Tax policy and entrepreneurial entry with information asymmetry and learning

At least since Schumpeter (1934) entrepreneurial entry has been seen as a major driver for economic growth. Entrepreneurs challenge incumbent firms thus stimulating improvements and productivity gains and can themselves bring innovations into the market, in the form of new products or processes. A reflection of this view is the widespread existence of policies designed to foster entrepreneurship, to support small young firms and to ease credit constraints. At the heart of the market failure that these policies try to solve is asymmetric information. First, there is an intrinsic riskiness in starting a new venture which makes investors require a risk premium thus raising the cost of capital. Second, the chances of entrepreneurial success depend on a number of factors including the entrepreneur’s human capital, which is not directly observable thus giving rise to adverse selection. Third, the entrepreneur himself faces asymmetric information at the time of acquiring input factors, notably when hiring personnel and in cases when third-party technologies have to be employed.

This paper focuses on simultaneous informational asymmetries in the credit market and in the labour market. We develop an agent-based computational model which is designed to mimic the mechanisms described in Boadway and Sato (2011). Our novel contribution lies in explicitly taking into account learning over time and its consequences on the effects of tax and subsidy policies. Simulation analysis is here used to test the effects of policies made of a tax on entrepreneurs and a subsidy to labour income, in a more realistic setting. We study a market that is not in an extreme condition of either full or no information, where excess entry favours learning and thus produces more information in less time.

The intuition behind our claim is rather straightforward. If agents over time learn about other agents’ ability or quality, then having more entrants in earlier periods increases the amount of information available and leads the market closer to a condition of full information. Consequently, the optimal level of entry with learning is larger than in a first-best scenario with full information; as the loss in surplus suffered as more bad entrepreneurs enter, the market is (partly, or entirely) compensated by an increase in future surplus due to more efficient market conditions.

In our model entrepreneurs and workers decide whether to enter an entrepreneurial market, entrepreneurs hire workers and fund investment costs by means of external financing, and a government may levy taxes or subsidies on both entrepreneurial income and wages. Asymmetric information plagues both the credit market and the input (labour) market. The estimated entrepreneur’s ability¹ affects the cost of financing she faces, while the estimated worker’s quality affects his expected wage. After replicating the main features of a market as described in Boadway and Sato (2011) for the polar cases with full information and with no information available, we then introduce the possibility that agents may learn over time, thus better estimating abilities and qualities thanks to informative signals.

Our simulation results point to the fact that the way information is produced in the economy meaningfully affects the scoring of different policy options. In some settings a tax on entrepreneurs, which would be optimal under a no-information regime, might be detrimental welfare-wise when learning occurs. Our results suggest that the optimal levels of a subsidy to workers and of a tax on entrepreneurs strongly depend upon the information regime observed in real markets and that learning always implies lower taxes on entrepreneurs at the optimum compared to the no-information regime.

In the following, Sect. 2 summarizes the relevant previous literature. Section 3 describes the model, and Sect. 4 discusses the simulation results. Section 5 concludes and points to future avenues for research.

This paper draws from several previous research contributions. The literature on adverse selection in credit and entrepreneurial markets, particularly with regard to new ventures, poses the basis for the analysis of the asymmetric information on the side of entrepreneurs (Stiglitz and Weiss 1981). The main message from this literature often closely resembles Akerlof (1970) in predicting underinvestment and less than optimal (from a social planner’s point of view) entry of new ventures, though subsequent research (De Meza and Webb 1987; Boadway and Keen 2006) finds conditions under which this outcome can be reversed to overinvestment.

Adverse selection on the side of labour inputs acquisition and its effects on new firms is relatively less studied. Weiss (1980) analyses a market with unobservable workers’ quality and shows how adverse selection would draw more workers with low skills from the pool of candidates, with overall lower employment than optimal. Most other studies focused on moral hazard in the form of unobservable effort provision (Shapiro and Stiglitz 1984; Holmstrom and Milgrom 1991).

The taxation literature has analysed tax and subsidy policies that may be employed to obtain first- or second-best optimality. (Good summaries of results and open questions are found in Rosen 2005; Keuschnigg and Nielsen 2003; Henrekson and Sanandaji 2011.) Most of these, though, again focus on the problem of non-monitorable effort; for instance, Keuschnigg and Nielsen (2003) develop a model where venture capitalists and entrepreneurs jointly provide effort, and they find how taxes on labour, capital and capital gains income should be designed. The effects of specific types of taxes on bonus compensation with unobserved work effort have been studied with regard to managers (Radulescu 2012; Dietl 2013), and with regard to innovative employees when also corporate taxes and tax incentives are levied (d’Andria 2016).

The possible interactions between the two informational asymmetries, however, remain largely unexplored. One exception is of course Boadway and Sato (2011) which we are employing here as a basis to develop our own agent-based computational model. Boadway and Sato (2011) discuss a theoretical model where entrepreneurs with unknown ability decide whether to start a risky project. Those who decide to start such a project hire workers whose quality is, as well, unknown. This kind of market generates inefficient levels of entrepreneurial activity and adverse selection simultaneously on the side of entrepreneurial borrowing and on the side of labour supply. Policy-wise one of the main results is that in a scenario where double adverse selection induces excessive entry of low-ability entrepreneurs and the hiring of too many low-quality workers, the second-best optimal policy is made of a subsidy to labour (which serves the purpose to attract high-quality workers) paired with a tax on entrepreneurs (which curbs the excessive entry of entrepreneurs, the latter being increased by the labour subsidy).

A related strand of literature models agents as facing the choice whether to become an entrepreneur or to work as an employee. Recent contributions have highlighted that the earnings from jobs alternative to entrepreneurship can either be randomly associated with the abilities as entrepreneurs (Scheuer 2013, where regressive profit taxation is found to be the optimal policy response) or correlated with abilities (d’Andria 2018a). In the latter case, taxes levied on entrepreneurial income can have very different effects on entry decisions based on the specific correlation assumed. In our simulation model, we assume that entrepreneurs only face the decision whether to become entrepreneurs or to invest in a safe asset, while workers decide whether to work for an entrepreneurial firm or for a non-entrepreneurial firm. Therefore, we rule out the possibility for an entrepreneurial-type agent to opt for employment. This choice stems from at least three reasons. First, we do so in order to allow for clearer comparisons with Boadway and Sato (2011) (and also with the previous literature, in particular, Stiglitz and Weiss 1981 and De Meza and Webb 1987) who opted for the same modelling choice. Second, as shown in d’Andria (2018a), different assumptions about how entrepreneurial ability and productivity as an employee correlate are not neutral and may completely change the way the model behaves. This would in turn multiply the number of scenarios and corresponding simulation runs needed to account for different assumptions, in a way that would be hard to manage in practice. Third, having an outside option that varies with own ability introduces another degree of heterogeneity across agents, which in turn would require larger populations and more replications for each simulation run, again posing technical issues with the optimization code used to find optimal policies.

Methodologically, our choice is agent-based computational economics (ACE) modelling, see Tesfatsion and Judd (2006) for an in-depth description and a number of examples taken from the literature. The rationale for using agent-based computational modelling techniques in economics has been widely discussed already, for example, in Tesfatsion (2003) and Judd (2005). In our case, as we aim at introducing learning over time—which is intrinsically a stochastic path-dependent process—together with heterogeneous agents, we believe this comes as a rather natural choice. We can then deal with multiple equilibria using a Monte Carlo approach and study the way the simulated model converges, on average, to different outcomes. We believe we avoid the critique, common to many agent-based models, of a lack of generality of the results stemming from simulated runs of the model with specific parametrizations thanks to the fact that we developed a computational optimizer to explore a wide range of policies and find the optimal mix of taxes and subsidies. Other parameters in the models are chosen following a minimal-assumptions approach to be as neutral as possible, often just taking the mean of the range of admissible values or deriving the parameters to meet a specific endogenous value for some variable (e.g. to obtain \( 50\% \) entry rates under the baseline benchmark scenario with full information).

Agent-based models have been employed in the past (though only occasionally) to study labour markets (i.e. in Tesfatsion 2001 and Neugart 2008) and taxation (mainly in relation to tax evasion, see, for instance, Bloomquist 2006; Hashimzade 2015 and Warner 2015). A relevant example is d’Andria and Savin (2018) where an agent-based model was developed to study a market for innovative workers with unobserved effort and workers’ qualities, multiple job tasks and taxes both at the corporate and personal level. We follow here a philosophy similar to d’Andria and Savin (2018) in first developing a model that resembles as closely as possible the features and mechanisms of a corresponding analytical model (in the case of the present paper the reference analytical model is Boadway and Sato 2011), and then we change only one key assumption (by introducing learning) to see how the behaviour of the model changes. A similar approach has been used in the past in Yildizoglu (2002) where an agent-based model was developed that first follows an existing and well-known model (in that case, Nelson and Winter 1982), and then a different element is introduced (in Yildizoglu 2002 the new element consisted of a different set of assumptions about investment behaviour based on a learning mechanism); finally, the convergence value of the model is computed as a mean across several replications, and such convergence values computed with and without the new assumptions are compared.

The model is run each time using the parameters listed in Table 1. It is just the case to stress that these parameters are not meant to resemble any level of realism nor are they calibrated based on real-world figures: they are meant to make the model behave in a certain way in order to support a theoretical argument. Table 1 summarizes the set of parameters employed.

The main output of a simulation is surplus, which (following Boadway and Sato 2011 and most of the literature on optimal taxation in partial equilibrium settings) is computed summing up all value generated by entrepreneurs (production minus labour costs times gross interest rates), less their opportunity costs (the alternative safe investments producing value \( \pi _0 \)), plus wages earned by workers less their opportunity costs (the wage they could have earned in sector T). Profit and wages entering S are gross of taxes and subsidies, meaning that S represents value generated (or destroyed) after compensating for any subsidy paid, or tax collected, by the government. For this reason, the following simulation results include a measure of the net financial position of the government, in order to provide information about the budgetary cost of the simulated policy. Dividing S by this net position provides a measure of the additionality of the policy, that is, of how much value is created per net unit of public money spent. We label a policy “optimal” when it is found to maximize S, regardless of the corresponding net financial position of the government.

Surplus is here computed at the beginning of each period; thus, as workers are paid upfront while success for entrepreneurial projects is determined at the end of a period, any surplus coming from entrepreneurs is discounted using the same safe rate \( \rho \) assumed in the credit market. All surplus figures provided in the following tables have to be interpreted as measuring the net present value of surplus at the beginning of each period. In symbols, surplus in a given period is:Surplus is computed in each period based on the expected profit of entrepreneurial projects rather than actual realizations. The reason for this choice is purely technical and meant to reduce randomness in order not to have to run several replications of the same simulation type, thus drastically reducing computation time for the optimization algorithm used to find optimal policies.

For the scenarios with either full or no information, the use of expected surplus allows us to run one single simulation for each policy to be evaluated. For the scenarios with learning, given the path-dependencies implied by model design, multiple replications are run (10, or 5 when using the optimization algorithm and many periods). When replications are performed, average values are taken across periods and replications (this is the case for entry and employment figures) or they are derived by summing up across periods and then averaging across replications. (This is the case for surplus.) These average values are what we refer to as results in the following text. When no replications are performed, the values are averaged or summed up only across periods.

We first run the model assuming full information to calibrate it. We chose parameters that make the model obtain an entry of 50% for both types of agents under full information and without any tax or subsidy. (We refer to the latter as a no-policy scenario.) We then looked for a policy mix (made of a subsidy to labour and a tax on entrepreneurs)⁷ that maximizes surplus under no-information first, and then under learning, using our custom optimization algorithm. Because of the stochastic behaviour of the simulation model under the scenario with learning, some of the most common optimizers (gradient-based, directed search) are either unusable or do not perform well, the problem being akin to the optimization of a “rugged landscape”. A genetic algorithm could be used but it would take too long to perform the search. We therefore wrote a grid-based optimizer that computes the outcome from several policy mixes by changing taxes and subsidies, one at a time and by a fixed value, and then in a second step performs the same search locally, centering a smaller grid around the maximum value found in the first step.

Table 2 summarizes the outcome of the main simulations. Surplus is reported both as non-discounted sum across all periods (as stated, this is net present value of surplus evaluated at the beginning of each period in which it is generated), and as net present value in the first period of the simulation (NPS in the table), where the discount rate used is the safe interest rate \( \rho \) (thus, a very large discount rate as \( \rho = 2 \) in our parametrization). Table 2 reports entry rates and mean abilities and qualities of entered agents. Also, in the last column, the net financial commitment of the government is shown as total subsidies paid less total taxes collected (summed across all periods).

As in Boadway and Sato (2011), total surplus is found to be greatest in the no information scenario, with a tax and subsidy policy mix. The optimal values found by the optimization algorithm are \(-75.7\) for the tax on entrepreneurs, and 3.85 for the subsidy to workers. Table 2 reports also the results for a subsidy-only policy (equal to 3.85) to allow for comparisons and to appreciate the effects of the subsidy in isolation. The subsidy-only policy even reduces surplus (total and NPS) below what was obtained without policy intervention.

We then allowed for agents to learn. We run simulations first without any policy, and then with the optimal policy found for the no-information scenario (\( \sigma = 3.85 \) and \( \tau =-75.7 \)). The previously found optimal policy reduced surplus to negative values in the scenario with learning. The optimal policy for the learning scenario was found to be made of a subsidy \( \sigma =0.76 \) and a tax \( \tau = -10.0 \), thus both smaller in absolute values than for the no-information scenario. Table 2 summarizes these results. With 10 replications⁸ the surplus obtained from the learning scenario has a standard deviation of less than 2.5%, which means that the difference from the no-policy case is statistically significant at p-value \( < 0.0001 \).

With learning and without policy actions, the market produces sub-optimal entry for both types of agents. The reason lies in the noisiness of ability and quality estimates, such that there is always a share of agents who are undervalued and thus do not enter sector E, and this share decreases in time as better estimates of abilities and qualities become available. Note that the optimal policy raises entry well above 50%, the reason being that with learning it is best to elicit larger entry in the first periods to improve the production of information over time. The latter result remains true even when comparing net present surplus which heavily discounts future surplus gains (but, see Sect. 4.1 for a sensitivity analysis w.r.t. the number of periods assumed). Table 2 also reports results for a scenario with learning and only a subsidy (\( \sigma =0.76 \)), again to allow for comparisons with the other policies.

An interesting property of the scenario with learning is that subsidies to workers elicit much more entry compared to no information. After in-depth examination of the microdata stemming from our simulations, our conclusion is that this larger reactivity is mostly due to the fact that even a small additional incentive to entry enhances the matching of workers and entrepreneurs. Improved matching greatly increases expected profit for the high-ability entrepreneurs, thus prompting their entry, which in turn allows for even larger entry of workers. This mechanism is reflected, in Table 2, in the relatively large average ability of entrepreneurs in the market (“large” relative to the fact that the entry rate is close to 70%).

Turning to the government position, one can see from Table 2 (last column) that optimal policies may produce both positive or negative net positions. Interestingly, our simulations suggest that the optimal policy under the scenario with learning produces very large additionality. On average, value generated in the latter scenario exceeds spent net public money by more than 14 times (obtained dividing S by the Government Net position from Table 2). Moreover, looking at individual simulations, after 100 replications of the scenario with learning and optimal policy we found that this ratio never fell below 3.5. While only suggestive as our model is not calibrated using real data, these results point to the possibility that taking into account dynamic (learning) effects the cost–benefit analysis of such policies generally might produce more favourable assessments.

We developed a simulation exercise to mimic in an agent-based fashion a market with adverse selection both on the side of entrepreneurial entry and on the input market for workers, in this following the theoretical work of Boadway and Sato (2011). Our simulation results show that the introduction of learning over time can significantly affect the optimality of tax and subsidy policies. A policy made of a subsidy to labour and a simultaneous tax on entrepreneurs, which would be socially second-best under a no-information scenario, was shown to be inferior welfare-wise to a policy made only of a labour subsidy (where the level of such subsidy was optimal under no information). An optimal policy under learning was found to require much smaller subsidy to workers (and consequently, also a much smaller tax on profit) than under no information, as the entry rate of agents tends to be more reactive to the policy due to the dynamic effects of learning and better matching of high-quality workers with high-ability entrepreneurs.

The intensity of information asymmetries probably varies across industries, countries and times. Highly innovative sectors are likely to be more plagued as it takes time to evaluate the capacity of a technical employee to innovate, an example of this being the highly skewed distribution of patent applications among the population of inventors where most employees never patent anything or at most manage to patent once in a lifetime. In such cases, the economy is likely to be represented quite closely as a polar scenario with no information, with the exception of “star” scientists and entrepreneurs for whom a sizable number of observations may exist about their performance so that other agents may evaluate them accordingly. The latter observation points to a candidate extension of this research by assuming a segmented market with learning over ability/quality happening only above a threshold number of observed successes or failures.

The simulation model here presented is in many respects a simplified representation of reality, and multiple improvements could be devised to increase its external validity. We would like to mention one, in particular, which would represent the entrepreneurial market as an overlapping-generations framework with several cohorts of entrepreneurs and workers (similar, for example, to a model with symmetric uncertainty as in Tervio 2009 and d’Andria 2018b). Here the learning dynamics of our simulation would apply to each cohort individually, but all cohorts would simultaneously interact on the markets for credit and jobs. In such context, and contrary to the present model, cohort-specific policies (such as age-conditioned subsidies) could also be studied.