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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. Dog
an (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. Progrowth policies targeting insurance brokers must be
well examined and tested, as this research provides proof that not all firm growth is
beneficial to firm profits. Researchers are encouraged to exploit these findings by
exploring this effect using different insurance datasets to bring out new contexts and
perspectives.
Note The nonlinear
1. A database of Ghanaian insurance broker financial statements is virtually nonexistant and most of effect of size
them do not have electronic copies of their statements online. To conduct this research, the authors
relied on individually collected data. The data have been uploaded unto the Mendeley Data
Repository (DOI: 10.17632/gx572w29sr.2).
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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
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