Impact of Audit Fees on Earnings Management and Financial Risk: An Analysis of Corporate Finance Practices

Abstract

This study employs a robust quantitative ex post facto research design to investigate the complex relationship between audit fees and earnings management. The financial information of 164 firms admitted to the Tehran Stock Exchange (TSE) was used from 2010 to 2019 (pre-COVID period) to achieve the research goal. Analysing data from the Tehran Stock Exchange firms, the study uncovers an inverted U-shaped relationship between audit fees and earnings management. This suggests that moderate audit fees can lead to higher earnings management. Key contributions of this paper include highlighting the role of audit fees in influencing financial reporting quality and risk management, providing empirical evidence on the asymmetric effects of normal and abnormal audit fees on earnings management, and emphasising the need for balanced audit fee structures to ensure financial transparency and mitigate risk. The findings offer valuable insights for academics, practitioners, and policymakers in understanding the nuances of audit fees and their impact on corporate financial practices. This study advances the literature on financial risk management and corporate finance. It emphasises the importance of balanced audit fee structures for management teams, auditors, and policymakers to ensure transparent financial reporting practices.

1. Introduction

As a measure of financial information quality, accounting comparability allows users to identify similarities and differences between items in financial statements and more rationally assess various lending-based investment opportunities (FASB 2010). For information comparability, similar items should be the same, and different items should seem different (Barth et al. 2018). The accounting comparability of financial information is so crucial that concept statement No. 8 of the Financial Accounting Standards Board addresses the increased financial information comparability as one of the most critical reasons that financial reporting standards are needed (Choi et al. 2019). Paying compensation and bonuses to managers as part of their wages is one of the most widely used practices motivating them to increase shareholders’ wealth (Henderson and Fredrickson 2001). Compensation for firm managers usually includes fixed salary, cash, and non-cash bonuses. Theoretically, cash bonuses paid to managers are expected to suit their performance, resulting in more shareholder benefits (Zhang et al. 2018). Healy (1985) shows that compensation plans encourage managers to employ earnings management practices to maximise rewards. Therefore, managers can manipulate earnings to increase their rewards. A solution to this problem is to improve accounting information comparability. This concept can be viewed from internal and external aspects. Internal accounting comparability refers to a firm’s consistency of practices over years of activity, whereas external accounting comparability shows a firm’s status among peer firms (Lobo et al. 2018). Companies whose accounting systems are similar to their peer firms are more likely to adjust their managers’ compensation contracts based on accounting profits.

Many studies have shown that audit fees affect the quality of financial reporting (Gu and Hu 2015; Gandía and Huguet 2021). The findings indicate that audit fees may affect the quality of financial reporting in different economic settings. Nevertheless, it is noteworthy that accounting comparability, as a measure of financial reporting quality, may be influenced by audit fees as a measure of audit quality. As mentioned earlier, since accounting comparability can affect managers’ compensation, it can be argued that audit fees, as a proxy for audit quality, can influence the relationship between accounting comparability and board compensation. This topic has not been investigated in previous research and has been neglected to some extent. This research examines the critical issue of audit fees and the relationship between comparability and compensation. Of course, looking at the previous study, it can be seen that the relationship between comparability and compensation has already been investigated by Lobo et al. (2018), Nam (2020), and Fattahi et al. (2021). However, in the scope of these studies, the effect of audit fees has not been investigated. Therefore, by taking the help of and following the previous literature, the current research tries to examine the existing literature in the field of financial reporting and the role of auditors’ fees in its change.

On the other hand, Frankel et al. (2002) state that companies paying higher audit fees exhibit a lower level of earnings management, suggesting the additional fee charged by auditing firms may increase the auditing quality. Ferguson et al. (2004) showed that non-audit services fees negatively affect the accountant’s independence. Their findings also reveal a positive relationship between the non-audit services fee and discretionary accruals. Antle et al. (2006) try to justify the relationship between audit fees and earnings management and argue that various economic factors and conditions may affect this relationship. Such studies indicate that audit fees can affect earnings management.

Given the above, in addition to examining the moderating effect of audit fees on the relationship between comparability and rewards, this study investigates the impact of audit fees on earnings management (actual and real) in a relatively risky environment with a high inflation rate. Previous research has investigated the relationship between audit fees and earnings management in other countries. For example, Gandía and Huguet (2021) investigated the relationship between remuneration and earnings management from the perspective of the type of auditor. Also, Donatella et al. (2019) investigated the impact of audit fees on earnings management in Swedish companies. In addition, Ben Abdelaziz et al. (2022) have conducted a similar study but introduced audit fees as a factor in reducing earnings management, which was followed by other studies such as Shehadeh et al. (2024) and Santos Jaén et al. (2023). Previous studies’ primary focus has been examining the direct relationship between these two variables. However, the current research is the first conducted in Iran’s economic environment, which has a high inflation rate and risky financial conditions. The audit fee is divided into normal and abnormal fees, and the asymmetric influences on earnings management are investigated. The study further investigates the relationship between earnings management, as the output of the financial reporting system (Wen et al. 2023), and compensation, which is influenced by the financial reporting system, with two measures of the financial reporting system, i.e., the comparability and audit fee.

The remainder of this paper is organised as follows: Section 2 presents the background and the development of the hypotheses. Section 3 outlines the data collection and describes the sample and research variables. Empirical models and econometrics results are shown in Section 4. Finally, discussion, conclusions and implications are provided in Section 5.

2. Literature Review

The audit fee is an essential indicator for assessing organisations’ financial statements (Christensen et al. 2021). Simunic (1980) suggests a relationship between audit fees and audit risk. Many studies have shown a direct association between audit risk and fees (Sonu et al. 2017). If comparability improves the quality of the accounting managerial estimates, the misstatement risk should be reduced irrespective of other factors. Comparability, which leads to the quality reporting of financial information, should decrease the inherent audit risk and reduce the audit fee.

On the other hand, the complexity of the entity is one of the factors that causes an increase in the audit fee (Lee et al. 2024). Entities that are more complex in operation and structure could pay more to the managers to control the process (Kalelkar et al. 2024). Furthermore, managers who gain a more significant earnings margin for the entity deserve more compensation. When the firm’s operation is large-scale and complex, demand for supervision in financial reporting increases. Entities with complex procedures require a high level of audit services. As a result, they pay higher fees to the audit firms, which suggests that as the complexity of the entity’s operation increases, the management’s compensation amount also rises (Saleh and Ragab 2023).

Audit fees could be considered as a measure of an entity’s reporting complexities (Wysocki 2010). Investors, shareholders, and other stakeholders pursue quality information and a lower level of risk simultaneously, and the management, as their representative, tends to maximise its compensation by improving its plans and performance and decreasing information uncertainty risk. Audits play an overriding role in bridging these groups together so that receiving a greater audit fee appears as an assurance concerning the management’s performance and compensation by the manager (Utomo and Machmuddah 2023). So, it could be predicted that the audit fee will decrease as comparability increases, resulting in a decline in executive compensation. However, it can be argued that an increase in comparability could lead to a rise in executive compensation, highlighting the contradictory impact of audit fees on the relation between the comparability of the accounting information and executive compensation. Wysocki (2010) argues that if the settlements concerning the compensation are determined appropriately, the management will be motivated to perform better, which may reduce the need for audit activities.

Concerning this argument, the negative association between audit fees and compensation could be predicted. However, the audit fee could be another proxy connected with earnings management and financial reporting quality, which justifies the negative association between the comparability of accounting information and executive compensation.

To pursue a better analysis of the modifier and contradictory influence of the audit fee, Simunic (1980) considered normal and abnormal audit fees. Ridzky and Fitriany (2022) divide audit fees into ‘normal’ and ‘abnormal’ to examine the impact of audit fees on audit quality. They define an abnormal audit fee as the difference between the actual and normal fees (which could be different in different cities and countries) paid by the auditee to the external auditor. They further divide the abnormal audit fees into ‘premium’ and ‘discount’ audit fees. They describe the premium audit fee as the actual audit fee above the normal and call it a negative abnormal audit fee (discount) if it is below the normal. Given the above, we propose our first hypothesis as follows:

Hypothesis 1 (H1): 

Audit fees have a differential impact on the relationship between accounting comparability and executive compensation performance.

Hypothesis 1a (H1a): 

Normal audit fees positively moderate the relationship between accounting comparability and executive compensation performance. This implies that standard audit fees contribute to improved accounting comparability, thereby enhancing the alignment of executive compensation with firm performance.

Hypothesis 1b (H1b): 

Abnormal audit fees (premium and discount) affect the relationship between accounting comparability and executive compensation performance. Specifically, premium audit fees (above the normal) are expected to strengthen this relationship by ensuring higher quality. In contrast, discount audit fees (below the normal) may weaken the relationship due to compromised audit quality.

Previous studies have examined the relationship between audit fees and earnings management (Gu and Hu 2015; Gandía and Huguet 2021). However, these studies produced mixed results. For instance, Frankel et al. (2002) indicated that firms that pay a higher audit fee reflect a lower level of earnings management, which refers to the additional fee required by audit firms that enhances the audit quality. Ferguson et al. (2004) demonstrated that fees related to non-audit services have a negative impact on an auditor’s independence. Their findings indicated a positive association between fees related to non-audit services and discretionary accruals. It is also argued that improved comparability increases the quality of financial information reporting, which can reduce the auditor’s assessment of the audit’s inherent risk, thus reducing the audit fee. So, we look for a probable asymmetric association between audit fees and earnings management to justify the relationship between comparability, earnings management, and audit fees.

Audit firms determine the required fee amount based on their clients’ observed features, such as size, complexity, risk structure of the firm, etc., which is called an audit fee. Conversely, any additional fee received based on the relationship between the audit firm and the clients that is not related to the client’s features, such as size, complexity, etc., is defined as the abnormal level of the audit fee. Antle et al. (2006) provide various reasons regarding the correlation between audit fees and earnings management. They believe that different economic factors can affect this correlation; therefore, different results ensue in other economic environments and conditions. While previous research has concentrated on total audit fees and their association with earnings management, recent studies follow a new method by dividing the entire fees into two levels, normal and abnormal, and investigating the correlation between the abnormal level of audit fees and earnings management (Mitra et al. 2009). However, these studies have produced mixed results. For instance, Asthana and Boone (2012) reported that both abnormal levels of positive and negative audit fees negatively correlate with the quality of financial reports. In contrast, Blankley et al. (2012) and Eshleman and Guo (2014) indicated that the positive level of abnormal audit fees is positively related to the quality of financial reporting.

Using five theories, Antle et al. (2006) assessed the relationship between audit fees and earnings management. Basic economic theory suggests that providing audit and non-audit services to the client creates a financial bond between the audit firm and the client, which can jeopardise the auditor’s independence. The supply and demand theories concerning services indicate that increased discretionary accruals lead to increased demand for audit services. For instance, a higher level of abnormal accruals is related to a higher probability of future litigation risk; therefore, auditors perform additional audit procedures to reduce these risks. Although the theory of bribery suggests that auditors perform audit procedures in line with client’s expectations to ensure their position as their clients’ audit firm in future periods, this point increases auditors’ chances of receiving non-audit service fees from clients; therefore, they receive additional fees (Sarhan and Cowton 2024). The theory of bias suggests a bias in audit procedures in favour of the client when a well-built relationship is built between the auditor and the client due to a lengthy tenure period. Finally, the theory of production assumes that the level of abnormal accruals is reduced due to the provision of non-audit services. This means that the rise in the effectiveness or efficiency of clients’ operations through non-audit services puts constraints on the flexibility of managers in earnings management. This literature demonstrates that the impact of audit fees on the earnings management process would differ depending on the condition of the auditor and the client. This means there is an asymmetric association between audit fees and earnings management. Figure 1 shows the conceptual model of the study.

Given the theoretical and empirical evidence, our second hypothesis about audit fees on earnings management is specified as follows:

Hypothesis 2 (H2): 

The relationship between audit fees and earnings management is asymmetric and contingent on the nature of the audit fees (normal versus abnormal).

Hypothesis 2a (H2a): 

Normal audit fees are associated with reduced earnings management. This suggests that standard audit fees provide adequate resources for auditors to conduct thorough audits, thereby mitigating earnings management practices.

Hypothesis 2b (H2b): 

Abnormal audit fees have an asymmetric effect on earnings management. Premium audit fees (above the normal) will likely reduce earnings management due to increased scrutiny and higher audit quality. In contrast, discount audit fees (below the normal) may be associated with increased earnings management due to potential reductions in audit quality and auditor independence.

3. Methodology

The present study employs a quantitative, ex post facto design. The population consists of all the companies listed on the Tehran Stock Exchange (TSE) from 2010 to 2019 (pre-COVID 19 period). We were able to add another 2–3 years of data to our sample, but due to the significant impact of COVID 19 on the performance and function of most firms, we excluded the data related to the COVID 19 Period. Data are primarily based on the TSE’s audited financial statements and board reports, a reliable source of information (Daryaei et al. 2022; Namakavarani et al. 2021; Zadeh et al. 2022; Shandiz et al. 2022). However, the study compiles a purposive sampling; thus, financial firms such as banks and insurance firms are absent, because they have different conditions concerning firm characteristics. Listing firms must also have continuous operations during the study period, and their information must be available. Following these criteria, the study includes 164 firms (1640 firm-years). Purposive sampling was used to select a representative sample with the following four inclusion criteria (see

Table 1. Sample computation for firms.

Sample Computation for the Year 2010–2019	Firms	(%)
Total population Less:	533	100
Firms inactive between 2010–2019	(189)	(35)
Financial services firms	(52)	(10)
Firms that did not provide complete information	(48)	(9)
Firms that were admitted to the stock market from 2010	(80)	(15)
Final sampled firms	164	31

Source: Created by authors.

).

4. Empirical Models and Econometrics Results

Table 2. Descriptive statistics.

Variables	Mean	Median	Max	Min	Std	n
COMPENSATE	4.534	6.291	12.004	0.000	3.394	1640
COMP_CFO	−0.072	−0.062	−0.006	−0.255	0.035	1640
COMP_RET	−0.120	−0.105	−0.025	−0.504	0.061	1640
COMP_PRC	−5047.168	−3422.600	−1.514	−42,814.63	5044.544	1640
SQR	22.816	24.000	42.000	0.000	6.651	1640
CORR_ROA	0.367	0.701	1.000	−1.000	0.689	1640
CORR_CF	0.200	0.384	0.999	−0.999	0.706	1640
CORR_RET	0.457	0.787	1.000	−1.000	0.648	1640
INDHERF	0.221	0.245	0.482	0.000	0.124	1640
SIZE	13.819	13.614	19.374	9.797	1.571	1640
BM	0.515	0.418	1.974	−1.559	0.409	1640
LEV	0.588	0.563	1.363	0.012	0.214	1640
ROA	0.170	0.145	0.803	−0.729	0.156	1640
ADJROA	0.002	−0.003	0.563	−0.938	0.135	1640
RET	0.106	0.093	0.989	−0.997	0.317	1640
ADJRET	0.001	−0.009	1.092	−1.200	0.284	1640
GROWTH	0.194	0.161	1.460	−0.964	0.327	1640
DIVYIELD	0.105	0.078	0.809	0.000	0.114	1640
RETVOL	0.218	0.186	0.768	0.002	0.141	1640
CFVOL	0.076	0.061	0.619	0.000	0.060	1640
EM_ACC	0.000	0.000	0.900	−0.699	0.103	1640
ABAFEE	−0.003	0.001	2.700	−2.657	0.655	1640
LAF	6.620	6.731	9.606	2.928	1.362	1640
NFEE	6.624	6.514	8.860	4.683	1.207	1640

presents the summary statistics of the variables. We utilised the one-way analysis of variance test (ANOVA) and Kruskal–Wallis test because they determine the difference between industrial sectors based on explanatory and control variables (see

Table 3. (Panel A): ANOVA and Kruskal–Wallis of variables across twenty-four industrial sectors. (Panel B): ADF–Fisher. Null: Unit root (assume standard unit root test).

Panel A			Panel B
Variables	ANOVA (F)	Kruskal-Wallis (χ2)	t-Statistics
COMPENSATE	16.071 ***	308.324 ***	497.251 ***
COMP_RET	12.011 ***	256.126 ***	519.336 ***
COMP_RET	19.203 ***	318.874 ***	609.562 ***
COMP_PRC	17.305 ***	128.347 ***	437.164 ***
SQR	23.622 ***	547.824 ***	692.3216 ***
CORR_ROA	14.459 ***	361.213 ***	806.228 ***
CORR_CF	18.154 ***	327.267 ***	659.450 ***
CORR_RET	11.240 ***	471.289 ***	647.330 ***
INDHERF	14.642 ***	241.478 ***	708.029 ***
SIZE	11.246 ***	502.545 ***	415.260 ***
BM	14.913 ***	139.115 ***	558.116 ***
LEV	11.315 ***	207.831 ***	352.283 ***
ROA	12.459 ***	336.643 ***	549.686 ***
ADJROA	18.914 ***	327.267 ***	553.628 ***
RET	10.210 ***	471.289 ***	967.044 ***
ADJRET	15.642 ***	141.478 ***	953.812 ***
GROWTH	11.246 ***	502.555 ***	977.738 ***
DIVYIELD	14.130 ***	139.115 ***	604.402 ***
RETVOL	11.243 ***	207.831 ***	466.964 ***
CFVOL	14.910 ***	236.643 ***	557.470 ***
EM_ACC	13.246 ***	241.873 ***	539.182 ***
ABAFEE	13.031 ***	539.551 ***	604.402 ***
LAF	15.142 ***	377.381 ***	664.694 ***
NFEE	13.019 ***	362.346 ***	575.074 ***

*** p < 0.001.

, Panel A). After data collection, we must ensure their stationary and non-stationary status to avoid false regression. ADF–Fisher tests were used, since the applied regression method involved ordinary data. Results are shown in Table 3.

To examine H1a, we estimate Equation (1) with the interaction term.

$$\begin{array}{cc}{COMPENSATION}_{i,t}=\hfill & {\beta }_0+{\beta }_1{COMP\text{\_}I}_{i,t-1}+{{\beta }_{2}ABAFEE}_{i,t}+{{\beta }_{3}ABAFEE}_{i,t-1}\ast {COM{P}_I}_{i,t-1}\hfill \\ & +{\beta }_4{CORR\text{\_}ROA}_{i,t-1}+{\beta }_5{CORR\text{\_}CFO}_{i,t-1}+{\beta }_6{CORR\text{\_}RET}_{i,t-1}\hfill \\ & +{\beta }_7{INDHERF}_{i,t-1}+{\beta }_8{SIZE}_{i,t-1}+{\beta }_9{BM}_{i,t-1}+{\beta }_{10}{LEV}_{i,t-1}+{\beta }_{11}{ROA}_{i,t-1}\hfill \\ & +{\beta }_{12}{ADJROA}_{i,t-1}+{\beta }_{13}{RET}_{i,t-1}+{\beta }_{14}{ADJRET}_{i,t-1}+{\beta }_{15}{GROWTH}_{i,t-1}\hfill \\ & +{\beta }_{16}{DIVYELD}_{i,t-1}+{\beta }_{17}{RETVOL}_{i,t-1}+{\beta }_{18}{CFVOL}_{i,t-1}\hfill \\ & +YEAR\&FIRMFIXED+{\epsilon }_{i,t}\hfill \end{array}$$

(1)

The dependent variable, COMPENSATION, is an indicator that equals the natural logarithm of cash compensation. We use three measures of accounting comparability (COMP_I is the annual decile rank of COMP_CFO, COMP_RET, COMP_PRC) based on the underlying logic that the accounting of two firms is more comparable if they report similar accounting amounts when they experience identical economic outcomes (Lobo et al. 2018).

Measure 1: The relationship between the profit in year t and the cash flow from year t − 1 operation is calculated using Equation (2).

$${Cfo}_{i,t+1}={\beta }_0+{\beta }_1{NI}_{i,t}+{\epsilon }_{i,t}$$

(2)

• CFO_(i,t) is cash flow from operations divided by beginning total assets.
• NI_(i,t) is net income after deducting the current year’s tax divided by the beginning total assets.

In the first step, each year, the firm calculates the ${\beta }_0$ and ${\beta }_1$ coefficients using Equation (2) and 14 years of data. Coefficients for each firm in each year represent the firm’s accounting systems characteristics. In the next step, the calculated coefficients are put into Equation (2), and cash flows from firm i’s expected operating activities are estimated for the same year. Suppose the logic is based on the similarity of firms’ i’s and j’s accounting systems. In that case, the output from the estimate of the cash flows from the expected operations of firm i must show similar figures to the output of firm j’s coefficients (Equation (3)).

Equation (3) is the estimate of the future cash flows for firm i based on the firm i’s coefficients:

$${E\left(Cfo\right)}_{i,i,t+1}={\widehat{\beta }}_{0,i}+{\widehat{\beta }}_{0,i}{NI}_{i,t}$$

(3)

Equation (4) is the estimate of the future cash flows for firm i based on firm j’s coefficients:

$${E\left(Cfo\right)}_{i,j,t+1}={\widehat{\beta }}_{0,j}+{\widehat{\beta }}_{1,j}{NI}_{i,t}$$

(4)

The more comparable the two firms’ accounting systems are, the smaller the difference in the expected cash flows of the peer firms would be. According to the above, the comparability between firms i and j based on measure 1 is calculated as follows:

$${CompCfo}_{i,j,t}=-{\displaystyle \frac{1}{10}}\times {\sum }_{t-9}^t\left|{E\left(Cfo\right)}_{i,i,t+1}-{E\left(Cfo\right)}_{i,j,t+1}\right|$$

(5)

Comparability is calculated for every pair of firms in the industry for the years under assessment. It means that, according to Equation (4), the cash flows from the expected operations for firm i are estimated based on this firm’s equation and firm j’s equation, which is its peer firm, and also the cash flow difference from operations of each firm and its peers is calculated every year. After organising all the obtained combinations of firm i, the COMP variable could be calculated for the COMP_i,j,t through the average of the obtained numbers. So, the comparability figure for each firm year is achieved.

Measure 2: Model (6) calculates the accounting comparability by using the firm’s schedule around the level and changes of the EPS and stock return.

$$\begin{gathered} {Return}_{i,t}={\beta }_0+{\beta }_1{\displaystyle \frac{{NI}_{i,t}}{P_{i,t}}}+{\beta }_2{\displaystyle \frac{{∆NI}_{i,t}}{P_{i,t}}}+{\beta }_3{LOSS}_{i,t}+{\beta }_4{LOSS}_{i,t}\times {\displaystyle \frac{{NI}_{i,t}}{P_{i,t}}} \\ +{\beta }_5{LOSS}_{i,t}\times {\displaystyle \frac{{∆NI}_{i,t}}{P_{i,t}}}+{\epsilon }_{i,t} \end{gathered}$$

(6)

• RETURN_(i,t): Annual stock return of the firm i in the current year.
• NI/P_(i,t): Net income after deducting tax per share in the current year divided by the beginning share price for firm i.
• ΔNI/P_(i,t): Changes in net income per share in the current year compared to the previous year divided by the beginning share price for firm i.
• LOSS_(i,t): An artificial measure of a firm’s loss. If the firm is unprofitable, it equals one. Otherwise, it equals zero.

To calculate accounting comparability through measure (2), the processes in Equations (2) and (3) are conducted. Therefore, comparability through measure (2) is calculated by using Equation (7):

$${CompReturn}_{i,j,t}=-{\displaystyle \frac{1}{10}}\times {\sum }_{t-9}^t\left|E({Return)}_{i,i,t}-E({Return)}_{i,j,t}\right|$$

(7)

Measure (3): In this measure, using model (8), the relationship between net income per share and book value of the shareholder’s equity per share with closing price per share in the current year is used to calculate accounting comparability.

$${Price}_{i,t}={\beta }_0+{\beta }_1{NIPS}_{i,t}+{\beta }_2{BVPS}_{i,t}+{\epsilon }_{i,t}$$

(8)

• Price_(i,t): Closing price per share in the current year.
• NIPS_(i,t): Net income after deducting tax per share for firm i in the current year.
• BVPS_(i,t): Book value of the shareholder’s equity per share at the end of the period for firm i.

To calculate financial information through measure (3), the processes in Equations (2) and (3) are conducted. Therefore, financial information comparability through measure (3) is calculated by using Equation (9):

$${CompReturn}_{i,j,t}=-{\displaystyle \frac{1}{10}}\times {\sum }_{t-9}^t\left|E({Price)}_{i,i,t}-E({Price)}_{i,j,t}\right|$$

(9)

ABAFEE refers to abnormal audit fees and is calculated by the residual of the following model (Blankley et al. 2012):

$$\begin{array}{c}\hfill {LAF}_{i,t}={\beta }_0+{\beta }_1{LTA}_{i,t}+{\beta }_2{CR}_{i,t}+{\beta }_3{CA\text{\_}TA}_{i,t}+{\beta }_4{ARINV}_{i,t}+{\beta }_5{ROA}_{i,t}+{\beta }_6{LOSS}_{i,t}\\ \hfill +{\beta }_7{FOREIGN}_{i,t}{+\beta }_8{LEV}_{i,t}+{\beta }_9{INTANG}_{i,t}+{\beta }_{10}{OPINION}_{i,t}+{\epsilon }_{i,t}\end{array}$$

(10)

where LAF denotes logarithm of audit fees in year t; LTA is the logarithm of end-of-year total assets in year t; CR is current assets divided by current liabilities in year t; CA_TA is current assets divided by total assets in year t; ARINV is the sum of accounts receivable and inventory divided by total assets in year t; ROA is earnings before interest and taxes divided by total assets in year t; LOSS is 1 if firm incurred a loss in year t and is 0 if otherwise; FOREIGN is 1 if the firm has any foreign operations in year t and is 0 if otherwise; LEV is long-term debt divided by total assets in year t; INTANG is the ratio of intangible assets to total assets in year t; OPINION is 1 if the auditor issues a going concern audit opinion and is 0 if otherwise in year t.

CORR_ROA_(i,t−1): Correlation between the average return of the current assets in the current year in firm i and its peer firms in the industry.

CORR_CF_(i,t−1): Correlation between the average cash flows from operations in the current year in firm i and its peer firms in the industry.

CORR_RET_(i,t−1): Correlation between the average annual return of the share in firm i and its peer firms in the industry.

INDHERF_(i,t−1): Herfindahl–Hirschman Index, which is calculated by adding a market share of all active firms in the industry to the power of 2 by using Equation (10):

$$HHI={\sum }_{i=1}^k{s_i}^2$$

(11)

HHI: Herfindahl–Hirschman Index. K is the number of active firms in the market, and Si is the market share of firm i, which is calculated using Equation (11).

$$S_i={\displaystyle \frac{X_j}{{\sum }_{l=1}^n{X}_j}}$$

(12)

X_j: Indicates sales of firm j, and 1 represents industry type.

SIZE_(i,t−1): Firm size equals the natural logarithm of the total closing assets.

BM_(i,t−1): Dividing the book value of the shareholder’s equity by the market value of the shareholder’s equity.

LEV_(i,t−1): Dividing total liabilities by total closing assets.

ROA_(i,t−1): Assets return obtained by dividing current year operating profit by the average of the firm’s total assets i.

ADJROA_(i,t−1): Firm’s assets return minus the average of the peer firm’s assets return.

RET_(i,t−1): Annual return of firm i.

ADJRET_(i,t−1): Annual return of firm i’s share minus the average return of the peer firm share in the industry.

GROWTH_(i,t−1): Firm growth equals the annual sales return, which is calculated using Equation (12).

$${Growth}_{i,t}={\displaystyle \frac{{Sales}_{i,t}-{Sales}_{i,t-1}}{{Sales}_{i,t-1}}}$$

(13)

Sales_i,t: Total firm sales in the current year.

Sales_i,t−1: The firm’s sales in the previous year.

DIVYIELD_(i,t−1): Dividing the total approved dividend in the current year by the market value of firm i’s shares.

RETVOL_(i,t−1): Standard deviation of firm i’s annual return of the shares. A three-year measure of the standard deviation of the annual return is used to calculate firm i’s yearly return on the shares.

CFVOL_(i,t−1): Dividing the standard deviation of the cash flows from operations in the current year by the total beginning assets of firm i. A three-year measure of the standard deviation of the cash flows from operations is used to calculate the standard deviation of the cash flows from firm i.

5. Findings

The findings from the H1a test are provided in

Table 4. Models for earnings management.

Models	R2 (Adj)	F Statistic	AIC (1)	SC (2)	HQC (3)
Jones (1991)	0.309	3.774	−1.232	−0.823	−1.136
Dechow et al. (1991)	0.386	3.716	−1.125	−0.833	−1.068
Kasznik (1999)	0.567	11.582	−1.310	−0.957	−1.105
Dechow and Dichev (2002)	0.510	9.202	−1.186	−0.733	−1.081
McNichols (2002)	0.586	12.162	−1.344	−0.984	−1.136
Kothari et al. (2005)	0.293	3.665	−0.919	−0.426	−0.814

(1) Akaike criterion; (2) Schwarz criterion; (3) Hannan–Quinn criterion.

. The results of this test indicate that abnormal audit fees did not influence the board’s compensation. Also, on the grounds of these findings, it could be raised that they improve the relationship between accounting comparability through the third criterion (relationship between stock price with book value and earnings per share) and board compensation. According to the existing literature, several studies have found that abnormal audit fees negatively affect financial reporting quality (Asthana and Boone 2012). However, Blankley et al. (2012) and Eshleman and Guo (2020) found that abnormal audit fees positively correlate with quality financial reports. Based on the findings of this research, audit fees have been influential on the quality of financial reports and their relationship with board compensation only through the informativeness of accounting information, which positively impacts the relationship between accounting comparability and board compensation.

To examine H1_b, we estimate Equation (14) with the interaction term:

$$\begin{array}{cc}{COMP\text{\_}C}_{i,t}=& {\beta }_0+{\beta }_1{COMP\text{\_}I}_{i,t-1}+{{\beta }_{2}NFEE}_{i,t}+{{\beta }_{3}NFEE}_{i,t-1}\ast {COM{P}_I}_{i,t-1}+{\beta }_4{CORR\text{\_}ROA}_{i,t-1}\hfill \\ & +{\beta }_5{CORR\text{\_}CFO}_{i,t-1}+{\beta }_6{CORR\text{\_}RET}_{i,t-1}+{\beta }_7{INDHERF}_{i,t-1}+{\beta }_8{SIZE}_{i,t-1}\hfill \\ & +{\beta }_9{BM}_{i,t-1}+{\beta }_{10}{LEV}_{i,t-1}+{\beta }_{11}{ROA}_{i,t-1}+{\beta }_{12}{ADJROA}_{i,t-1}+{\beta }_{13}{RET}_{i,t-1}\hfill \\ & +{\beta }_{14}{ADJRET}_{i,t-1}+{\beta }_{15}{GROWTH}_{i,t-1}+{\beta }_{16}{DIVYELD}_{i,t-1}+{\beta }_{17}{RETVOL}_{i,t-1}\hfill \\ & +{\beta }_{18}{CFVOL}_{i,t-1}+YEAR\&FIRMFIXED+{\epsilon }_{i,t}\hfill \end{array}$$

(14)

where NFEE refers to the normal audit fee and is calculated using the following:

$${LAF}_{i,t}-{\epsilon }_{i,t}$$

The findings of the H1b test are provided in

Table 5. Abnormal audit fee and accounting comparability.

Variable	COMP_CFO	COMP_RET	COMP_PRC
COMP_CFO	6.287 ** (3.043)	−	−
COMP_RET	−	2.739 *** (0.744)	−
COMP_PRC	−	−	3.86 × 10−5 *** (1.48 × 10−5)
ABAFEE	0.267 (0.226)	−0.160 * (0.089)	0.065 (0.054)
ABAFEE * COMP_CFO	5.434 (2.858)	−	−
ABAFEE * COMP_RET	−	−0.722 (0.707)	−
ABAFEE * COMP_PRC	−	−	2.14× 105 *** (8.15× 10−6)
CORR_ROA	0.105 (0.106)	0.059 (0.049)	0.069 (0.042)
CORR_CF	−0.119 (0.103)	−0.044 (0.045)	−0.066 (0.041)
CORR_RET	0.109 (0.117)	0.035 (0.057)	0.022 (0.047)
INDHERF	−2.124 (1.862)	−2.300 * (1.176)	−3.015 *** (1.004)
SIZE	0.642 *** (0.076)	0.365 *** (0.044)	0.691 *** (0.038)
BM	0.493 ** (0.226)	0.120 (0.111)	0.072 (0.105)
LEV	1.391 ** (0.542)	0.558 ** (0.247)	0.476 ** (0.222)
ROA	0.462 (1.282)	1.011 * (0.609)	0.277 (0.533)
ADJROA	3.210 ** (1.280)	0.805 (0.610)	1.596 *** (0.504)
RET	1.659 *** (0.406)	0.503 *** (0.180)	0.595 *** (0.161)
ADJRET	−1.466 *** (0.444)	−0.504 ** (0.207)	−0.664 *** (0.176)
GROWTH	−0.213 (0.236)	−0.020 (0.109)	−0.025 (0.097)
DIVYIELD	1.356 ** (0.736)	0.903 ** (0.389)	0.977 *** (0.367)
RETVOL	1.324 (0.552)	0.573 ** (0.246)	0.459 ** (0.226)
CFVOL	0037 (1.278)	0.282 (0.612)	0.594 (0.457)
Hausman Test (${\mathit{\chi }}^2$)	32.619	39.004	39.860
R2 (Adj)	0.504	0.862	0.899
F statistic	7.627 ***	47.029 ***	67.487 ***
DW	1.764	1.961	1.857

*** p < 0.001, ** p < 0.01, * p < 0.05.

. The results of this test depict that normal audit fees were productive on the board compensation only in the presence of the third criterion of comparability. However, the interaction between comparability criteria and normal audit fee indicates that the normal audit fee positively affects (rectifies) the relationship between accounting comparability and board compensation. These findings show that a normal audit fee is a productive factor in the quality of the financial reporting, impacts the information comparability, and ultimately affects the board compensation.

To test the H2, the non-linear method of smooth panel transition regression (PSTR) was used. The PSTR has the advantage of solving the baseline model’s nonlinearity, heterogeneity, and time instability problems. Based on the PSTR specification, the regression coefficients change smoothly as a function of a threshold variable. Because the threshold variable is individual-specific and varies with time, it is possible to estimate regression coefficients at any time and for any firm in a panel. Therefore, this new econometric technique is an attractive approach for investigating the relationship between audit fees and earnings management. The PSTR model comprises many regimes and panel data observations regarding thresholds (Chiou and Lee 2011). We employed a PSTR model, recently developed by González and Teräsvirta (2006). to model the non-linear impact of audit fees on earnings management. This method has been employed in recent financial and accounting studies (Daryaei and Fattahi 2020). Interestingly, as discussed in the literature, this method renders satisfactory results because of its robust theoretical foundations.

In this research, discretionary accruals have been used to measure earnings management. In the financial and accounting literature, these items are defined as reflections of the methods and procedures available to management (Kashmiri 2014). To estimate discretionary accruals, several models and patterns exist, such as Healy (1985), McNichols (2002), amd Kothari et al. (2005). There are two approaches to profit or loss, and the balance sheet approach is used to calculate the accruals. In the profit and loss approach, accruals are obtained through the difference between net profit and cash flows from operations, in which a cash flow statement plays a role. However, balance sheet-based accruals are measured by deducting current liabilities (except the current portion of long-term debt) from the changes of the non-cash current assets. In this study, due to the limitation in gathering information related to the current portion of long-term debt, the profit and loss-based approach was utilised to measure the accruals, which are calculated according to the following relationship:

$${TA}_{it}={EBIT}_{it}-{CFO}_{it}$$

As mentioned above, there are various models to evaluate discretionary accruals as the measure of earnings management, which means that under these circumstances, a model that is best compatible with the research environment and can test the characteristics of the firms should be utilised. Reviewing conducted research on Iran’s economic climate indicates that there is more of a tendency towards the model of Jones and its modified model than any other model among discretionary accruals measurement models. However, irrespective of its reasons, another model may be more compatible with Iranian firms and could better describe this variable. Also, in this research, the measurement of discretionary accruals as earnings management was conducted on the grounds of Jones (1991), Kasznik (1999), Dechow and Dichev (2002), McNichols (2002), and Kothari et al. (2005), and the explanatory power, error level, and other estimated statistics and the model have had more favourable statistics to be selected as the model of the discretionary accrual’s evaluation and earnings management criterion. Based on the results from

Table 6. Normal audit fee and accounting comparability.

Variable	COMP_CFO	COMP_RET	COMP_PRC
COMP_CFO	18.252 ** (8.928)	-	-
COMP_RET	-	3.015 *** (0.613)	-
COMP_PRC	-	-	0.0001 ** (5.98 × 10−5)
NFEE	0.083 (0.152)	−0.131 (0.120)	0.373 *** (0.087)
NFEE * COMP_CFO	3.032 ** (1.378)	-	-
NFEE * COMP_RET	-	0.485 *** (0.162)	-
NFEE * COMP_PRC	-	-	3.30 × 10−5 *** (1.01 × 10−5)
CORR_ROA	0.043 *** (0.014)	0.042 * (0.023)	0.057 (0.055)
CORR_CF	−0.070 *** (0.023)	−0.053 * (0.030)	−0.096 ** (0.048)
CORR_RET	0.014 (0.033)	0.042 (0.042)	0.201 ** (0.094)
INDHERF	−2.870 ** (1.407)	−2.297 (1.572)	−8.034 *** (0.374)
SIZE	0.689 *** (0.064)	0.627 *** (0.067)	0.720 *** (0.037)
BM	0.074 (0.073)	0.108 (0.079)	0.449 *** (0.098)
LEV	0.394 *** (0.138)	0.468 *** (0.152)	−0.185 (0.214)
ROA	0.435 * (0.248)	1.209 *** (0.363)	4.476 *** (0.606)
ADJROA	1.520 *** (0.376)	0.710 * (0.431)	0.177 (0.826)
RET	0.514 *** (0.137)	0.483 *** (0.135)	0.814 *** (0.203)
ADJRET	−0.605 *** (0.124)	−0.517 *** (0.139)	−0.821 *** (0.177)
GROWTH	−0.031 (0.081)	−0.027 (0.078)	−0.324 *** (0.124)
DIVYIELD	0.924 *** (0.299)	0.911 *** (0.328)	−0.501 (0.689)
RETVOL	0.558 *** (0.198)	0.486 *** (0.176)	0.426 * (0.239)
CFVOL	0.351 (0.418)	0.330 (0.473)	−1.841 *** (0.704)
Hausman Test (${\mathit{\chi }}^2$)	35.483	37.124	40.011
R2 (Adj)	0.892	0.865	0.518
F statistic	62.111 ***	48.591 ***	91.106 ***
DW	1.764	1.753	1.965

*** p < 0.001, ** p < 0.01, * p < 0.05.

and

Table 7. LM and LR tests for linearity.

Tests	M = 1	M = 2
Lagrange multiplier test (LM) H0: r = 0 vs. H1: r = 1	6.003 ***	0.657
Likelihood ratio test (LR.) H0: r = 0 vs. H1: r = 1	21.586 ***	1.554

*** p < 0.001.

, it is shown that the coefficients of determination—the F statistic, Adjusted R-squared, Akaike criterion (AIC), Schwarz criterion (SC), and Hannan–Quinn criterion (HQC)—in the McNichols model yielded a more favourable condition compared to other models. For instance, the Adjusted R-squared in McNichol’s model was 0.586, which indicates that it is the more influential the explanatory variable in the accruals.

Moreover, this model’s AIC, SC, and HQC criteria were lower than in other models, indicating the model’s higher precision. Therefore, the absolute value of the remainder of the McNichols (2002) model was utilised as the discretionary accruals to evaluate earnings management. Equations (15)–(20) show how to estimate discretionary accruals as an earnings management criterion:

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={{\beta }_0+\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left({\displaystyle \frac{\mathsf{\Delta }{REV}_{it}}{A_{it-1}}}\right)+{\beta }_3\left({\displaystyle \frac{{PPE}_{it}}{A_{it-1}}}\right)+\epsilon$$

(15)

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={{\beta }_0+\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left[{\displaystyle \frac{\left(\mathsf{\Delta }{REV}_{it}-\mathsf{\Delta }{AR}_{it}\right)}{A_{it-1}}}\right]+{\beta }_3\left({\displaystyle \frac{{PPE}_{it}}{A_{it-1}}}\right)+\epsilon$$

(16)

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={\beta }_0+{\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left[{\displaystyle \frac{\left(\mathsf{\Delta }{REV}_{it}-\mathsf{\Delta }{AR}_{it}\right)}{A_{it-1}}}\right]+{\beta }_3\left({\displaystyle \frac{{PPE}_{it}}{A_{it-1}}}\right)+{\beta }_4\left({\displaystyle \frac{\mathsf{\Delta }{CFO}_{it}}{A_{it-1}}}\right)+\epsilon$$

(17)

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={\beta }_0+{\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left({\displaystyle \frac{{CFO}_{it}}{A_{it-1}}}\right)+{\beta }_3\left({\displaystyle \frac{{CFO}_{it-1}}{A_{it-1}}}\right)+{\beta }_4\left({\displaystyle \frac{{CFO}_{it+1}}{A_{it-1}}}\right)+\epsilon$$

(18)

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={{\beta }_0+\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left({\displaystyle \frac{\mathsf{\Delta }{REV}_{it}}{A_{it-1}}}\right)+{\beta }_3\left({\displaystyle \frac{{PPE}_{it}}{A_{it-1}}}\right)+{\beta }_4\left({\displaystyle \frac{{CFO}_{it}}{A_{it-1}}}\right)+{\beta }_5\left({\displaystyle \frac{{CFO}_{it-1}}{A_{it-1}}}\right)+{\beta }_6\left({\displaystyle \frac{{CFO}_{it+1}}{A_{it-1}}}\right)+\epsilon$$

(19)

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={\beta }_0+{\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left[{\displaystyle \frac{\left(\mathsf{\Delta }{REV}_{it}-\mathsf{\Delta }{AR}_{it}\right)}{A_{it-1}}}\right]+{\beta }_3\left({\displaystyle \frac{{PPE}_{it}}{A_{it-1}}}\right)+{\beta }_4{ROA}_{it}+\epsilon$$

(20)

The variables used in the various models of accrual earnings management are defined as follows:

TA is the total accruals in year t defined as earnings before extraordinary items and discontinued operations minus operating cash flows (from continuing operations); A denotes the total assets in year t − 1; ΔREV is the change in net sales from year t − 1 to year t; PPE is the gross value of property, plant, and equipment; ΔAR is the change in account receivables from period t − 1 to t; CFO denotes the operating cash flows from t; ROA is the annual income before extraordinary items divided by the beginning total assets.

The simplest case of a PSTR model with two extreme regimes is defined as follows:

$$\begin{array}{ll}{EM\text{\_}ACC}_{i,t}={\mu }_1+& {\beta }_0\left({ROA}_{i,t}+{Lev}_{i,t}+{Size}_{i,t}\right)\\ & +{\displaystyle \sum _{J=1}^r}{\beta }_{j}g\left({LAF}_{i,t};{\gamma }_j;c_k\right)\left({ROA}_{i,t}+{Lev}_{i,t}+{Size}_{i,t}\right)+{\epsilon }_{i,t}\end{array}$$

(21)

Let $\mathrm{i}=1,\dots ,\mathrm{N}$, and let $\mathrm{t}=1,\dots ,\mathrm{T}$, where N and T denote the total number of firms and the size of the sample period in the panel, respectively. The variable of EM_ACC is a dependent variable and refers to accrual earnings management estimated using the McNichols (2002) model.

$${\displaystyle \frac{{TA}_{it}}{A_{it-1}}}={{\beta }_0+\beta }_1\left({\displaystyle \frac{1}{A_{it-1}}}\right)+{\beta }_2\left({\displaystyle \frac{\mathsf{\Delta }{REV}_{it}}{A_{it-1}}}\right)+{\beta }_3\left({\displaystyle \frac{{PPE}_{it}}{A_{it-1}}}\right)+{\beta }_4\left({\displaystyle \frac{{CFO}_{it}}{A_{it-1}}}\right)+{\beta }_5\left({\displaystyle \frac{{CFO}_{it-1}}{A_{it-1}}}\right)+{\beta }_6\left({\displaystyle \frac{{CFO}_{it+1}}{A_{it-1}}}\right)+\epsilon$$

(22)

The variables used in the McNichols (2002) model are already defined. The variables LAF, ROA, Lev, and Size are explanatory variables and refer to the natural logarithm of the audit fee, the ratio of the asset (defined as net income before extraordinary items scaled by total assets), the leverage (debt to asset), and the firm size (natural log of assets). Here, the dependent variable is LAF (the audit fee). Also, ${\mu }_1$ denotes the vector of fixed firm effects, $g\left({LAF}_{i,t};{\gamma }_j;c_k\right)$ is the transition function, and ${\epsilon }_{i,t}$ is the error term. Based on the works of González and Teräsvirta (2006) n a panel framework, the current research considered the following logistic transition function:

$$g\left({LAF}_{i,t};{\gamma }_j;c_k\right)={(1+\mathrm{e}\mathrm{x}\mathrm{p}(-{\gamma }_j{\prod }_{k=1}^m{INS}_{i,t}-c_k\left)\right)}^{-1}\gamma >0,c_1\le c_2\le \dots \le c_m$$

(23)

where $c=(c_1,\dots ,c_m)$ is an m-dimensional vector of location parameters, and the slope parameter determines the smoothness of the transitions. The restrictions $\gamma >0$ and $c_1<\dots <c_m$ are imposed for identification purposes. In practice, it is usually sufficient to consider $m=1$ or $m=2$, as these values allow for commonly encountered types of variation in the parameters. For $m=1$, the model implies that the two extreme regimes are associated with low and high values of ${LAF}_{i,t}$ with a monotonic transition of the coefficients from ${\beta }_0$ to ${\beta }_0+{\beta }_1$ as ${LAF}_{i,t}$ increases, where the change is focused around $C_1$. When $\gamma \to \infty$, $g\left({LAF}_{i,t};{\gamma }_j;c_k\right)$ becomes an indicator function I [${LAF}_{i,t}>c$], which is defined as I [$A$] = 1 when the event A occurs and as zero otherwise. In that case, the PSTR model in (1) reduces to the two-regime panel threshold model of Hansen and Seo (2002). For m = 2, the transition function has its minimum at $(c_1+c_2)/2$ and attains a maximum value of 10 both at low and high values of ${LAF}_{i,t}$.

A generalisation of the PSTR model to allow for more than two different regimes occurs in another model, which is presented below:

$${EM\text{\_}ACC}_{i,t}={\mu }_1+{\beta }_0\left({ROA}_{i,t}+{Lev}_{i,t}+{Size}_{i,t}\right)+\sum _{J=1}^r{\beta }_{j}g\left({LAF}_{i,t};{\gamma }_j;c_k\right)\left({ROA}_{i,t}+{Lev}_{i,t}+{Size}_{i,t}\right)+{\epsilon }_{i,t}$$

(24)

In the transition functions $g\left({LAF}_{i,t};{\gamma }_j;c_k\right)$ and j = 1, …, r, the slope parameter ${\gamma }_j$ and the location parameter $c_j$ are critical. Specifically, the multiple regime model (31) serves as a crucial alternative when performing diagnostic tests for the absence of heterogeneity. If $\mathrm{m}=1$, then all slope parameters are ${\gamma }_j$. As ${\gamma }_j$ approaches infinity, the PSTR model (Panel Smooth Transition Regression) simplifies to multiple regime panel threshold regression models (PTRs), indicating a sharp transition between regimes (Heidari et al. 2015).

Table 7 presents the linearity test results. Before estimating the final panel smooth transition regression model, it is essential to perform both the linearity test and the test for no remaining non-linearity to identify the optimal specification of the panel soft transition regression model. In testing for no remaining non-linearity, the null hypothesis suggests the existence of a single transition function. In contrast, the alternative hypothesis posits the need for at least two transition functions within the panel smooth transition regression model. This study utilized the Lagrange Multiplier (LM) and Likelihood Ratio (LR) tests to assess non-linearity. The results from these tests indicate that considering just one transition function is sufficient to capture the non-linearity between the model variables.

The optimal threshold is identified when the Residual Sum of Squares (RSS), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) reach their minimum values as indicated in Equation (7).

Table 8. Test results of the threshold value in PSTR estimates.

Search Range	Optimal Threshold Value (c)	Transition Parameter (γ)	RSS	AIC	BIC
LAF	4.951 *** (2.026)	846.237 *** (322.361)	−4.743	−55.709	−46.152

*** p < 0.001.

presents the threshold value ccc and the transition parameter γ. For the threshold variable of the audit fee (LAF), the RSS, AIC, and BIC values recorded at the 28th estimate are displayed in Table 7. It is evident that the optimal threshold of 4.651 is lower than the mean audit fee of 6.620. Additionally, the slope parameter γ, which indicates the transition speed between regimes, is 846.237. This high value suggests a relatively swift shift from the first regime to the second.

Table 9. Parameter estimates of the PSTR model.

Panel A: Linearity Model
	Coeff.	SE.	t-value
LAF	0.001	0.001	0.304
ROA	0.602	0.025	23.729
Lev	−0.015	0.010	−0.136
Size	0.009	0.001	5.809
Adjusted R2	0.632
F statistic	17.362 ***
Panel B: Non-linearity Model (Regime 1)
LAF	0.014 ***	0.005	2.823
ROA	-	-	-
Lev	-	-	-
Size	-	-	-
C1	4.651 ***	1.806	2.573
γ	846.237 ***	319.117	2.651
Adjusted R2	0.621
F statistic	10.713 ***
Panel C: Non-linearity Model (Regime 2)
LAF	−0.004 ***	0.001	−4.424
ROA	-	-	-
Lev	-	-	-
Size	-	-	-
C2	-	-	-
γ	-	-	-
Adjusted R2	0.682
F statistic	35.399 ***
DW	1.94

*** p < 0.001.

shows the results of estimating the two-regime panel smooth transition regression model.

The gradient parameter (γ) indicates the transfer velocity of one regime to another, which equals 846.237, and the audit fee threshold equals 4.951. The threshold is the two regimes’ turning point and specific point expressed in the panel smooth transition regression model. The threshold is the defining point of the two regimes described in the panel soft transition regression model, which varies according to the amount of the slope parameter estimates and the values of the transition variable (audit fee); these are the model estimates from one regime to another. Of course, the two first and second regimes are some of the limit states of the panel smooth transition regression model. The values of the regression coefficients vary somewhat concerning the observations of the transition variable. The number 4.951 indicates that the impact of audit fees before 4.951 and after 4.951 differs on the actual earnings management. In other words, the audit fee has a positive effect until the level of 4.951, and it has a different impact on accrual earnings management after the level of 4.951. In other words, an audit fee has a positive effect until 4.951 and negatively impacts the accrual earnings management above that level.

The regression F statistic is equal to 35.399 and is significant. In other words, independent variables have been able to explain the changes in the dependent variable. Also, the modified coefficient of determination of the model is equal to 0.682. This indicates that independent variables explain 68% of the changes in the dependent variable and demonstrates the high explanatory power of the model.

The Durbin–Watson value equals 1.94, which indicates that there is no consecutive correlation among error parts. As shown in Table 9, audit fees have a positive impact on accrual earnings management in the first regime and a negative effect on the accrual earnings management in the second regime; in a way that, as audit fees increase to a certain amount (4.951), accrual earnings management increases, and after that, an increase in the audit fee leads to the reduction in the accrual earnings management.

However, we observed (please see

Table 10. Accounting comparability and board compensation: Audit Fee*SQR.

Variable	COMP_CFO	COMP_RET	COMP_PRC
COMP_CFO	6.614 ** (2.627)	-	-
COMP_RET	-	3.876 *** (0.851)	-
COMP_PRC	-	-	5.35 × 10−5 *** (1.19 × 10−5)
LAF	−0.122 * (0.069)	−0.101 *** (0.024)	−0.037 (0.024)
SQR	0.062 (0.157)	−0.033 (0.041)	0.262 *** (0.078)
SQR*LAF *COMP_CFO	−0.131 (0.669)	-	-
SQR*LAF *COMP_RET	-	−0.293 *** (0.105)	-
SQR*LAF *COMP_PRC	-	-	3.66 × 10−6 ** (1.55 × 10−6)
CORR_ROA	0.090 (0.066)	0.039 * (0.022)	0.049 *** (0.019)
CORR_CF	−0.139 (0.093)	−0.054 ** (0.036)	−0.072 *** (0.023)
CORR_RET	0.126 (0.127)	0.052 (0.036)	0.028 (0.029)
INDHERF	−2.155 (1.198)	−2.540 * (1.479)	−3.328 ** (1.426)
SIZE	0.635 *** (0.141)	0.639 *** (0.056)	0.679 *** (0.055)
BM	0.494 *** (0.136)	0.109 (0.076)	0.058 (0.084)
LEV	1.372 *** (0.405)	0.522 *** (0.126)	0.455 *** (0.127)
ROA	0.321 (1.356)	1.009 *** (0.351)	0.030 (0.253)
ADJROA	3.196 ** (1.499)	0.957 ** (0.403)	1.894 *** (0.327)
RET	1.679 *** (0.577)	0.531 *** (0.147)	0.633 *** (0.122)
ADJRET	−1.471 ** (0.664)	−0.584 *** (0.135)	−0.757 *** (0.110)
GROWTH	−0.178 (0.283)	0.000 (0.067)	−0.010 (0.063)
DIVYIELD	1.407 * (0.848)	1.010 *** (0.329)	1.065 *** (0.322)
RETVOL	1.263 *** (0.445)	0.505 *** (0.143)	0.377 ** (0.175)
CFVOL	−0.010 (0.918)	0.306 (0.439)	0.521 (0.409)
Hausman Test (${\mathit{\chi }}^2$)	28.335	31.415	30.483
R2 (Adj)	0.497	0.837	0.876
F statistic	6.995 ***	38.586 ***	53.047 ***
DW	1.858	1.873	1.861

*** p < 0.001, ** p < 0.01, * p < 0.05.

) that the interaction of the audit fees with the quality of reporting and the accounting comparability could lead to increased managers’ compensation through the relationship between the accounting variables and stock prices.

Moreover,

Table 11. Parameter estimates of the PSTR model.

Panel A: Linearity Model
	Coeff.	SE.	t-value
LAF	0.021	0.008	2.625
ROA	0.536	0.083	6.457
Lev	−0.142	0.130	−1.092
Size	0.044	0.0.13	3.384
Adjusted R2	0.616
F statistic	14.222 ***
Panel B: Non-linearity Model (Regime 1)
LAF	0.010 ***	0.004	2.506
ROA	-	-	-
Lev	-	-	-
Size	-	-	-
C1	3.614 ***	1.679	2.152
γ	514.293 ***	119.202	4.299
Adjusted R2	0.621
F statistic	18.357 ***
Panel C: Non-linearity Model (Regime 2)
LAF	−0.012 ***	0.005	−2.418
ROA	-	-	-
Lev	-	-	-
Size	-	-	-
C2	-	-	-
γ	-	-	-
Adjusted R2	0.621
F statistic	28.106 ***
DW

*** p < 0.001.

and Figure 2 present the testing and results of the second hypothesis for companies with high-quality sustainability reporting. In this method (PSTR), we should use only panel data. So, we identified the companies with higher quality (higher than the median) using the following method: Suppose the number of sustainability reporting quality in more than half of the research period is more than the median (24.00). In that case, this company is recognised for sustainability reporting quality throughout the research period. The results show that earnings management increased with the audit fee increase from its lowest amount (2.928) to 3.614 in the first regime. These findings indicate that the auditors’ efforts to a certain extent—because they were not of the required quality—could not reduce the process of earnings management and even coincided with the increase in earnings management. Of course, one can rely on the assumption that managers in companies seek earnings management, and this trend is constantly increasing. Auditors, as a solid regulatory arm seeking financial accreditation, have been able to make dramatic changes in the impact of managers’ efforts on profit accruals in line with their personal goals. In this case, by observing the second regime, we can see that with the increase in auditors’ efforts and in consequently receiving more fees from the level of 3.614 onwards, this effect becomes reversed, and these efforts led to reduced earnings management by company managers. Point C in Figure 2 indicates the change in the impact of the auditors’ actions on earnings management.

6. Discussion

This study employed a robust quantitative ex post facto research design to investigate the complex relationship between audit fees and earnings management. Analysing data from firms listed on the Tehran Stock Exchange, we uncovered an inverted U-shaped relationship between audit fees and earnings management, indicating that moderate audit fees can lead to higher earnings management. The key contributions of this paper include the following:

• Highlighting the role of audit fees: This study underscores the influence of audit fees on financial reporting quality and risk management.
• Providing empirical evidence: We demonstrate the asymmetric effects of normal and abnormal audit fees on earnings management.
• Emphasising balanced audit fee structures: The need for balanced audit fee structures to ensure financial transparency and mitigate risk is evident from our findings.

The results show that normal audit fees positively affect the relationship between accounting comparability and executive compensation, while abnormal audit fees do not influence executive compensation. Specifically, our non-linear model reveals that audit fees positively impact accrual earnings management up to a certain threshold (4.951). Beyond this threshold, higher audit fees result in decreased accrual earnings management. These findings align with the results of Blankley et al. (2012) and Eshleman and Guo (2014).

Moreover, our results suggest that the interaction of audit fees with reporting quality and accounting comparability, through the relationship between accounting variables and stock prices, can lead to increased executive compensation. Audit fees up to a certain threshold (3.614 in our sample) significantly impact earnings management in companies with higher reporting quality. This inverted U-shaped relationship between audit fees and earnings management indicates that an initial increase in audit fees may reflect a lack of accounting comparability and provide room for higher earnings management. However, beyond a certain level, higher audit fees imply the need for more rigorous scrutiny of accounting transactions, thereby reducing earnings management.

In Iran’s reporting and auditing environment, similar conditions may prevail. Given the limitations in Iran’s audit market and the potential for insufficient competition among audit firms, increasing audit fees up to a certain level may reduce the comparability of financial statements, thus increasing earnings management. However, beyond that point, higher audit fees can enhance the accuracy and quality of audits, thereby reducing earnings management. These findings are particularly relevant for regulators and policymakers in Iran’s accounting and auditing fields.

7. Conclusions

This study provides critical insights into the relationship between audit fees and earnings management within the context of the Tehran Stock Exchange. Our findings highlight an inverted U-shaped relationship, where moderate audit fees can lead to increased earnings management, while higher audit fees beyond a specific threshold can reduce it. The differentiation between normal and abnormal audit fees adds a nuanced understanding of how audit costs influence financial reporting quality.

Regulators and policymakers should consider these dynamics when developing guidelines for audit fee structures to ensure financial transparency and mitigate earnings management risks. Further research is recommended to explore these relationships in different economic and regulatory contexts, including comparative studies across various markets. Additionally, longitudinal studies could provide a deeper understanding of how these relationships evolve over time and under different economic conditions. Finally, integrating qualitative methods could offer more comprehensive insights into the practical implications of audit fees on financial reporting and earnings management.

Limitations:

While robust in its quantitative approach and comprehensive analysis, this study has several limitations. First, the sample was restricted to 164 companies listed on the Tehran Stock Exchange from 2010 to 2019. This specific economic and regulatory environment may limit the generalizability of the findings to other markets with different characteristics. Additionally, the study focuses on the impact of audit fees on earnings management within a high-inflation and high-risk economic context, which might not be directly applicable to more stable economies. Another limitation is the division of the audit fees into normal and abnormal categories, which, while innovative, might oversimplify the complex dynamics between audit fees and financial reporting quality.

Suggestions for Further Research:

Future research could address these limitations by expanding the sample to include companies from diverse economic and regulatory environments to enhance the generalizability of the findings. Comparative studies across different countries and markets would provide deeper insights into the role of audit fees in varying contexts. Additionally, examining the interplay between audit fees and other factors such as corporate governance practices, auditor expertise, and economic conditions could provide a more holistic understanding of the determinants of financial reporting quality. Longitudinal studies that track changes over more extended periods and in different economic cycles would also be valuable in understanding the temporal dynamics of these relationships. Furthermore, qualitative research methods, such as case studies and interviews with auditors and company executives, could complement the quantitative findings and provide more prosperous, nuanced insights into the mechanisms at play.