The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/2040-0705.htm Exploring the nonlinear effect of The nonlineareffect of size size on profitability: evidence from an insurance brokerage industry in an emerging market 381 Richard Angelous Kotey Received 16 May 2020 Finance, Business School, University of Ghana, Accra, Ghana and Revised 3 July 202028 January 2021 City of Westminster College, London, UK 23 May 2021 Accepted 24 May 2021 Richard Akomatey Business School, University of Ghana, Accra, Ghana, and Baah Aye Kusi Department of Banking and Finance, Central University, Tema, Ghana and Department of Finance, University of Ghana Business School, Accra, Ghana Abstract Purpose – This study examines the possible nonlinear effect of size on stakeholder and shareholder profitability in the Ghanaian insurance brokerage industry. Design/methodology/approach –This study employs a panel dataset of 64 Ghanaian insurance brokerage firms spanning 2011–2015. Static [ordinary least squares (OLS), fixed effect and random effect and dynamic (two-step generalized method of moments (GMM))] estimation techniques are employed to analyze the data. Findings – The study finds the existence of both economies and diseconomies of scale and scope theories in the Ghanaian insurance brokerage industry confirming the existence of nonlinear nexus between size and performance. This finding is consistent for both stakeholder and shareholder profit performance. Thus, the results show that size improves profitability of insurance brokerage firms, but beyond a certain threshold, the relationship turns negative as size negatively affects profitability. Practical implications – The research findings have implications for both policy and research; the study recommends that Ghanaian brokerage managers should understand that not all growth is good and exercise a duty of care when applying growth strategies by monitoring size effect on performance so as not to go beyond the inflection point. Further research can be done to examine this effect in other contexts, timeframes and jurisdictions. Originality/value –This research is unique in that it employs a panel dataset consisting of 96% of insurance brokerage firms in Ghanawhilst employing both static and nonstatic regressionmodels to examine the effect of size. The research analysis adopted is robust, and the findings are significant. Also, the lack of empirical studies on the operations and dealings of auxiliary institutions such as the insurance brokerage firms adds value to this research. Keywords Diversification, Organization, Insurance brokerage firms, Profitability, L25 – firm performance: size, Scope < L2 – firm objectives, Behavior < L – industrial org Paper type Research paper Introduction Financial institutions are in the business of transforming asset maturities, matching financial market participants, creating liquidity, evaluating projects for efficient and effective allocation of resources, pooling and sharing risk, and providing credit information for better or informed lending decisions (Choi et al., 2013, 2016; De Haan et al., 2009; Kotey and Abor, 2019; Kotey, 2019; Kotey et al., 2019, Kusi et al., 2017; Madura, 2006; Mishkin and Eakins, 2006). Across industries and economies, these businesses undertaken by financial African Journal of Economic andManagement Studies institutions propel economic growth and development (Becks and Levine, 2004; De Haan Vol. 12 No. 3, 2021 pp. 381-399 et al., 2009; Demirguc-Kunt et al., 2003; Kargbo and Adamu, 2009). In light of this, financial © Emerald Publishing Limited 2040-0705 institutions carry huge risks and if they fail, can cause significant negative effects on the DOI 10.1108/AJEMS-05-2020-0228 AJEMS whole financial system. The insurance sector exists to resolve this problem bymitigating the 12,3 risks associatedwith doing business in the financial sector (Owusu-Sekyere and Kotey, 2019). Due to the potential risk effects associatedwith financial institution practices (the 2007–08 financial crises being a case in point (see Crotty, 2009)), practitioners, policymakers, academics and researchers have continually investigated and critically scrutinized the actions of financial institutions with the aim of curbing future occurrences and to control the risk-taking behavior of these institutions. The majority of these investigations focus on 382 banking financial institutions (including microfinance institutions, commercial, universal, rural, development and investment banks) because of their ability to affect the stability of the financial system. Because risk cannot be completely eradicated from the financial system, insurance companies and their associated auxiliaries play a key role in stabilizing the financial system. Thankfully, the insurance sector continues to receive much-needed attention in terms of research and advocacy, especially in Africa (Alhassan and Biekpe, 2017, 2018). This is summed up by Akotey et al. (2013) who highlight that the risk absorption function of the insurance sector promotes a “sense of peace within the business world.” But despite this increased attention, to the best of our knowledge, there are inadequate empirical studies on the operations and dealings of the auxiliary institutions (such as insurance brokerage firms) that support and promote the ability of insurance firms to perform their duties. It may be argued that the survival and sustainability of these auxiliary institutions are crucial for the efficient and effective functioning of the insurance sector, thereby influencing its ability to stabilize the financial system. The findings of Owusu-Sekyere andKotey (2019) bring to bear the need for further research into the size–profitability nexus in the insurance brokerage sector, as firm size has been proven to be a significant controlling factor. The theories of economies and diseconomies of scale and scope purport that the size of a firm is crucial for survival and profit performance and may either propel or derail performance. But this has been less studied and discussed in the insurance brokerage empirical literature. Given that the economies and diseconomies of scale and scope literature suggest that there are economic benefits and costs associated with size, there is a possibility that a nonlinear relationship may exist between size and profitability performance in the insurance brokerage industry of Ghana. Thus, similar to a study by Jaisinghani and Kanjilal (2017), we suspect that depending on the level, firm size may exhibit a linear positive relationship on firm profitability, where firm size positively affects firm profitability. But beyond a certain limit (or threshold), the relationship may turn inverse signaling a nonlinear relationship where bigger-sized (or overgrown) firms exhibit a negative relationship on firm profitability. We find no empirical evidence in the insurance brokerage literature, hence the motivation for this research. Again, following the literature on stakeholder and shareholder profitability or performance (see Kotey et al., 2019; Kusi et al., 2017, 2018), the effect of firm size on shareholder and stakeholder profitability has not been extensively examined; for example, is the effect linear or nonlinear, direct or indirect? Is the effect the same on stakeholder (measured by return on assets [ROA]) and shareholder (measured by return on equity [ROE]) profitability or are there significant differences? If there is evidence of nonlinearity, what is the threshold? These unanswered questions justify the need to deeply examine the size effects on profitability. Hence, this study attempts to contribute to the literature on size and performance by providing empirical evidence on the nonlinear relationship between size and stakeholder and shareholder profitability or performance using a Ghanaian insurance brokerage dataset. The rest of the paper is organized into overview, theoretical review, empirical review and hypothesis development, model specification, findings and discussions, robustness diagnostics, concluding remarks and recommendations, as well as references. General overview The nonlinear The Ghanaian insurance sector consists of 24 life insurance, 27 nonlife insurance, 3 reinsurance effect of size and 78 insurance brokerage companies (National Insurance Commission (NIC) Report, 2016). Between 2011 and 2016, the sector has seen 35 additional companies registered representing a 36% growth. The insurance brokerage sector has however seen more growth compared to the life, and nonlife insurance sectors showing how economically vibrant the sector is. While the brokerage companies have increased by 25 companies between 2011 and 2016 (representing a 47.17%growth), life, nonlife and reinsurance companies have increasedby6, 3 and 1 companies 383 between 2011 and 2016 (representing 33.33%, 12.5 and 50%) respectively (See Table 1). In 2015, Ghanaian insurance brokers earned commission totaling GHC 64.7 million from 48.6million the previous year, representing a 33%growth (See Table 2). By 2016, commission earned had risen by 13% toGHC 73million. From 2009 to 2016, brokerage commission earned grew by almost 423%, averaging about 53% per year. This sustained growth trend within the period shows the brokerage sector is economically viable. The authors estimate this growth to have been significantly influenced by certain occurrences: the IFRS adoption in 2012, the oil find leading to oil and gas exploration, and mining revenues accrued within the period. It is also important to note that the top ten insurance brokerage firms consistently bag over 60% of total annual commissions earned. In 2015, for example, KEK insurance brokers received GHC 40.5 million in commission and by 2016, their earned commission increased by GHC 5 million. Whilst these figures indicate the top companies have more market control, it promotes the idea of the presence of more market growth opportunities through market entry, innovation, creativity and competitive trading. A number of factors explain the positive growth trend in the insurance sector. Aforetime, insurance has principally being sold by insurance companies and their direct agents. However, new trends have emerged where insurance companies have leveraged on bank 2016 2015 2014 2013 2012 2011 Average growth Life 24 24 20 18 18 18 33.33% Table 1. Nonlife 27 27 25 25 25 24 12.50% Trends in the Brokers 78 74 70 60 57 53 47.17% establishment of Reinsurers 3 3 3 2 2 2 50.00% companies in the Total companies 132 128 118 105 102 97 35.75% insurance sector Source(s): the National Insurance Commission (NIC) Reports, 2011–2016 of Ghana Commission earned Earnings by top 10 insurance Percentage Percentage Year (GHC) brokers (GHC) earnings change 2016 73,144,221 45,138,831 62.00 13.01 2015 64,722,972 40,544,266 63.00 33.11 2014 48,623,536 30,640,273 63.00 38.24 2013 35,173,727 23,539,265 67.00 27.21 2012 27,651,046 19,060,875 68.00 34.35 2011 20,581,124 14,124,111 68.00 21.73 2010 16,907,668 11,939,132 71.00 20.91 Table 2. 2009 13,983,561 10,315,913 74.00 Contribution of top ten Overall 37,598,482 24,412,833 67.00 26.94 insurance broking average companies to total Source(s): the National Insurance Commission (NIC) Reports, 2009–2016 commission AJEMS relationships to sell their insurance products to bank customers.With the added convenience, 12,3 ease and flexibility, more customers are opting for these bancassurance products. From the insurance company’s perspective, they are able to sell their products to customers at reduced operational and transaction cost. With bank-based insurance products becoming a “national favourite”, brokers are left to reinvent themselves to stay relevant or phase-out of the market. Also, the imposition of a “No Premium, No Cover directive” by the National Insurance Commission (NIC) has had a significant impact on the industry as a whole (NIC report, 2014). 384 This directive abolished the 90-day premium warranty, which allowed insurance holders to buy insurance on credit. Insurance brokers were significant in educating clients on why their premiums payments had changed. Another factor accounting for growth in the insurance sector is the 400% increment on motor tariffs by the Ghana Insurers Association which agitated insurance buyers (Larbi, 2015). Through industry collaborations, the increment was staggered over three instalments which satisfied insurance buyers (Larbi, 2015). The yearly increase in premiums from 2010 and the relatively stable premium growth rate show a boisterous Ghanaian insurance market with the tendency to grow and develop (See Table 3). Because the insurance market is linked to the insurance brokerage market, growth in the former could positively affect the later. Although the commission growth rates may have fallen since 2015, the yearly insurance brokerage revenues from 2010 to 2016 show an upward trend indicating economic viability, hence creating more opportunities for insurance brokers. Theoretical review The theoretical literature on size is based on the economies and diseconomies of scale and scope (Kusi et al., 2017; Terraza, 2015; Naceur and Orman, 2011; Dietrich and Wanzenried, 2011; Athanasoglou et al., 2008). The economies and diseconomies of scale and scope are two opposing views on how size affects the performance of firms. The economies of scale and scope advance that there are cost benefits associated with size; economies of scope state that there is an average cost advantage when a firm offers more variety of products whilst economies of scale is a decrease in average cost per unit a firm benefits from by producing more of a product (Stigler, 1958). Insurance brokerage firms increase in size through either channel; offering a variety of services (e.g. consumer tailored services) or selling more of a product through innovative channels (e.g. bancassurance). Terraza (2015) posits that larger institutions have the financial muscles to undertakemore business opportunities and provide services at a lower cost, hence propel performance. Other authors also argue that larger institutions have market power and dominance through information asymmetry, which enables them to amass a majority of the profits in an industry (Armstrong et al., 2011; Kale and Loon, 2011). Hence, there are efficiency gains and financial benefits associated with size which positively improves the performance of firms (Terraza, 2015). Total gross premium Prem. growth rate Commission Comm. growth rate Year (GHC) (GHC) (GHC) (GHC) 2016 1,928,838,573 24% 73,144,221 13.01% 2015 1,567,400,946 26.42% 64,722,972 33.11% 2014 1,239,853,442 17.85% 48,623,536 38.24% 2013 1,052,090,982 23.68% 35,173,727 27.21% Table 3. 2012 850,657,054 35.34% 27,651,046 34.35% Growth rates of 2011 628,528,775 37.20% 20,581,124 21.73% premium and 2010 458,117,751 33.60% 16,907,668 20.91% commissions Source(s): the National Insurance Commission (NIC) Reports, 2010–2016 On the other hand, Kasman (2010) and Terraza (2015) advance that size may reduce the The nonlinear performance of firms through diseconomies of scale and scope; diseconomies of scope occur effect of size when the long-term benefit of expanding the scope of the business negatively affects profits whilst diseconomies of scale occurwhen the complexity and bureaucracy emanating from the long-run increase in firm size negatively affects profits. The authors argue that diseconomies of scale and scope can cause larger institutions to be bureaucratic, have low levels of supervision and monitoring and duplication of functions, which reduces the efficient use of resources and slows down decision-making leading to reduced profits. 385 Given these opposing views on the firm size, it is intuitive to argue that there is a possibility of a nonlinear relationship between size and performance. Hence, we hypothesize and test the economic theory that a nonlinear nexus exists between the size of insurance brokerage firms and firm profitability. On the issue of profit maximization, two theories shape our thinking: stakeholder and shareholder theory. The shareholder profit maximization theory has remained dominant in the value maximization discourse (Friedman, 1970; Greene, 1993; Jackson, 2011) while the stakeholder profit maximization theory is a more recent and less dominant perspective (Freeman, 1984; Jackson, 2011). While the shareholder value maximization theory advances that the business belongs to shareholders andmust be run in the sole interest of shareholders (premised on the fact that managers are hired as agents of the shareholders to run the business for their economic benefit and therefore have legal and moral obligation to serve the interest of shareholders), the stakeholder value maximization theory advances a broader scope by justifying that although shareholders are the owners of the business corporation, managers have a wider responsibility to all other persons or groups (shareholders, suppliers, creditors, employees, competitors, customers and the community) of whom the actions of the business may affect and recognizes the responsibilities of managers beyond economic and legal perspectives to cover ethical and philanthropic perspectives. Though the shareholder and stakeholder theories are both profit maximization perspectives, they vary in approach and measurement (see Table 4) (Kusi et al., 2017; Kochan andRubinstein, 2000). Given howprofitabilitymeasured, it is possible for size to have varying effects on firm performance. Based on this, we adopt two measures of profitability; ROA to support the stakeholder theory and ROE to support the shareholder theory. Empirical review and hypothesis development Literature on profit performance on insurance brokerage firms remains scanty. Therefore, where possible, we explore the profitability of other institutions like banks and manufacturing companies to augment our literature because of its applicability. Shareholder theory Stakeholder theory Purpose Maximizes shareholder value Pursues multiple objectives of parties with different interests Governance Principal-agent model Team production model Governance Control and ownership Coordination, cooperation and conflict resolution process Performance Shareholder value sufficient to Fair distribution of value created to maintain Table 4. metrics maintain investor commitment commitment of multiple stakeholders Difference in Residual risk Shareholder All stakeholder shareholder and holders stakeholder value Source(s): Adapted from Kochan and Rubinstein (2000) maximization theories AJEMS Niresh and Thirunavukkarasu (2014) explored the size–profitability effects of 15 listed 12,3 manufacturing firms in Sri Lanka between 2008 and 2012. Using ROA as a proxy for profitability and total assets and total sales for size, they found no size–profitability relationship in the data. Analyzing the data of 100 listed Indonesian manufacturing companies from 2009 to 2014, Kartikasari and Merianti (2016) found that size had a significant negative impact on profitability. Dogan (2013) conducted a similar study using 200 listed companies on the Istanbul Stock Exchange (ISE) between 2008 and 2011. However, 386 he found a positive relationship between size and profitability using ROA as an indicator for firm profitability and total assets, total sales and number of employees as indicators for size. John and Adebayo (2013) used similar variables on an eight-year data of Nigerian manufacturing firms, and the positive size–profitability nexus was also realized. These studies, with varying results, have not explored the size effect on ROE (supported by the stakeholder theory) as a measure of profitability. Another study by Titko et al. (2015) explored the drivers of profitability among banks in Latvia and Lithuania using data from 2008 to 2014. The authors found a positive relationship between profitability and size whilst using profitability ratios as a measure of firm performance. Lun and Quaddus (2011) also studied the nexus between firm size, use of electronic commerce and performance of container transport operators in Hong Kong. They identified that sale growth is positively related to firm size and electronic commerce. Owusu- Sekyere and Kotey (2019) also examined the factors that determine the profitability of insurance brokers in a Ghanaian panel dataset of 64 insurance brokerage firms over a five year period (2011–2015). They found that firm size positively affected profitability. However, they did not examine the long-term effects of size, whether its relationship on profit was linear or nonlinear. Furthermore, Terraza (2015) investigated the effects of bank capital and liquidity ratios on banks’ profitability by observing the behavior of the banks in terms of risk. Using a sample of 1,270 European banks spanning 13 years (2005–2012), she analyzed the banks according to size by categorizing them into small, medium and large banks. Her result showed that medium-sized banks had a positive and significant effect on profitability. Similarly, Fernandez et al. (2019) examined whether the relative importance of firm and industry effects in explaining performance variation is the same regardless of the firm size. Their results show that the performance of small and large firms is mainly explained by the firm effect while the performance of medium-sized firms is explained by industry effects. Thus, firm size positively affects performance in the form of sales growth. These studies imply different size levels have different profit effects. These studies, however, do not examine size from a long- term perspective. The above studies show the importance of size as a determinant of firm performance. The gaps identified show the limited exploitations of the relationship between firm size and profitability in the insurance brokerage context, especially from a Ghanaian perspective. Again, economies and diseconomies of scale and scope theory suggest a linear relationship between size and performance. However, we argue and hypothesize that a nonlinear relationship may exist between size and performance where both economies and diseconomies of scale and scope may exist. Moreover, following the literature on stakeholder and shareholder profitability performance, we hypothesize that size may affect shareholder and stakeholder profitability differently. However, there is no empirical evidence to support this, hence the need for this research. Model specification and procedure In this study, a panel data framework, which consists of both time series and cross-sectional data, is employed. It is argued that the panel data framework captures both time and firm- level variations and controls for omitted variable biases (Wooldridge, 2009; Brooks, 2008). The nonlinear Secondary data on insurance brokerage firms is obtained from the annual financial effect of size statements of 64 insurance brokerage firms between 2011 and 2015. The sample represents 96% of insurance brokers in Ghana. The choice of data and time frame is influenced by data availability [1] and convenience. Macroeconomic variables including gross domestic product (GDP) and inflation are extracted from the World Development Indicators (WDI). The panel data framework is expressed as 387 Yit ¼ αi þ γt þ βXit þ εit (1) where subscript i signifies the cross-sectional dimension (i.e. brokerage firm) i5 1. . . N and t signifies the time-series dimension (i.e. year), t5 1. . .T;Yit is the dependent variable; αi is the scalar and constant term for all periods (t) and specific to a firm fixed effect (i); γt is the time fixed effect t; β is a k3 1 vector of parameters to be estimated on the independent variables; Xit is a 13 k vector of observations on the independent variables comprising input variables in the model, which includes controlled variables and εit which is iid is the error term. The model is adopted fromOwusu-Sekyere and Kotey (2019) and modified to examine the nonlinear effect of size on profitability (ROE and ROA). The study employs a number of estimation strategies including static and dynamic strategies. Specifically, ordinary least squares, generalized least squares (fixed and random) and two-step generalized methods of moments are used to ensure consistency and reliability in the results and findings. Following the literature on dynamic models, especially GMM (Asongu and Tchamyou, 2016; Arellano and Bond, 1991; Arellano and Bover, 1995), the GMM estimator is suitable for data structure where the number of entities (firms) is more than the number of years (time span) (Arellano and Bond, 1991; Arellano and Bover, 1995) which is a case for the data used in this study. Again, while endogeneity can be resolved by identifying an instrumental variable which is correlatedwith the endogenous independent variable but not the error term, the identification of a suitable instrumental variable that is consistent with literature is often very difficult and near impossible. Hence, the next best alternative is the GMM estimator, which generates its own instruments internally to control the endogeneity suspected (Arellano and Bond, 1991; Arellano and Bover, 1995). For the GMM results to be valid, efficient and reliable, the arguments of Asongu and Ach-Anyi (2019) are examined and reported. That is, (1) the number of firms (insurance brokerage firms (64)) is significantly larger than the number of periods in each cross-section (5 years – 2011 to 2015), (2) the dependent variable exhibits persistence given the correlational values of 0.857 and 0.910 between the dependent variables (ROA and ROE) and their lag terms, respectively, which are the rule of thumb threshold of 0.800 required for establishing persistence, (3) the GMM strategy, which employs a panel structure, captures cross-firm variations, (4) accounts for endogeneity arising from simultaneity in the independent variables through an instrumentation process on the one hand and controlling unobserved heterogeneity with time invariant indicators on the other hand and corrects biases that are features of difference estimator. The static and dynamic models estimated are expressed as Shareholder profitability model ROEit ¼ β0 þ β1SIZE þ β2SQSIZEit þ β3RISKit þ β4FLEXit þ β5LNFIXEDit þ β6TDTAit þ β7INFLATIONt þ β8GDPt þ εit (1 - Static Model) AJEMS ROEit ¼ β1ROEit 1 þ β2SIZE þ β3SQSIZEit þ β4RISKit þ β5FLEXit þ β6LNFIXED− it 12,3 þ β7TDTAit þ β8INFLATIONt þ β9GDPt þ εit (2 - Dynamic Model) 388 Stakeholder profitability model ROAit ¼ β0 þ β1SIZE þ β2SQSIZEit þ β3RISKit þ β4FLEXit þ β5LNFIXEDit þ β6TDTAit þ β7INFLATIONit þ β8GDPit þ εit (3 - Static Model) ROAit ¼ β1ROAit 1 þ β2SIZE þ β3SQSIZEit þ β4RISKit þ β5FLEXit þ β6LNFIXED− it þ β7TDTAit þ β8INFLATIONt þ β9GDPt þ εit (4 - Dynamic Model) SIZE and SQSIZE are our main variables of interest meant to capture the nonlinear effect of size on profitability. SQSIZE is the squared value of SIZE. It is meant to capture the long-term effect of size. If the effect of size is linear, the coefficients of both variables would have the same sign (i.e. positive or negative). But if the signs of the coefficients are different, it means the relationship of size on the dependent variable is not linear. The technique is well supported by empirical literature (see Ban~os-Caballero et al., 2012; Kebewar, 2013). The dependent variable, variables of interest and control variables are all defined and explained in Table 5. Additionally, the measurement, expected signs, underlying theories and source of variables are also presented. Empirical results and discussions Table 6 presents the summary statistics of the variables employed in the study. From the table, ROA on average is 8.5% over the period under study while ROE is nearly 1%. This shows that return to stakeholders which is represented by the ROA is higher compared to return to shareholders represented by ROE. Themean values of size (which is a logged value) and sqsize (size squared) implies that size shows an average growth and squared of growth of 12.82 and 166.07% between the periods under study. Risk, which measures the variations in earnings before interest and tax (EBIT) averaged 1.56 units implying that the earnings of Ghanaian insurance brokerage firms varied by 1.56 units. Liquidity (flex) of the insurance brokerage firms is averagely 62.8% of total assets indicating insurance brokerage firms keep large amounts of monetary or liquid assets on average. Tangibility (lnfixed), which measures the availability and use of fixed asset (a logged variable) reports a value of 11.48% growth on the average in fixed assets. Leverage (tdta), which is debt financing, also constitutes about 30%of the total financing options used by the brokerage firmswithin the period under study. With regards to the macroeconomy, inflation over the period averaged at 12.4% while GDP growth averaged 7.7%. For a developing economy, these macroeconomic indicators suggest a stable and conducive state of economy in the period under study. The Pearson’s correlationmatrix is used to check formulticollinearity (Table 7). A cursory look at the ROA column shows there is very low correlation among the variables, an indicator of the presence of no multicollinearity. To further ensure that this is the case, we conduct a variance inflation factor (VIF) test (see Appendix 1). The VIF test figures for our variables of interest and the mean VIF were below 2, which is lower than the rule of thumb of 4. The nonlinear effect of size 389 Table 5. Summary of variables Expected Symbol Meaning and interpretation Source Underlying theory sign ROA Dependent Return on assets. Measures how efficient management is in Computed by authors based on Stakeholder theory variables using the firm’s assets to generate returns. It is measured as the financial statements of earnings before interest and tax divided by total assets brokerage firms ROE Return on equity. Measures the returns management get Shareholder theory from the total equity invested by shareholders. It ismeasured as net profit divided by total equity size Variables of Natural logarithm of total assets. This variable is employed Economies and þ interest as a proxy to measure the size of the brokerage firm diseconomies of scale and scope theory sqsize Squared of natural logarithm of total assets. This variable is Economies and  employed as a proxy to measure extreme increase in size of diseconomies of scale and the brokerage firm scope theory tdta Control Total debt to total assets. Measures the total debt of the Financial distress theory /þ variables brokerage firm as a ratio to its total assets lnfixed Natural log of fixed assets. This measures the amount of Going concern concept of /þ tangible assets kept by insurance brokers finance and accounting flex Monetary assets to total assets. The variable also measures Liquidity premium theory þ/ how much of the total assets are not fixed assets (or current assets) risk Standard deviation of EBIT to average value of EBIT. This Standard asset pricing /þ variable as a proxy for measuring risk of the brokerage firm theory inflation Inflation. Measured as a percentage change in the cost to the World Bank database Purchase power theory  average consumer of acquiring a fixed basket of goods and services at specified intervals GDP Gross domestic product (GDP) growth rate. It is the Economic growth theory þ/ percentage of change of themonetary value of all the finished goods and services produced within a country’s borders in a specific time period AJEMS Variable Obs. Mean Std. dev. Min. Max. SWILK 12,3 ROA 214 0.085 0.311 2.156 0.810 8.873*** ROE 214 0.0096 1.195 13.215 0.9516 8.368*** size 215 12.824 1.274 10.159 16.771 3.539*** sqsize 215 166.071 33.589 103.211 281.272 4.743*** risk 307 1.559 7.087 42.369 95.766 11.895*** 390 flex 215 0.628 0.303 0.021 1.416 5.687*** lnfixed 207 11.481 1.755 6.122 15.616 3.229*** tdta 214 0.295 0.286 0.163 1.834 7.153*** inflation 335 0.124 0.034 0.087 0.171 7.063*** GDP 335 0.077 0.038 0.039 0.141 7.165*** Note(s): ROA – return on assets (stakeholder profit); ROE – return on equity (shareholder profit); size – natural log of total assets; sqsize – squared natural log of total assets; risk – standard deviation of earnings before interest and tax; flex – liquidity; lnfixed – tangibility; tdta – leverage; inflation- economic stability; GDP – gross Table 6. domestic product growth rate; SWILK – Shapiro–Wilk test results ; significance level: ***p < 0.01, **p < 0.05 Summary statistics and *p < 0.1 Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1) ROA 1.000 (2) ROE 0.637 1.000 (3) size 0.229 0.207 1.000 (4) sqsize 0.212 0.195 0.998 1.000 (5) risk 0.003 0.019 0.071 0.069 1.000 (6) flex 0.246 0.156 0.112 0.114 0.045 1.000 (7) lnfixed 0.070 0.089 0.689 0.686 0.004 0.621 1.000 (8) tdta 0.257 0.305 0.204 0.206 0.044 0.030 0.165 1.000 (9) inflation 0.078 0.020 0.186 0.177 0.098 0.131 0.170 0.124 1.000 (10) GDP 0.065 0.013 0.206 0.196 0.161 0.121 0.167 0.105 0.607 1.000 Note(s): ROA – return on assets (stakeholder profit); ROE – return on equity (shareholder profit); size – natural Table 7. log of total assets; sqsize – squared natural log of total assets; risk – standard deviation of earnings before Pearson’s correlation interest and tax; flex – liquidity; lnfixed – tangibility; tdta – leverage; inflation – economic stability; GDP – matrix gross domestic product growth rate; significance level: ***p < 0.01, **p < 0.05 and *p < 0.1 Tables 8 and 9 present results on the nonlinear effect of size on stakeholder and shareholder profitability, respectively, in the dataset. For each of the two tables, seven models are estimated and presented on the nonlinear relationship between size and stakeholder and shareholder profitability. Specifically, we present the results on random effects (see Models 1, 2, 8, 9), fixed effects (see Models 3, 4, 10 and11), ordinary least squares (OLS) (see Models 5, 6, 12 and13) and two-step GMM (see Models 7 and 14) in Tables 8 and 9. For each of the static models, we include robust estimations to control for biased standard errors (seemodels 2, 4, 6, 9, 11 and 13). These regression results are based on the estimated static and dynamic models presented in the previous chapter. Size of insurance brokerage firms, our variable of interest, presents a positive and significant relationship on ROA across all themodels in Table 8. This results indicate that the short-term effect of increment in the size of insurance brokerage firms positively affects stakeholder profits. This finding agrees with Owusu-Sekyere and Kotey (2019). It is consistent with the economies of scale and scope theories which advance that there are economic, efficient and cost reduction benefits associated with size increments, which enable firms improve their performance. However, a significantly high increase in the size of The nonlinear effect of size 391 Table 8. Nonlinear effect of insurance brokerage size on stakeholder profits in Ghana (1) (2) (3) (4) (5) (6) (7) Variables Random Robust random Fixed Robust fixed OLS Robust OLS Two-step GMM size 1.311*** 1.311** 1.662*** 1.662** 1.107*** 1.107** 1.708* (0.274) (0.601) (0.354) (0.662) (0.256) (0.477) (1.018) sqsize 0.0462*** 0.0462** 0.0554*** 0.0554** 0.0389*** 0.0389** 0.0600 (0.0101) (0.0209) (0.0133) (0.0225) (0.00926) (0.0166) (0.0363) risk 0.00137 0.00137 0.00106 0.00106 0.000758 0.000758 0.000589 (0.00213) (0.00113) (0.00220) (0.000891) (0.00243) (0.00105) (0.00130) flex 0.272* 0.272* 0.139 0.139 0.268* 0.268 0.170 (0.156) (0.159) (0.207) (0.178) (0.148) (0.170) (0.158) lnfixed 0.0151 0.0151 0.0210 0.0210 0.0100 0.0100 0.578*** (0.0407) (0.0368) (0.0488) (0.0465) (0.0398) (0.0365) (0.184) tdta 0.406*** 0.406*** 0.363*** 0.363** 0.401*** 0.401*** 0.00516 (0.0715) (0.147) (0.0892) (0.165) (0.0697) (0.124) (0.0379) inflation 1.743 1.743 2.262* 2.262 1.583 1.583 3.339 (1.265) (1.414) (1.320) (1.528) (1.512) (1.379) (3.008) GDP 0.340 0.340 0.0308 0.0308 0.00712 0.00712 1.456 (1.332) (1.402) (1.375) (1.490) (1.578) (1.404) (3.771) L.ROA 0.0945 (0.172) Constant 9.026*** 9.026** 11.94*** 11.94** 7.610*** 7.610** 11.19* (1.786) (4.013) (2.378) (4.642) (1.637) (3.122) (6.626) Observations 198 198 198 198 198 198 133 R-squared 0.3354 0.3354 0.368 0.368 0.310 0.310 Number of firms 64 64 64 64 60 Inflection 2.86*** 2.08** 1.62* 1.54* 2.73*** 2.23** 1.45* Turning Point 14.1891 14.189 152 15 14.2293 14.229 Sargan 10.41 (0.238) Hansen 6.72 (0.568) AR(1) 2.23 (0.026)** AR(2) 0.74 (0.461) Instrument 18 Note(s): ROA – return on assets (stakeholder profit); ROE – return on equity (shareholder profit); size – natural log of total assets; sqsize – squared natural log of total assets; risk – standard deviation of earnings before interest and tax; flex – liquidity; lnfixed – tangibility; tdta – leverage; inflation – economic stability; GDP – gross domestic product growth rate; significance level: ***p < 0.01, **p < 0.05 and *p < 0.1 – standard errors in parentheses; 1[–1/2] 3 [1.311/–0.0462] 5 14.189 (GHC 1,451,795.593); 2[–1/2] 3 [1.662/–0.0554] 5 15 (GHC 3,269,017.372); 3[–1/2] 3 [1.107/–0.0389] 5 14.229 (GHC 1,511,770.1) AJEMS 12,3 392 Table 9. Nonlinear effect of insurance brokerage size on shareholder profits in Ghana (8) (9) (10) (11) (12) (13) (14) Variables Random Robust random Fixed Robust fixed OLS Robust OLS Two-step GMM size 2.888*** 2.888 5.152*** 5.152** 2.663*** 2.663 4.809*** (0.696) (1.759) (1.056) (2.511) (0.676) (1.613) (1.785) sqsize 0.0993*** 0.0993 0.166*** 0.166** 0.0917*** 0.0917 0.167** (0.0253) (0.0617) (0.0398) (0.0802) (0.0244) (0.0568) (0.0635) risk 0.000720 0.000720 0.00157 0.00157 3.20e-05 3.20e-05 0.000619 (0.00632) (0.00253) (0.00656) (0.00254) (0.00642) (0.00248) (0.00339) flex 0.199 0.199 0.243 0.243 0.228 0.228 0.197 (0.401) (0.364) (0.618) (0.681) (0.392) (0.328) (0.429) lnfixed 0.0366 0.0366 0.139 0.139 0.0198 0.0198 1.574** (0.107) (0.0790) (0.146) (0.195) (0.105) (0.0672) (0.749) tdta 1.091*** 1.091* 1.250*** 1.250 1.063*** 1.063* 0.0896 (0.188) (0.638) (0.266) (0.800) (0.184) (0.600) (0.0979) inflation 5.075 5.075 8.719** 8.719 4.554 4.554 12.70 (3.854) (4.209) (3.942) (5.652) (3.993) (4.172) (9.212) GDP 1.092 1.092 0.819 0.819 0.563 0.563 8.782 (4.038) (3.036) (4.106) (3.724) (4.169) (3.161) (10.76) L.ROE 0.00340 (0.127) Constant 19.12*** 19.12* 35.05*** 35.05** 17.83*** 17.83* 29.97*** (4.474) (11.15) (7.101) (16.46) (4.325) (10.25) (11.01) Observations 198 198 198 198 198 198 133 R-squared 0.3562 0.3562 0.385 0.385 0.266 0.266 Number of firms 64 64 64 64 60 Inflection 2.21** 1.36* 1.19 1.24 2.16** 1.36* 1.99** Turning point 14.5421 15.5182 15.518 14.5203 14.3984 Sargan 1.68 (0.989) Hansen 4.67 (0.792) AR(1) 1.86 (0.063)* AR(2) 0.81 (0.420) Instrument 18 Note(s): ROA – return on assets (stakeholder profit); ROE – return on equity (shareholder profit); size –natural log of total assets; sqsize – squared natural log of total assets; risk – standard deviation of earnings before interest and tax; flex – liquidity; lnfixed – tangibility; tdta – leverage; inflation- economic stability; GDP –gross domestic product growth rate; significance level: ***p < 0.01, **p < 0.05 and *p < 0.1 – standard errors in parentheses; 1[–1/2] 3 [2.888/–0.0993] 5 14.542 (GHC 2,067,379.762); 2[–1/2] 3 [5.152/–0.166] 5 15.518 (GHC 5,487,988.15); 3[–1/2] 3 [2.663/–0.0917] 5 14.520 (GHC 2,023,166.633); 4[–1/2]3 [4.809/–0.167]5 14.398 (GHC 1,790,854.777) brokerage firms (represented by sqsize which is the squared value of size) is observed to The nonlinear negatively affect ROA across all the models in Table 8. This implies that when insurance effect of size brokerage firms become extremely large or increase in size rapidly, the expected positive effect on firm profits reverses showing a fall in firm profits. Based on the diseconomies of scale theory, we suspect the negative effect may be as a result of supervision and monitoring difficulty, and bureaucracy and laxity in decision-making and operations causing firms to be inefficient hence reduced profitability. The results also show an inflection point where the effect of size on profitability changes from positive to negative (see Tables 8 and 9). This 393 implies that size improves the performance of insurance brokerage firms but growth in size beyond a certain threshold leads to a fall in firm profits. Specifically, when we compute threshold points following the approaches of Brambor et al. (2006) and Lind and Mehlum (2010), the random effect model (Model 8), fixed effect models (Model 10), ordinary least square models (Model 12) andGMM (Model 14) models in Table 9 report a threshold of GHC 2,067,379, GHC 5,487,988.150, GHC 2,023,166.633 and GHC 1,790,854.777, respectively, implying that beyond the specified monetary value of brokerage firm size, the effect of size on performance changes from a positive effect to a negative effect. This finding suggests the existence of an inverted nonlinear “U-shape” relationship between size and performance of brokerage firms in Ghana. These findings suggest that a nonlinear relationship exists between size and performance where both economies and diseconomies of scale and scope exist separated by an inflection point where size-induced profits is at its peak. Beyond the threshold, the effect of size becomes negative on firm profits. We find similar results reported in Table 8 where the nonlinear effect of size of insurance brokerage firms on stakeholder profitability is examined. This is an indication that size has a nonlinear invertedU-shape effect on both shareholder and stakeholder profitability in Ghanaian insurance brokerage firms. Furthermore, liquidity is found to be positively and significantly related to profitability in Models 2 and 5 in Table 8. This implies that insurance brokerage firms that are relatively more liquid increase in profitability comparatively. This is not surprising and conforms to the argument that liquidity serves as a booster for client confidence, hence attracting more clients and businesses, which leads tomore operations and increased performance. Also, we find that fixed assets reduce performance contrary to the finance and accounting concept that posits that fixed assets are the economic resources of firms, which assist and propel performance. However, we argue following Himmelberg et al. (1999) and Margaritis and Psillaki (2010) that when fixed assets are idle, obsolete, worn out and require major repairs and maintenance, they tend to increase the operating cost of firms leading to low performance. This finding is also consistent with Owusu-Sekyere and Kotey (2019) who explained that the acquisition of capital-intensive fixed assets means less liquidity for operations, which affects firm profits. These results are also observed in the two-step GMM models (Model 7 and 14) in Tables 8 and 9. Similarly, the results show that leverage reduces performance across the models with the exception of the two-step GMMmodels (Models 7 and 14). Following the financial distress theory, leverage increases the risk profile of firms and hence their performance is reduced. This finding is true for both stakeholder and shareholder profitability in the dataset. Finally, the results also show that inflation in Models 3 and 10 reduces stakeholder and shareholder profitability, respectively. Thus, inflation weakens the purchasing power of the local currency, hence the fall in value of both stakeholder and shareholder profitability. From the two-stepGMMmodels, profits are not persistent as the lags of profitability are not significantly related to current year profitability. Model diagnostic checks To enhance reliability, efficiency and accuracy of the result, the study employs a number of techniques. First, using the statistic table, the study screens for outliers in order to reduce the AJEMS biases caused by outliers. Hence, no evidence of outliers was identified. Second, the normality 12,3 of each variable is assessed by the use of the Shapiro–Wilk normality test (Table 6). Third, the study employs the Pearson’s correlation to screen for multicollinearity and realized high correlations between size and its squared which is accepted in nonlinear studies (Allison, 2012). Fourth, the study employs Breusch and Pagan Lagrangianmultiplier test (Appendix 2) to justify the use of OLS or the random effects. From the results inAppendix 2, random effects models are preferred to the OLSmodels for both ROA and equity models. Fifth, the Hausman 394 specification test (Appendix 3) is employed to justify the choice between fixed effects and random effects models. Subsequently, while the Hausman test results for ROA indicates preference for the use of fixed effects models, the Hausman test results for ROE indicate preference for random effects models. Similarly, cross-sectional dependence is tested using the Pesaran (2015) approach because our panel is unbalanced.With a null hypothesis of weak cross-sectional dependence, the Pesaran (2015) results (seeAppendix 4) fail to reject the null of weak cross-sectional dependence implying that the severity and presence of cross-sectional dependence can be ignored for both ROA and ROE models, respectively. More so, financial asset pricing theories show that risk and profits have reverse causality characteristics. Hence, to avoid problems of reverse causality leading to endogeneity problems in our results, the GMM estimator is employed. Specifically, the two-step GMMmodel is employed ahead of the one-step GMM to control for heteroscedasticity, (Appendix 5) which was present in the data. On the problem of autocorrelation, no evidence of first-order autocorrelation is found (see Appendix 6). Given all the processes and procedures undergone, it is safe to say the results are reliable, consistent and efficient, and fit for generalization of insurance brokerage firms in Ghana. Conclusion and policy recommendation This study examines the possible nonlinear effect of size on stakeholder and shareholder profitability in the Ghanaian insurance brokerage industry between 2011 and 2015. The study is motivated by the limited studies on the auxiliary firms, including insurance brokerage firms that support the effective and efficient operation of the insurance industry and the entire financial system. Employing a panel data of 64 insurance brokerage firms in Ghana across both static (OLS, fixed effects and random effects) and dynamic models (two-step GMM), findings are presented on the nonlinear effect of size of insurance brokerage firms stakeholder and shareholder profitability. We find the existence of both economies and diseconomies of scale and scope theories in the Ghanaian insurance brokerage industry implying the existence of a nonlinear inverted U-shape nexus between size and performance of insurance brokerage firms. This finding is consistent for both stakeholder and shareholder profit performance. Thus, size improves the performance of the Ghanaian insurance brokerage firms within the period studied but beyond a certain threshold, size impedes or reduces the performance of brokerage firms in Ghana. These findings have policy implications and recommendations for insurance brokerage managers, researchers and policymakers in the Ghanaian insurance industry. Thus, managers of insurance brokerage firms must manage the firm size carefully by measuring firm performance vis-a-vis size, as an uncontrolled increase in firm size may go beyond the threshold (i.e. the inflection point), which is harmful to stakeholder and shareholder value maximization. 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Appendix 1 VIF test results Variable VIF 1/VIF size 1.08 0.922145 tdta 1.07 0.937158 lnfixed 1.02 0.978469 risk 1.01 0.991510 Table A1. Mean VIF 1.05 VIF test AJEMS Appendix 2 12,3 Breusch and Pagan Lagrangian multiplier test for random effects Breusch and Pagan Lagrangian multiplier test for random effects (ROA) ROA [firmcode,t] = Xb + u[firmcode] + e[firmcode,t] Estimated results: 398 | Var sd = sqrt(Var) ---------+----------------------------- ROA | 0.0985966 0.314001 e | 0.0450626 0.2122794 u | 0.029569 0.1719565 Test: Var(u) = 0 chibar2(01) = 15.45 Prob > chibar2 = 0.0000 Breusch and Pagan Lagrangian multiplier test for random effects (ROE) ROE[firmcode,t] = Xb + u[firmcode] + e[firmcode,t] Estimated results: | Var sd = sqrt(Var) ---------+----------------------------- ROE | 0.6464261 0.8040063 e | 0.4018667 0.6339296 u | 0.0351327 0.1874373 Test: Var(u) = 0 chibar2(01) = 4.40 Prob > chibar2 = 0.0180 Appendix 3 Coef. Hausman (1978) specification test (ROA) Chi-square test value 11.192 P-value 0.191 Table A2. Hausman (1978) specification test (ROE) Hausman (1978) Chi-square test value 20.169 specification test P-value 0.01 Appendix 4 Pesaran (2015) test for weak cross-sectional dependence Pesaran (2015) test for weak cross-sectional dependence (ROA) Residuals calculated using predict, e from xtreg. (137 missing values generated) Unbalanced panel detected, test adjusted. H0: errors are weakly cross-sectional dependent. The nonlinear CD ¼ −0:793 effect of size p-value ¼ 0:428 Pesaran (2015) test for weak cross-sectional dependence (ROE) Residuals calculated using predict, e from xtreg. 399 (137 missing values generated) Unbalanced panel detected, test adjusted. H0: errors are weakly cross-sectional dependent. CD ¼ −0:519 p-value ¼ 0:604 Appendix 5 Modified Wald test for groupwise heteroskedasticity In fixed effect regression model H0: sigma(i)^2 5 sigma^2 for all i chi2ð64Þ ¼ 5:6eþ 36 Prob > chi2 ¼ 0:0000 Appendix 6 Wooldridge test for autocorrelation in panel data Wooldridge test for autocorrelation in panel data (ROA) H0: no first order autocorrelation Fð1; 33Þ ¼ 0:850 Prob > F ¼ 0:3632 Wooldridge test for autocorrelation in panel data (ROE) H0: no first-order autocorrelation Fð1; 33Þ ¼ 0:067 Prob > F ¼ 0:7977 Corresponding author Baah Aye Kusi can be contacted at: baahkusi@gmail.com For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: permissions@emeraldinsight.com