four models (see Table 3). When comparing each model, there are notable differences in the significance or the coefficient value for KIBS, CQ, and the GDP. For example, the GDP shows an elasticity of 0.054 in OLS (significant at the 0.01 level) and 0.084 in SUR (significant at the 0.01 level), and KIBS exert an impact on the GDP with an elasticity of 0.262 in OLS (insignificant) and 0.515 in SUR (significant at the 0.01 level). This result highlights that the error terms are correlated, meaning that the SUR model would be a better model to estimate the effect of KIBS on the urban economy because the OLS model brings a biased result in this situation.

Table 3 Relationship between KIBS (CQ) and the GDP in OLS and SUR
Full size table

To be specific, in Eq. 1 of model 2, all explanatory variables except the diversity of KBI and regional innovation systems have a positive effect on the GDP at the 0.01 level, and the elasticity of each variable is as follows: population (0.871) > IIT (0.108) > specialization of KBI (0.100) > the GDP (0.084) > education achievement (0.016). This result shows that the population is the most important variable for bringing KIBS in the model, and it is reasonable given that the population is highly related to the worker’s pool and the markets. Also, the result shows that governments should develop KIBS by considering knowledge-based environments, such as IIT and the specialization of KBI, as well as human capital.

In Eq. 2, the biggest difference between model 1 and model 2 is that KIBS is insignificant for the GDP in OLS, whereas it is positively related to the GDP at the 0.01 level in SUR. In contrast, the capital stock has a positive impact on the GDP at the 0.01 level in OLS, while the effect and significance of capital stock decrease for the GDP in SUR. This may be because the OLS model cannot consider the relationship between KIBS and the GDP, and the error terms correlated affect the results of equations. In other words, the OLS model may cause a serious problem, that is, KIBS are insignificant for the GDP even though they are positively related to the GDP. Moreover, KIBS have the highest elasticity (0.515) for the GDP among all explanatory variables in the SUR model. In particular, they are positively associated with the GDP when all industries (0.069) are controlled, implying that the higher proportion of KIBS can also contribute to economic development.

In model 3 and model 4, OLS and SUR show different results for the relationship between CQ and the GDP. For instance, the GDP is positively associated with CQ with an elasticity of 0.019 in OLS (significant at the 0.1 level) and 0.024 in SUR (significant at the 0.05 level), and the effect of CQ on the GDP is 0.139 in OLS (insignificant) and 0.216 in SUR (insignificant). To be specific, in Eq. 1 of model 4, the GDP, the diversity and specialization of KBI, education achievement, and IIT exert a positive impact on CQ, and the diversity of KBI shows the highest elasticity for CQ. This result shows that development strategies based on the diversity of KBI would be better than the specialization of that for increasing the magnitude of KIBS clusters. In Eq. 2 of model 4, the capital stock shows the highest elasticity for the GDP (0.819), ahead of all industries (0.079), and education achievement (0.012).

Next, this study further highlights the relationships between KIBS and the GDP by each field (see Table 4). All KIBS fields except insurance and R&D interact with the GDP. Insurance industries are positively affected by the GDP, whereas it does not exert an impact on the GDP in the model. R&D industries are not associated with the GDP in the model. This may be because R&D industries have some unique characteristics compared to other KIBS. For example, R&D industries are the only industrial field, which is not affected by the GDP and positively affected by the innovation variable. This is reasonable given that innovation environments and research funding play an important role in R&D industries and the GDP may not be an important location factor for R&D. One more notable characteristic in R&D is that R&D (and technology) are not associated with the population and positively related to the diversity of KBI.

Table 4 Relationship between KIBS and the GDP by each field in SUR
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On the other hand, the specialization of KBI, education achievement, and IIT play a positive role in all KIBS fields, meaning that governments design policies based on those factors regardless of the industrial fields and should develop those factors to grow KIBS.

Also, this study finds that the GDP and each KIBS field differently interact with each other. In other words, they show different elasticities by their fields. The elasticities of the GDP for each KIBS field (at the 0.01 level) are as follows: technology (0.125) > legal (0.116) > telecommunications (0.075) > accounting (0.074) > finance (0.072) > education (0.071) > insurance (0.067). Those of KIBS for the GDP (at the 0.05 and 0.01 level) are as follows: telecommunications (0.349) > finance (0.342) > education (0.328) > legal (0.304) > technology (0.296) > accounting (0.288). The results show that the relationships are differentiated by industrial fields and governments and urban planners should develop urban planning by looking at the different characteristics of each KIBS field. For instance, governments and urban practitioners should promote innovation environments and give weight to the diversity of knowledge environments to attract R&D industries. They should take full advantage of telecommunication industries as a first driver for economic development given that it shows the highest elasticity for the GDP.

1.6 The local impact of KIBS: a case study of Washington, DC

In order to specifically highlight how KIBS exert a positive impact on economic development and suggest more urban planning implications, this study provides a case study of Washington, DC, which ranks first in the CQ index. Figure 5 demonstrates that IQ, EQ, and CQ in Washington, DC, are largely differentiated by fields and the values of those vary across the fields. For instance, Washington, DC, has the highest IQ value in the R&D field, while the MSA has the highest EQ value in the technology field. This result suggests that governments should design a different urban planning based on their purpose. For example, governments should focus more on the R&D field, which ranks first in IQ, when they try to advance industrial networks among films to create cluster effects, whereas they would rather concentrate their efforts on the technology field, which has the highest EQ, if they aim to cause job creation effects.

Fig. 5
figure 5

Value of IQ, EQ, and CQ by each field in Washington, DC (telecommunications, finance, insurance, legal, accounting, technology, R&D, and education)

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The figure also highlights that even though Washington, DC, ranks first in the CQ index, some industry fields in the MSA are underdeveloped than the national industry fields. For example, IQ, EQ, and CQ in technology and R&D fields are higher than two, whereas they in finance and insurance fields are lower than one. This result shows that governments should look into the industry fields in detail and develop strategies based on their strength and weakness of industrial fields.

Next, this study shows how KIBS exert a positive local impact on Washington, DC, based on further empirical evidence. Indeed, many authors and articles have highlighted that Washington, DC, has evolved into a leading-edge knowledge economy and KIBS, especially technology and R&D, play an important role in regional growth consistent with the findings of this article. For example, according to the Office of the Deputy Mayor for Planning and Economic Development, Washington, DC, ranks first for women in technology and places third in technology. Washington, DC, is not only one of the best tech ecosystems in the USA; it is one of the most inclusive (https://dmped.dc.gov/page/technology-and-innovation). Also, according to EMSI data (https://www.economicmodeling.com/data/), the largest industry in Washington, DC, is professional, scientific, and technical services. The knowledge-based sector accounts for more than half a million jobs, consisting of a full 15 percent of the metro’s workforce. The region has added nearly 17,000 new professional services jobs since 2009. Florida (2013) supports that Washington, DC, has in fact developed a diversified tech and knowledge economy. He highlights that the MSA is home to nearly 110, 000 private educational service jobs, which grew at a 13 percent rate, nearly 100,000 finance and insurance jobs, which grew 3 percent and 76,000 information jobs (https://www.citylab.com/life/2013/10/truth-about-dcs-growing-knowledge-based-economy/7317/). In sum, the economy of Washington, DC, has become a highly developed economy driven by KIBS. This case study provides a more nuanced look into the positive impact of KIBS for local economy.

2 Conclusions

KIBS play an important role in the economy and make a pivotal contribution to regional innovation (see, e.g., Corrocher et al. 2009; Corrocher and Cusmano 2014; Pinto et al. 2015). The distribution and quality of KIBS have important effects on the economic system in terms of innovative capacity and economic development because they are highly innovative and also facilitate innovations in other economic sectors (Antonelli 1998; Hipp and Grupp 2005). KIBS play a pivotal role in knowledge transfer structure and are thus a pivotal factor for economic development. Therefore, it is worth exploring their role in our knowledge-based economy in depth (Gotsch and Hipp 2012).

In this background, this study highlights the spatial patterns of KIBS clusters by employing a new CQ index. This article finds that Washington, DC, plays an important role in KIBS clusters in the USA, followed by California, MD, Boulder, CO, Huntsville, AL, and Boston, MA. This study also finds that the CQ index would be a better index than the LQ index for measuring the magnitude of clusters given that LQ cannot consider the agglomeration of industries into its index. For instance, the LQ index cannot find some high IQ MSAs that are located in the West and South region. This can be a serious problem for finding clusters given that the agglomeration of industries is directly related to the definition of clusters. In contrast, the CQ index could consider both the agglomeration of industries and workers and be utilized for finding other industries’ clusters.

Next, this study employs four econometric models to reflect the interaction between KIBS and the urban economy. The study both runs OLS models and SUR models to compare their results and finds that there are notable differences in the significance or the coefficient value for KIBS, CQ, and the GDP. For example, the GDP shows an elasticity of 0.054 in OLS (significant at the 0.01 level) and 0.084 in SUR (significant at the 0.01 level), and KIBS exert an impact on the GDP with an elasticity of 0.262 in OLS (insignificant) and 0.515 in SUR (significant at the 0.01 level).

By exploring econometric models, the study finds that KIBS and the GDP positively interact with each other, and the SUR model would be a better model than the OLS model given that the OLS model underestimates or insignificantly estimates the relationship between them because of the error terms correlated. The results of this study suggest that the number and proportion of KIBS can be an economic driver for the US MSAs, and urban practitioners should develop policies for KIBS to promote regional economic growth. Also, this study finds that the GDP and each KIBS field differently interact with each other. In other words, they show different elasticities by their fields. The results show that the relationships between the GDP and KIBS are differentiated by industrial fields and governments and urban planners should develop urban planning by looking at the different characteristics of each KIBS field.

The findings in this article also allow governments and urban planners to find KIBS clusters, analyze strength and weakness of KIBS in their region, and establish policies for economic development based on KIBS. For example, they can invest their specialized KIBS field by analyzing the CQ index, compare their KIBS industry structure with other MSAs by looking into the magnitude of KIBS clusters in each field, and develop strategies based on the results of empirical models across US MSAs. This study would contribute to the KIBS literature by proposing a new cluster quotient index, which can consider both the agglomeration of industries and workers, and employing a SUR model, which can reflect the mutual relationship between KIBS and the urban economy.

As this study and previous papers indicate, KIBS can be regarded as an engine for the economic growth and would play an essential role in translating the potential of new technology into business results and improved economies (see, e.g., Corrocher et al. 2009; Corrocher and Cusmano 2014; Gallouj et al. 2015; Gotsch and Hipp 2012). Developing strategies for utilizing KIBS would be one of the best ways forward to the successful future of countries.