Tax Compliance among Managers: Evidence from Randomized Audits1

The 1,974 audited companies were randomly drawn from a target population of about 31,000 companies, representing 13 percent of all Norwegian businesses. When defining this target population, the NTA started off with all companies defined as legal employers who reported working conditions and other tax-relevant information in the monthly reporting (A-melding) to the NTA during the year 2017 (Norwegian Tax Administration 2019). The NTA then restricted this main population in order to target the audits to industries and businesses more at risk of noncompliance. Hence, the randomization is not valid for the whole taxpayer population, but rather a subpopulation where the risk perception is higher than average. This limitation is based on a total of fourteen criteria that are explained in more detail in appendix, table A1. It implies that the number of industries was reduced from 38 to 22, and that the number of businesses was reduced from 231,753 to 30,961.

Country of birth and citizenship are taken from the National Population Register. Information about the company’s revenues and expenses in 2016 is taken from business reports to the Tax Administration (Income Statement I and II), while turnover is taken from the VAT Register. Information on NACE codes; establishment dates and termination dates are obtained from the Register of Legal Entities.

The target population is stratified according to the industry branch specified in the appendix, i.e., each industry branch represents a stratum, or industry sector. The purpose of the stratification is primarily to enable a more effective selection for the audits, to draw more businesses from industries with a large proportion of working conditions associated with increased risk of noncompliance. The sample selection method is proportional to the number of reported, foreign employees arrived in the last three years, combined with a minimum and maximum number of businesses in the lower and upper part of the distribution.

The main dependent variable is firm compliance, which is an individual score of the most central, responsible person in the firm, i.e., typically a CEO or an owner. The dependent variable is not a continuous variable in reported income or tax liability as in, for example, Kleven et al. (2011), but rather a binary variable intended to measure compliance by any individual manager responsible for firm reporting liabilities, equivalent to that of Fellner, Sausgruber, and Traxler (2013). It takes the value 1 if there is no error in the four variables for the year 2017: tax deduction, existence of payroll accounts, correct monthly reporting, and existence of general accounts.

Managers are liable for more reporting and contact points with the tax administration, and thus more subject to regulatory oversight. Even if the perceived audit probability is low, the frequency of contact points (e.g., monthly reporting) may create a stronger incentive for managers to comply, although the evidence on this effect seems to go in both directions (Snow and Warren 2005). Furthermore, managers are often responsible for establishing and implementing internal governance mechanisms within the firm. They have the authority to develop and enforce policies and procedures to ensure compliance with various regulations, including tax liabilities. Failure to enforce tax compliance within the organization can be seen as a failure of managerial responsibility, leading to potential internal control and governance issues (Alm 2019a). Managers, therefore, have a vested interest in promoting tax compliance as part of their overall responsibilities. Finally, managers with ownership or financial holdings in the firm have a direct financial interest in maintaining compliance. Tax compliance ensures the stability and sustainability of the firm’s operations (Bird and Davis-Nozemack 2018), but there is mixed evidence for a positive association between tax compliance and a firm’s financial performance and value (Watson 2015).

In our context, manager compliance is closely related to reporting obligations where only the manager is liable, not the employee. Thus, there are different evasion schemes available to the manager than to an employee, and thus more opportunities to evade. However, to which extent noncompliance can be due to honest mistakes or deliberate withholding of information, is still difficult to assess. The random audits focus on business reporting routines and standards rather than undeclared income. Tax deduction is one direct route in which the manager may underreport. Not having payroll accounts and general accounts of the firm, represent two other opportunities for noncompliance. The firm may intentionally underreport the number of employees or misclassify them as independent contractors or consultants. By doing so, they can avoid the obligation of deducting and remitting payroll taxes. The firm also may engage in cash transactions or pay employees “off the books” without proper documentation or recording. This allows them to avoid reporting the income and associated payroll taxes.

An error in the firm’s monthly reporting can involve an employer deliberately reporting lower income for employees than what is actually paid. This can lead to employees evading taxes on the unreported income, but it presumes some sort of collusion between the employer and employee, especially in a tax regime with high levels of third-party reporting (cf. Bjørneby, Alstadsæter, and Telle (2021)). Other items in the monthly reporting may also provide opportunities for evasion, such as providing incorrect information about deductible expenses or attempting to claim deductions for expenses that are not eligible. Failure to report the correct number of employees can be an attempt to evade tax liabilities and other tax-related obligations related to the firms’ workforce.

Despite other opportunities to evade, managers may also have stronger incentives or reasons for compliance than employees. For instance, managers may not themselves gain much from noncompliance, as they mainly report for others, i.e., their employees and owners, which could partly explain a high compliance rate among managers. Also, firms whose owners care about compliance may hire managers who are likely to be compliant or monitor their compliance more. Managers typically possess a higher level of responsibility and accountability within organizations. Noncompliance with tax obligations may expose the firm to legal risks, including penalties, fines, and potential legal actions. Moreover, a manager’s tax noncompliance can tarnish the firm’s reputation, leading to negative publicity, loss of customer trust, and damage to long-term business relationships. Managers, being responsible for the overall functioning and success of the organization, have a greater stake in safeguarding the firm’s legal and reputational standing.

As control variables, we add the managers’ gender (men as 0 and women as 1), age as a continuous variable, and whether they have a foreign background. Managers with a different birth country than Norway are defined as “Foreign.” If information on birth country is missing, we use citizenship. For foreign managers, residence time is calculated based on arrival date to Norway. For Norwegian managers without any registered long-term stays abroad, residence time coincides with age. In the regression models, we do not assume a linear relationship between residence time and compliance, but divide the sample into three different residence time groups, in line with Bastani, Giebe, and Miao (2020) (i.e., 0–5 years, 5–10 years, and over 10 years). There are no Norwegian managers in the first two residence groups.

A foreign manager’s CPI score gives the score for this person’s birth country at the year of arrival to Norway. Norwegian managers are given the CPI score for Norway in 2018. We want to capture the manager’s “last impression” of his or her country of origin at the time of arrival in Norway. To do so, we use the CPI score of the year of arrival in Norway as a representation of a time-precise image of the tax morale in the country of origin. We assume that any development in this index, following arrival in Norway, will not affect individual tax morale, and that immigrants assimilate the tax morale of Norway with time. Whenever this value is missing for that particular year, we have used the nearest value available. We have also inverted the CPI scale so that a higher number reflects a higher corruption level as a continuous variable. Testing a CPI dummy where managers with CPI scores at the same level of Norway or lower are given the value 1, and 0 otherwise, rendering no significant CPI-coefficients.

One may argue that the last year in the home country is not representative of the corruption level experience in their country of origin, especially if a regime changes or government volatility leads people to leave the country. In that case, a cumulative average or the level at a certain age might be more appropriate. But there are also caveats with such an approach, as an average will not capture recent changes (in either direction), and such changes may influence a person more than their lifetime perception. Nevertheless, CPI scores do not change much over time for the countries in the sample; see appendix, table A1B.

We include armed conflict as a dummy. Conflict is synonymous with the destruction of trust between ethnic, religious, or other groups, and institutions typically do not bounce back immediately after a cycle of violence (Collier and Sambanis, 2002; Bellows and Miguel, 2006; Miguel, Saiegh, and Satyanath, 2011. Feldman and Slemrod (2009) find a positive effect of external threats on compliance attitudes because external threats may affect social identification and patriotism. However, war exposure in their setting is limited to violence outside the country of residence and will most likely not reduce trust nor increase trauma in the population, in the way we expect civil war to impose. Lange and Melsom (2022) find a counterintuitive positive effect on employees’ compliance from the ratio of employees in the enterprise exposed to armed conflict, and so we include this variable in our OLS models as well.

We use a recovery period of twenty-five years, i.e., an immigrant exposed to armed conflict from zero to twenty-five years prior to registration in Norway, gets the value 1, and 0 otherwise. Thus, we do not measure armed conflicts older than twenty-five years. This specification follows that of Miguel, Saiegh, and Satyanath (2011). The restriction entails that 37.8 percent of the foreign managers in our sample come from countries involved in armed conflicts. Some of these are Western countries, such as the US and the UK, who have intervened in armed conflicts outside their own territory. However, the number of managers from these countries is small, and unlikely to drive the results. For details on the conflict dummy and which countries it comprises, see appendix, table A4. We have also tried different versions of the conflict dummy, measuring exposure up to five, ten, fifteen, and twenty years prior to migration. None of these yield significant coefficients.

We include the use of an external accountant as a control variable. An external accountant provides an “arm’s length” distance from the manager, and typically has more accounting competence than the latter.

The first stage of the GA and LASSO performs variable selection among the 100 independent variables in our data set. The selected variables from these model runs are included in the summary statistics table. Thus, Table 1 gives summary statistics for variables in all models, broken down by Norwegian versus foreign managers. In appendix table A2, summary statistics are broken down by compliant versus noncompliant managers.

In the sample, 89.50 percent is compliant. In addition, there are only 394 foreign managers, who constitute about 20 percent of the sample. The results on residence time, CPI score, and conflict exposure are thus based on a quite small sample with relatively little variation. Both appropriate sample sizes and sufficient variation in the dependent variables are necessary to provide reliable, reproducible, and valid results. Even though a larger sample with more variation is always preferable, our sample is significantly larger than other studies using randomized data (Blackford, 2017; Jenkins and Quintana-Ascencio, 2020. It has been difficult to obtain consistent and clear guidelines for minimum N in regression analyses, but the sample size in our study far exceeds the recommendations in a recent study attempting to do so (Jenkins and Quintana-Ascencio 2020).

Of the foreign managers, 22.4 percent are female, compared to 16.1 percent of the Norwegian managers. 87.3 percent of the foreign managers use external accountants, compared to 78.6 percent for the Norwegian managers. The fraction of employees exposed to armed conflict is larger in foreign-managed firms (20.2 percent) than in Norwegian-managed firms (5.0 percent). Company characteristics such as company type, salary system, and work training are quite evenly distributed between the two manager groups. Foreign managers advertise less for vacancies than their Norwegian counterparts.

In the OLS model, we explain manager compliance through three independent variables, namely, residence time in Norway, CPI score of native country upon migration to Norway, and armed conflict exposure in the past twenty-five years upon migration to Norway. We include the control variables gender, age, foreign-born, fraction of employees exposed to armed conflicts, and the use of an external accountant. We use fixed effect regressions on four-digit NACE codes to control for differences between industries and, as mentioned we also use fixed effect estimations to control for systematic differences between auditors.

We run one OLS without fixed effects to study the overall effects, irrespective of industry sector variance, and then two OLS with fixed effects, first on NTA auditor ID, and then on both NTA auditor ID and industry sector (NACE code on the two-digit level). To obtain consistent estimates, we cluster standard errors by NACE-code (two-digit level). We estimate specifications of the following type: 1Yi=β1Ti+β2CPIi+β3Wari+β4Xi′+εi,{Y_i} = {\beta _1}{T_i} + {\beta _2}CP{I_i} + {\beta _3}Wa{r_i} + {\beta _4}X_i^\prime + {\varepsilon _i}, where the dependent variable is compliance by manager i. T_i is residence time of that person, CPI_i is his or her CPI score, and War_i is the exposure to armed conflict. X is vector controls, including gender, age, and other variables of interest. As managers are exposed to the Norwegian compliance environment over time, we expect the time coefficient to be positive. Both CPI and war should influence compliance negatively because they reflect lack of trust in government, and so we expect the coefficients of these two variables to be negative. There may be problems with potential multicollinearity, which we address by estimating the variance inflation factor (VIF) in the robustness section.

We rely on Broadhurst et al. (1997) in specifying our GA. This is a stochastic optimization technique in which a population of n subsets is created, each containing a random variation of variables. Then, the cost function for each subset is sequentially evaluated, creating a new population. We then apply a weighted random selection to the original population, where the probability of a particular subset being selected is a function of its cost function response (i.e., the better the cost function response, the greater the chance of selection). The selection process is repeated until n new subsets are created and their cost functions are evaluated; the selection process is repeated until a stopping criterion is reached.

The GA model consists of two parts: first, a variable selection, where independent variables are selected through a specified number of iterations, and second, a linear regression is run over these selected variables. We limit the stopping criterion to eight independent variables. Allowing a higher stopping criterion will, eo ipso, increase the explanatory power, but also include variables with very low coefficients, despite their being statistically significant. LASSO deals with this problem through the tuning parameter. We build the model on a training set using .50 of the data and validate the results on the remaining .50. A total of 100 independent variables (continuous and dummies) from our random audit data set are included in the iterations. We set the number of iterations to 150, as the fitness function does not improve beyond this cut-off; see appendix figure A1.

The GA model aims to find the best OLS-model on the eight-variable subset of the 100 independent variables that we have available. To do so, it randomly generates an initial population of 200 possible models of eight variables from our 100 available variables and performs the OLS on all of them. The resulting set of 200 eight-variable OSL models are then ranked and the most promising ones, those with the lowest mean squared error (MSE), are crossed to form a new population of 600 eight-variable models. The best ones are crossed to form 600 new possible models, and the algorithm continues. This algorithm eventually converges to a local maximum of the best OLS model on eight variables and halts. To explore the different local maxima, the GA algorithm is re-initialized 2,000 times.

The GA algorithm selects the following unique linear model in 754 out of 2,000 runs: 2Yi=α+β1Xi′+εi,{Y_i} = \alpha + {\beta _1}X_i^\prime + {\varepsilon _i}, where the dependent binary variable is compliance by manager i, α is a constant, and X is a vector of the following variables: private limited company, salary system, work training, external accountant, job advertisement, timesheet, terms, and conflict employees. ε is the error term. Note that residence time is not selected by the GA, and thus is not estimated. The results from the first stage of the model (variable selection) are shown in the appendix, table A5. In the final step, we run this model on the total sample with fixed effects on NTA auditor ID, and then on industry sector (NACE code), and cluster standard errors by NACE code (twodigit level).

More common than the GA model in economics are Ridge and LASSO regressions (Pereira, Basto, and da Silva 2016; Hansen and Liao, 2019). While Ridge regressions are more suitable in multicollinear data containing a higher number of independent variables than observations, LASSO regressions are suited both for models with high levels of multicollinearity, or when we want to automate variable selection, perhaps because no theory is available to guide this selection. In our data set, the observations outnumber the variables by far, so a Ridge model is not suitable. A LASSO model will in our case also fit the purpose, but our assessment is that the LASSO entails more preconditions (such as “best subset” under a regularized lp-norm (Zhou, Zhang, and So, 2015) than the GA, so that the variable selection is more restricted. The upside of the LASSO compared to the GA is that the latter typically include some variables with little predictive power in the regression equation, which are likely be removed in a LASSO model.

Like the GA model, a LASSO also performs variable selection. The results are often easier to interpret than those of a linear regression because the dependent variable will only be explained by a small subset of the predictors, i.e., those with nonzero coefficient estimates (James et al. 2013). The LASSO coefficients minimize the quantity: 3∑i=0n(yi−β0−∑i=0nβjxij)2−λ∑j=1p| βj |=RSS+λ∑j=1p| βj |,{\sum\limits_{i = 1}^n {\left( {{y_i} - {\beta _0} - \sum\limits_{i = 0}^n {{\beta _j}{x_{ij}}} } \right)} ^2} - {\rm{\lambda }}\sum\limits_{j = 1}^p {\left| {{\beta _j}} \right| = } RSS + {\rm{\lambda }}\sum\limits_{j = 1}^p {\left| {{\beta _j}} \right|} , where ∑i=1n(yi−β0−∑i=0nβjxij)2{\sum\nolimits_{i = 1}^n {\left( {{y_i} - {\beta _0} - \sum\nolimits_{i = 0}^n {{\beta _j}{x_{ij}}} } \right)} ^2} is the residual sum of squares (RSS), and λ is the tuning parameter determining the punishment of the large coefficients, i.e., if λ = 0, then the model is equal to a standard OLS. The only hyperparameter we need to determine when running the LASSO algorithm is the λ-value. Following James et al. (2013), we use tenfold cross-validation optimized for the MSE to select the optimal λ-value. However, choosing the folds for the cross validations introduces randomness in the LASSO algorithm, and hence cross validation generates different values for optimal λ. To avoid selecting a λ-value at random, we run 2000 tenfold cross validation and end up with fifteen unique values for λ, and hence fifteen different models, estimating the effects of from nine and up to twenty-nine independent variables.

After 2,000 runs on tenfold cross validation and selecting the model with the closest approximation to the OLS and GA on the number of variables, the resulting model is 4Yi=α+β1Xi′+εi,{Y_i} = \alpha + {\beta _1}X_i^\prime + {\varepsilon _i}, where the dependent binary variable is compliance by employer i, α is a constant, and X is a vector of the following variables: private limited company’ self-employed, salary system, work training, external accountant, audited employees, timesheet, terms, and conflict employees. ε is the error term. As for the GA, we run this LASSO model on the total sample with fixed effects on NTA auditor ID, and then on industry sector (NACE code), and cluster standard errors by NACE code (two-digit level). The results from the LASSO variable selection are shown in the appendix, table A6.

The results from the OLS model runs are presented in Table 2.

Foreign managers are 5 percent less likely to reach full compliance (3). Bastani, Giebe, and Miao e(2020) reveal that immigrants are more likely to miss the declaration deadline and to be fined for noncompliance, regardless of their residence time in Sweden, but no such effects are replicated in this context. Part of their explanation is the language barrier among immigrants, which may be lower among non-native managers in our sample. On the contrary, we find only a significant and negative effect among the most recently arrived (<5), suggesting a learning effect after fiv years of stay. We find lower coefficients for those managers with residence time < 5 years than those with 5–10 years, compared to those with >10 years of stay in Norway. This tendency brings again some associations to Bastani, Giebe, and Miao (2020), who find that the probability of taking up the commuting deduction in the Swedish tax system is lower among immigrants with residence time < 5 years than those with 5–10 years of stay in Sweden, compared to Swedish natives. As the significance level of our result is weak, one should be careful to suggest common influence from confounding variable(s), even though the patterns appear similar to that of Bastani, Giebe, and Miao (2020).

We find a negative association between an employee’s conflict exposure and a manager’s compliance (3). While Lange and Melsom (2022) find a positive effect on employees’ compliance from other peer employees’ conflict exposure, the effect on manager compliance is negative. A 10 percent increase in the fraction of employees exposed to armed conflict is associated with a 15.2 percent decrease in probability of management compliance (3). As a robustness test, we have run all model specifications with each of the four components of the dependent variable. From the appendix, table A7, we see that only the component “Tax deduction” is driving this result, i.e., a 10 percent increase in the fraction of employees exposed to armed conflict is associated with a 14.9 percent decrease in probability of correct tax deduction filing by the manager. One explanation could be selection. Firms with many marginalized employees, such as war refugees, may have other characteristics that result in poorer compliance, i.e., higher staff turnover or less experienced managers.

We find no stable associations between the manager’s own conflict exposure and compliance, and no effects from CPI score in this sample. Fisman and Miguel (2007) find that home country corruption norms are an important predictor of propensity to behave corruptly among diplomats, but the cultural mechanism explaining noncompliance, i.e., unpaid parking violations, in their sample, seems not to be at play in our case. One explanation may be that codes of conduct in the workplace environment “eradicate” or “neutralize” cultural background characteristics such as corruption because managers are exposed to tax reporting standards as an integrated part of their everyday business. Diplomats’ parking routines, or lack thereof, on the other hand, are not an integrated part of their occupations as diplomats, but rather their personal character. Indeed, Fisman and Miguel (2007) find that the time and space of many violations is strong evidence that these are not even work-related and that third-party reporting closes the incentives to misreport.

We find a small negative, but statistically significant, effect of age on management compliance across all three model specifications. The age effect is stable, i.e., the probability of management compliance decreases with a ratio of .003 (3) as the manager gets one year older. Nevertheless, the sign of the age coefficient may not be surprising, as age correlates with seniority in any position, and thus the more senior, the more knowledge about the loopholes in the tax system. Furthermore, perhaps managers over time get a more realistic view of the (low) probability of audit selection by the tax authorities. This effect may also be explained by a higher understanding of tax legislation among managers in our sample than in the population in general. The age-learning effect may be equivalent to the age gradient identified by Bastani, Giebe, and Miao (2020). They find an age gradient in the take-up of commuter deductions for natives and immigrants with long residence time in Sweden, who presumably have adapted more to the tax system compared to newly arrived and younger immigrants. Furthermore, this learning effect resembles a learning effect in Fisman and Miguel (2007), where diplomats become bolder in their violations once they “successfully ‘got away with it’ a few times (or heard stories about others doing so).” (Fisman and Miguel 2007, 1042)

However, the negative age-effect partly contradicts more recent findings. Hofmann et al. (2017) conducted a comprehensive metastudy on tax compliance across sociodemographic categories, including age, and find a small positive, but significant relation between the age of taxpayers and their tax compliance. This confirms findings in Nordblom and Žamac (2012) and Kirchler (2007), as well as older studies, such as Tittle (1980), Witte and Woodbury (1985), Dubin and Wilde (1988), Feinstein (1991), and Hanno and Violette (1996). Ashby, Webley, and Haslam (2009), Braithwaite and Ahmed (2005), and Muehlbacher, Kirchler, and Schwarzenberger (2011) find no age effect, however.

Furthermore, we find a significant positive effect of an external accountant across all model specifications. In column (3) of Table 2 we observe that hiring an external accountant is associated with an increase in compliance with a ratio of .092 when controlled for auditor and industry sector. Most of the effect stems from the mandatory monthly reporting; see appendix, table A7. The effect is expected, as one would typically infer that accountants possess more knowledge on tax filing and liability than business managers in particular and people in general. The positive effect may both be causal and due to selection. Using an external accountant means hiring someone who is authorized to keep accounts and is obliged to ensure compliance to rules and regulations. In addition, using an external accountant is not mandatory. Thus, it seems likely that firms more concerned with compliance will do so to a greater extent than other firms. Saad (2014) finds some degree of trust in accountants’ tax knowledge as reasons for outsourcing tax filing. Further to this, managers with different characteristics and compliance attitudes may be selected to different sectors. However, adding fixed effects on NACE code (two-digit) on the third model specification, does not alter the significance level, and so this prospective selection bias is unlikely to drive the results.

For foreign managers, residence time is calculated based on arrival date in Norway. For Norwegian managers without any registered long-term stays abroad, residence time coincides with age. As about 80 percent of the managers are Norwegian, age and residence time are highly correlated in the full sample. In addition, residence time has a slightly different meaning for foreign and Norwegian managers. To address these issues, we have tested interaction terms between residence time and foreign background to see if the association between residence time is different for Norwegian and foreign managers but find no significant interaction effects. We have also tried to run the regressions on residence time separately on Norwegian and foreign workers. Limiting the sample to Norwegian managers, the variables on CPI, conflict, and residence time are omitted, leaving only gender, age, and external accountant as independent variables. The coefficient for age is till significant for Norwegian managers. For foreign managers, neither age nor residence time yield significant coefficients.

Conflict and corruption variables are also correlated. The average CPI score is not surprisingly substantially higher in countries who have records of armed conflict. To check this association more closely, we have regressed compliance over these two variables separately and then combined them. In these models, the coefficients remain stable in all models; see appendix, table A10. This indicates that CPI scores measure something different than armed conflict, and we thus argue that it is possible to separate their association with compliance from one another.

There is also considerable variation in CPI scores in both groups. For managers from countries exposed to armed conflict, the CPI score ranges from 12 to 85. For managers from nonconflict countries, it ranges from .6 to 80 Except for the vast majority of Norwegian managers with the CPI score for Norway in 2018, the CPI scores are quite evenly distributed in both groups.

The results from the GA model specification are displayed in Table 3.

We observe that holding a private limited company increases the probability of compliance by a ratio of .103 (3) and using an external accountant increases the probability of compliance by a ratio of .111 (3). There is a positive effect of .021 (3) on firm compliance of terms. A firm reporting salaries or benefits for employees has sustained activity and therefore reporting liabilities, but, perhaps equally important, more contact points with NTA throughout the year. The negative effect from the fraction of firm employees exposed to armed conflict is reproduced in this model, although it is slightly weaker.

The returns from the GA model yield intuitive results. A private limited company is more transparent, have more reporting liabilities and is under easier surveillance and scrutiny by the tax authorities than self-employed or registered foreign companies. Thus, one would expect a higher probability of compliance for private limited companies. The use of an external accountant also increases the probability of compliance, and this coefficient replicates the effects from the OLS models. Most of the effects from holding an external accountant is driven by monthly reporting; see appendix, tables A7–A9.

The results from the LASSO model specification are displayed in Table 4.

The LASSO model results by and large reproduce the effects from the GA model, except the significant effect of holding a private limited company. Neither company type, Ltd. Company nor self-employed are significant predictors of management compliance in this model. This variance between the algorithms is not surprising, however. The inconsistency between the two algorithms is expected, since the two algorithms optimize different functions defined over different spaces. The LASSO algorithm optimizes a carefully modified linear regression problem, while the GA algorithm optimizes over the space of all possible linear regressions.

These different goals mean that there is neither reason expect the algorithms to agree about everything, nor an indication of an arbitrary result. The surprise is rather that the GA and LASSO agree on seven out of eight variables, and that there is low variance in the size of the coefficients between the two.

The appendix, table A11 gives the results of the OLS, GA, and LASSO model runs with fixed effects on NTA auditor and NACE code (two-digit) in one table.

There are a number of predictive performance indicators in the literature, such as the Akaike Information Criterion (SakamotoIshiguro, and Kitagawa. 1986), the Bayesian Information Criterion (Watanabe 2013), or Adjusted R-squared (Mullainathan and Spiess 2017). The latter demonstrate the need for a hold-out sample to assess performance. Certain ML algorithms’ tendency to overfit is also prevalent in our GA model. Thus, one may expect performance to be overstated in the training sample. A second lesson to learn from Mullainathan and Spiess (2017) is that ML algorithms can perform significantly better than OLS, even when sample sizes and number of covariates are limited. In our setting, it makes less sense to compare performance of predictive models with the OLS, as we are mainly using the ML models to guide variable selection. However, as we want to check how well the ML models’ predictions match the observed data, we find MSE to be appropriate (James et al. 2013). The performance of the models is displayed in Table 5, where we also include a column for adjusted R-squared for illustration purposes.

Although the ML models have their obvious limitations with respect to causal inference (Pearl 2018), when lack of previous empirical findings or theory cannot guide any explanations of the relationships, there are still lessons to be drawn from a comparison between who ML models performing variable selection in the first stage. We see that the performance is very similar, and so the choice of models should be guided by other criteria, such as, for example, the number of parameters one would have to “arbitrarily” set.

To get a clearer picture of the origins of significant effects, we have run all model specifications on each component of the dependent variable, namely, tax deduction, payroll accounts, monthly reporting, and general accounts. An unambiguous result of this test is that most of the effects from holding an external accountant is driven by monthly reporting. All results are given in the appendix, tables A7–A9.

As NTA auditors have suggested independent variables, it is likely that some multicollinearity between variables exist. We estimate VIF of the individual variables in all regressions and find that none of the variables in the standard OLS regressions has a VIF higher than 4.22, and none in the GA- and LASSO-specified regressions has a higher VIF than 1.21, and hence we can disregard multicollinearity.

For the same reason related to variable selection by NTA auditors, we may expect some endogeneity in the final model specifications. Thus, for all fixed effects regressions, we have run the Hausman test for endogeneity (Hausman 1978), and find that no difference in coefficients is systematic.