Optimal Taxation, Informality, and Welfare: Redistribution Costs and Efficiency Gains

Abstract

We characterize the welfare effects of the informal sector by proposing a decomposition into efficiency and redistribution components. We focus on an economy where a planner wants to redistribute income with taxation and sets the optimal tax scheme. Since the informal sector can limit the taxation possibilities for the government but at the same time provide a shelter against tax distortions for individuals, we show that the net welfare effect can be positive or negative. We show that the relative advantage between informal and formal employment across different income levels is the key dimension that shapes the welfare costs of the informal sector. Using the model estimated with Colombian microdata, we show that, conditional on the optimal tax policy, the Colombian shadow economy benefits efficiency at the expense of redistribution. Consequently, the presence of the informal sector reduces welfare only when preferences for redistribution are strong. (JEL codes: H21, H26, J46).

1. Introduction

Informality significantly impacts developing economies, where, on average, the shadow sector represents 30% of output (Schneider et al. 2011) and a larger portion of employment. In Colombia, for example, approximately 55% of workers are employed in the informal sector.¹ This prevalence of informality is often perceived as an obstacle to development, undermining government capacity for revenue collection and investment. Recognizing its importance, the United Nations has prioritized reducing informality among its sustainable development goals (UN General Assembly 2017). Despite these challenges, informality serves as a crucial survival strategy for the impoverished, offering an escape from tax burdens and potentially reducing the efficiency costs of taxation for vulnerable populations. Thus, the welfare implications of the informal sector are complex and multifaceted.

This paper introduces a theoretical framework to assess informality’s welfare impact, employing a model calibrated with Colombian microdata. Our analysis concentrates on how informality influences the optimal scope for redistribution. While informality may seem to undermine social welfare by facilitating tax evasion and compromising redistribution efforts, our findings suggest a nuanced reality.

In certain contexts, the informal sector may actually enable greater redistribution or reduce tax distortions, improving overall welfare.

We model an economy with heterogeneous agents differentiated by their productivity in both formal and informal sectors. Given the existing income tax structure, agents choose their sector of employment (extensive margin) and work hours (intensive margin). A benevolent government designs a nonlinear income tax to maximise social welfare. Formally, we assume that individual productivities as well as earnings from the informal sector are unobserved by the planner, while only earnings from the formal sector are observable. Thus, the planner chooses the allocation to maximise the social objective subject to the adequate incentive-compatibility constraints. Our evaluation considers two scenarios: one where agents can engage in informal work and another where the informal sector is artificially eliminated. This approach allows us to isolate the welfare effects attributable to informality.

Using a simple model with two types, we show that the impact of informality on social welfare is ambiguous—depending on the productivity profiles, it can be either negative or positive. To shed light on the mechanisms behind this result, we decompose the impact of informality into two welfare-relevant dimensions: the degree of redistribution and the efficiency of labour supply. Informality generates a redistribution gain if it allows the government to decrease taxes on, or to increase transfers to, agents favoured by the social welfare function (presumably, the poor). Informality generates an efficiency gain if it leads to the overall lower amount of labour supply distortions in the economy. Informality can enhance efficiency by sheltering agents from distortionary taxes or by making the government choose a less distortionary tax schedule to start with.

The simple model allows us to derive analytical comparative statics of these two dimensions of social welfare. Suppose that the government wants to redistribute from the rich to the poor. We find that the redistribution gain is strictly decreasing in the informal productivity of the rich, and is strictly positive if the informal productivity of the rich is sufficiently low. In turn, the efficiency gain is strictly increasing in the informal productivity of the poor, and is strictly positive if the informal productivity of the poor is above a threshold (that lays strictly below the formal productivity of the poor). Thus, if the informal employment is sufficiently attractive to the poor and sufficiently unattractive to the rich, it will improve social welfare.

Further, we explore a more comprehensive model featuring a continuum of productivity types, heterogeneous fixed costs of informal employment, and the possibility of dual-sector employment. This model, parameterized with Colombian microdata and solved using recent advancements in optimal taxation theory, allows for a sophisticated comparison between scenarios with and without informality. We discover that the informal sector in Colombia contributes positively to labour efficiency while having a negative effect on redistribution. Importantly, the net effect depends on the extent of redistribution that the planner wants to implement. When the planner’s redistributive preferences are weak, the shadow economy facilitates a welfare improvement comparable to a 1% increase in consumption. However, when the redistributive preferences are strong, the shadow economy negatively impacts welfare, with a welfare loss equivalent to about 3% decrease in consumption.

1.1 Related literature

Kopczuk (2001) studies optimal redistribution with tax avoidance. He provides an example where tax avoidance is socially beneficial by allowing for more redistribution. da Costa and Lobel (2022) investigate the welfare implications of the shadow economy using Brazilian data and the social preferences implicit in the actual income tax schedule in Brazil. Our study diverges from theirs by considering the possibility for agents to concurrently engage in both formal and informal sectors. We further dissect the welfare impact of informality into two distinct aspects: efficiency and redistribution. Moreover, we show how varying redistributive preferences influence the costs and benefits associated with informality, offering a nuanced understanding of its role within an economy. Takikawa (2024) offers a complementary perspective by studying formalization of the informal sector and its implications for the optimal tax schedule. Other studies that note a potential role of an informal sector in reducing distortions include Cowell (1985) and Davidson et al. (2007).

Our analysis leverages the theoretical advancements in the optimal nonlinear income taxation in the presence of an informal sector, as developed by Doligalski and Rojas (2023). Other papers studying optimal tax systems with evasion or avoidance opportunities focus on the role of consumption taxes (Emran and Stiglitz 2005; Boadway and Sato 2009; Huang and Rios 2016), tax thresholds (Kanbur and Keen 2014), income shifting (Piketty et al. 2014; Selin and Simula 2020), nonlinear costs of evasion (Grochulski 2007; Casamatta 2023), or non-expected-utility approach to decisions under uncertainty (Piolatto and Trotin, 2016). Kanbur et al. (1994) study nonlinear income taxation under a non-welfarist objective of minimizing poverty. Simula and Trannoy (2010) study optimal income taxation under the threat of migration to a different country, which shares some similarities with moving to an informal sector.

2. Two-Type Model and Welfare Decomposition

This section characterizes the welfare implications of the shadow economy by dissecting its effects into redistribution and efficiency gains. We employ a simplified model that facilitates an analytical exploration of the comparative statics associated with these welfare components. Our model posits an economy populated by two distinct worker types denoted as L (low productivity) and H (high productivity) without the complexities of shadow employment costs or the feasibility of simultaneous formal and informal sector employment.

The population is partitioned into L and H types, with respective shares μ_L and $μH=1−μL$⁠. These individuals derive utility from consumption c and labour supply n, modelled through a quasilinear utility function $U(c,n)=c−v(n)$⁠, where v is a strictly increasing, strictly convex, and twice differentiable function with $v′(0)=0$⁠. Although our analysis adopts a linear utility perspective for consumption to simplify the exposition, extending these findings to scenarios with concave utility from consumption remains straightforward.

Each agent is endowed with two linear production functions corresponding to two labour markets, enabling formal (f) and informal (s) sector employment. An agent of type $i∈{L,H}$ working in sector $j∈{f,s}$ exhibits productivity $wij$⁠. Income generated in each sector is defined as $yij=wijnij$⁠, where $nij$ represents labour supplied to sector j. We designate type H as having superior formal sector productivity: $wHf>wLf$⁠. Additionally, we assume that all types have higher productivity in the formal sector: $∀i wif>wis$⁠, suggesting an inherent inefficiency in the shadow economy that precludes its use in optimal scenarios where individual types are observable. This assumption is relaxed in the full model.

2.1 The planner’s problem

If agents have any formal earnings, their shadow earnings are zero. If instead they have no formal earnings, they are unconstrained in choosing their shadow income. Given this function, we can specify agents’ consumption $ci=yif+yis(yif)−Ti$ and labour supply $ni=yif/wif+yis(yif)/wis$⁠, conditional on a truthful revelation of types.

The incentive compatibility constraints capture the limited information available to the planner. They imply that no agent can be better off by choosing formal income of the other type and, if this income level is zero, freely adjusting shadow earnings. 

Lemma 1 extends the classical no distortion at the top principle to our context. When $λi>λ−i$⁠, there’s an incentive for the social planner to redistribute income from type –i to type i. Consequently, the incentive constraint for type –i becomes binding, and the planner cannot improve the social objective by distorting the labour supply of type –i. Since an agent will opt for the shadow economy employment only if their formal sector labour supply is distorted downwards, type –i will invariably abstain from shadow economy participation in the optimum. Conversely, introducing distortions into type i’s labour decision relaxes the binding incentive constraint, thereby allowing for greater redistribution. As such, there exists a scenario where type i might engage in the shadow economy.

Note that the shadow economy may be utilized in the optimum due to the agents’ private information about their productivity. If individual productivities were publicly known, the planner would rely on non-distortionary, individualized lump-sum taxes. Given that all agents are more productive in the formal sector (an assumption we will relax in the next section), no one would then find it optimal to work informally.

2.2 Welfare decomposition

Suppose that $λi>λ−i$⁠, such that the planner wants to redistribute resources from type –i to type i. There are two candidate allocations for the optimum: a ‘Mirrleesian allocation’ in which type i works formally (denoted with superscript M) and a ‘shadow economy allocation’ in which type i works informally (denoted with superscript SE). Note that the ‘Mirrleesian allocation’ is also the optimum in the setting without the shadow economy. We examine the welfare ‘gain’ from the existence of the shadow economy by comparing these two allocations. 

Proposition 1 decomposes the welfare gain from the shadow economy into an ‘efficiency gain’, measuring the difference in distortions imposed on type i, and a ‘redistribution gain’, capturing the change in the level of transfers received by type i.

2.2. 1 Efficiency gain

In the shadow economy allocation, type i supplies the efficient level of labour to the inefficient shadow sector (an extensive margin distortion). In the Mirrleesian allocation, due to the distortions imposed by the planner, type i supplies an inefficient amount of labour to the efficient formal sector (an intensive margin distortion). The relative inefficiency of the shadow sector depends on the productivity difference $wif−wis$⁠. When this difference is sufficiently small (⁠$wis>w¯is$⁠), distortions in the shadow sector are smaller than distortions in the formal sector and the shadow economy improves the efficiency of labour allocation. Intuitively, in this case, the shadow economy provides a shelter against tax distortions. If instead the shadow economy distortions are large (⁠$wis<w¯is$⁠), the efficiency gain of the informal sector will be negative.

2.2. 2 Redistribution gain

The shadow economy improves redistribution if the planner is able to provide type i with a higher transfer (or equivalently raise a higher tax from type –i). The scale of redistribution is determined by the payoff of type –i from misreporting. In the Mirrleesian allocation, the deviating worker works formally and can earn only as much as type i. In the shadow economy allocation, the deviating worker cannot supply any formal labour, but is unconstrained in supplying shadow labour. As the shadow productivity of type –i increases, the payoff from misreporting in the shadow economy allocation rises and the redistribution is reduced. On the other hand, when $w−is$ is sufficiently low (⁠$w−is<w¯−is$⁠), the shadow economy deters the deviation of type –i, helping the planner to tell the two types of agents apart. In this case, the informal sector is used as a screening device.

Proposition 1 is illustrated in Figure 1, where we assume that the planner maximises the utility of type L: $λH=0$⁠. Intuitively, the shadow economy does not have to strengthen both redistribution and efficiency simultaneously to be welfare improving. Particularly interesting is the region where the redistribution gain is negative, but the efficiency gain is sufficiently high such that welfare is higher with the shadow economy. In this case, the shadow economy allocation Pareto dominates the Mirrleesian allocation. Type L gains since the welfare is higher with the shadow economy. Type H benefits as well, as the negative redistribution gain implies a lower tax burden on this type.

Kopczuk (2001) provides an example in which, starting from the allocation without tax evasion, a marginal increase in evasion yields welfare gains.² According to our decomposition, in his example, welfare improves due to greater redistribution, but at the cost of efficiency. It may suggest that the shadow economy improves welfare by allowing for more even division of a smaller aggregate output. We show that such a scenario is only one of many possibilities. For instance, the shadow economy can reduce redistribution while still being welfare-improving, in which case all agents benefit from the presence of the shadow economy.

3 Full Model and Quantitative Methodology

In this section, we present an extension of the model to quantitatively assess the significance of the informal economy on welfare, focusing on the gains related to efficiency and redistribution. This extension corresponds to the framework developed in Doligalski and Rojas (2023), which introduces comprehensive heterogeneity in productivity profiles and the costs associated with participation in the informal sector. There, we provide the optimal tax formula across various social welfare functions and utilize Colombian data for empirical estimation.

Our approach involves comparing the welfare outcomes under the optimal tax scheme—both in scenarios where the informal sector exists and in hypothetical situations where it is absent—with the optimal tax formula accordingly applied. To analyse the welfare impact, we employ our decomposition method across three distinct social welfare functions, each representing different redistributive preferences towards less productive individuals.

The empirical aspect of our analysis leverages the model calibrated with data from the Colombian economy, aiming to quantify the welfare implications of the informal sector under the implementation of an optimal tax scheme. This evaluation specifically considers how these welfare outcomes vary in relation to the redistributive priorities of the policy planner.

Following this introduction, we detail the model’s structure and our approach to welfare decomposition within the comprehensive framework. Subsequently, we briefly discuss Doligalski and Rojas (2023) model’s estimation process. The forthcoming section will then present our findings, shedding light on the impact of the informal sector on welfare.

3.1 Model setup

The economy is populated by a continuum of heterogeneous workers that differ in productivity type $θ∈[θ_,θ¯]⊆R+$ and in participation cost in the informal sector $κ≥0$⁠. There is no participation cost in the formal sector. Workers decide (i) whether to participate in the informal sector, which involves a fixed cost κ, and (ii) how much labour to allocate to each of the sectors they participate in. Wages in the formal and the informal sector are functions of the productivity type and are given by $wf(θ)$ and $ws(θ)$⁠, respectively. Note that workers have an option of working in both sectors simultaneously.

Note that consumption is given by the total after-tax income $yf−T(yf)+ys$ and function $v(nf+ns)$ captures the disutility of working. The last term captures the fixed cost of participating in the informal economy.

The function $V(θ,κ,T)$ then represents the utility attained by a worker with productivity type θ and participation cost κ under the tax scheme T.

3.2 Government’s problem

Doligalski and Rojas (2023) tackle this optimisation problem, deriving a sufficient statistics formula for the optimal tax schedule. This formula extends the Diamond-Saez optimal tax formula by incorporating behavioural responses of workers engaged in part-time informal activities as well as extensive-margin transitions out of formality.

In what follows, we denote by T(y) the optimal tax schedule in the economy with an informal sector. We also consider a hypothetical scenario in which the informal sector is not present. Since then, the model coincides with the Mirrlees model, we call the optimal allocation in this scenario a ‘Mirrleesian’ allocation. The tax schedule consistent with a Mirrleesian allocation is denoted by $TM(y)$⁠.

3.3 Generalized welfare decomposition

We extend the welfare decomposition to the full model in the following proposition. 

The efficiency gain $EG$ is the difference in the social welfare between the optimal and the Mirrleesian allocations if each agent where to consume her total income. Intuitively, it is a measure of social welfare before redistribution. It captures the influence of the informal sector on the allocation of labour supply, including the fixed cost of shadow employment. Suppose that some workers are more productive in the informal sector than in the formal sector and that for the others, the marginal tax rates are higher in the Mirrleesian economy. Then, as long as the aggregate fixed cost of shadow employment of non-formal workers is not too large, the efficiency gain will be positive. In that case, the informal sector enhances the efficiency of labour supply. Alternatively, if the shadow productivity is relatively low and the fixed cost of shadow employment is high, the efficiency gain can be negative.

The redistributive gain $RG$ is the difference in welfare-weighted taxes and transfers. It captures the influence of the informal sector on the optimal allocation of tax burden among workers. If in the absence of the informal sector, the planner is able to reduce taxes for individuals with high Pareto weights (for example, low-productivity individuals) and increase taxes for individuals with low Pareto weights (for example, high-productivity individuals), then the redistributive gain will be negative. In that case, the informal sector restricts redistribution. Alternatively, if the shadow economy allows the planner to raise transfers at low-income levels, the redistributive gain can be positive.

3.4 Parametrisation

For our empirical calibration, we adopt the parameter estimates from Doligalski and Rojas (2023), utilizing data from the Colombian household survey from 2013. This dataset enables distinction between formal and informal incomes and includes various individual and job characteristics. The model is estimated using maximum likelihood, where key assumptions include a log-linear relationship between individual characteristics and sector-specific wages, and the distribution of κ is modelled using a generalized Pareto distribution. This methodology accounts for self-selection into sectors without imposing restrictions on the productivity distribution. Figure 2 shows the estimated productivity profiles and the density of productivity types in Doligalski and Rojas (2023).

The density of productivity types (⁠$θ$⁠) is approximately normal, excluding the tails, resulting in sectoral wages being distributed roughly log-normally with a Pareto tail. Central to our analysis is the relative productivity between shadow and formal work across the population. According to our calibration, the bottom quarter of workers are more productive in the shadow sector, while the median worker is 16% more productive in the formal sector. For the 90th percentile worker, productivity is 40% higher in the formal sector.

This widening of the relative advantage across sectors is depicted in Figure 2. Low-productivity individuals face minimal or no productivity loss by participating in the shadow sector, while this loss increases with productivity. For each percentage point increase in the productivity type, shadow productivity increases on average by 1.2%, whereas formal productivity increases by 1.9%.

We want to examine the impact of the shadow economy under different assumptions about the government’s redistributive preferences (controlled by the parameter r). To that end, we consider three scenarios that span the varying degree of government’s concern for inequality, ranging from a weak to a strong concern. The scenarios are: (i) weakly redistributive (r = 1.1), (ii) moderately redistributive (r = 1.4), and (iii) strongly redistributive (r = 1.8). To illustrate the three scenarios, let us compare the Pareto weights of the bottom type $θ_$ and the type in the 90th percentile of the productivity distribution. In the weakly redistributive case, the Pareto weight of the bottom type is 26% higher than the weight of an agent in the 90th percentile of θ. In a moderately and strongly redistributive cases, the Pareto weight of the bottom type is 150% and 530% higher, respectively.

4. Results

This section quantifies the welfare impact of the informal sector by comparing the optimal allocation in our calibrated model with a counterfactual scenario where the informal sector is absent (termed the Mirrleesian economy).

In the left column of Figure 3, we present a comparative analysis of the optimal tax schedules in both economies. The Mirrleesian economy is characterized by sharply increasing marginal tax rates at lower income levels. At higher income levels, the tax rates level out and, in more redistributive cases, exhibit a U-shape, whereby they first fall and then rise again. Conversely, in scenarios incorporating the informal sector, tax rates remain relatively stable at lower income levels, escalating only near the median income level (approximately $10,000). The tax schedules for economies with weak redistributive preferences align above this income threshold. With strong redistributive preferences, the informal sector’s presence generally lowers tax rates across a broad income spectrum, excluding the highest earners.

Our model, calibrated with Colombian data, illustrates the nuanced welfare considerations introduced by informality. We observe a positive efficiency gain and a negative redistributive impact from the Colombian informal sector (refer to the right column of Figure 3). Under weak redistributive preferences, the informal sector’s net effect is welfare-enhancing, equating to a 1% up-tick in consumption. With moderately strong preferences, the welfare gain is reduced to 0.25%. When we consider strongly redistributive preferences, the welfare gain from the informal sector becomes negative, and is equivalent to a 3% decrease in consumption.

Applying the welfare decomposition, we find that the informal sector bolsters efficiency but dampens redistribution (see Table 1). The reason behind that is two-fold. First, the least productive individuals exhibit higher productivity in the informal versus the formal sector, amplifying efficiency gains. Second, the informal sector leads to lower optimal tax rates on formal income. That contributes to lower labour distortions in the formal sector, enhancing efficiency but simultaneously curtailing redistribution. Notably, the adverse impact on redistribution becomes particularly pronounced under strong redistributive preferences, where the shortfall in redistribution outweighs efficiency benefits.

Figure 4 dissects the efficiency and redistribution gains across different levels of productivity and participation costs for each social preference scenario, revealing substantial heterogeneity among the population. Focusing first on the redistribution gain, we observe that low-productivity individuals lose and high-productivity individuals gain from the presence of the informal sector, which is due to lower income redistribution. Both the magnitude of losses and gains, as well as the proportion of agents losing, increase with the strength of the planner’s redistributive preferences. Furthermore, the redistribution gain is particularly high for high-productivity individuals with low fixed cost of informality (the right column), who further decrease their tax bill by working partially in the informal sector.

Consider now the efficiency gain. Agents with high fixed cost of informality who work only in the formal sector (the left column) experience small efficiency gains from the informal sector due to lower marginal tax rates and, thus, lower labour supply distortions. In comparison, agents who face no fixed cost of working informally (right column) are affected on the efficiency dimension not only via the marginal tax rates in the formal sector but also via their productivity in the informal sector (where they tend to supply a part of their labour). Among them, low-productivity agents are more productive informally than in the formal sector and experience additional efficiency gains, while high-productivity agents are less productive informally and, thus, suffer efficiency losses.

Finally, consider the total impact of the shadow economy on agents’ utilities. When social preferences for redistribution are weak, both low-productivity agents who can engage in informal activities and all high-productivity agents gain from the existence of the informal sector. As a result, the shadow economy is, overall, welfare-improving. However, as the strength of the redistributive motive increases, the losses of low-productivity types due to restricted income redistribution become more severe, implying that all low-productivity types lose because of the informal sector. Since the social welfare function places a higher weight on these individuals, the shadow economy becomes less beneficial (moderately redistributive scenario) or harmful (strongly redistributive scenario) for social welfare.

5. Policy Implications

The standard view is that the shadow economy harms welfare by reducing tax capacity and limiting the government’s ability to redistribute. However, our analysis shows that this view is incomplete. The shadow sector also provides efficiency gains by allowing low-productivity individuals to avoid tax distortions. These efficiency gains can offset the redistribution costs of informality, which are mainly imposed by high-productivity individuals who use the shadow sector to evade taxes.

Building on this insight, our paper provides a more nuanced understanding of the role of the informal sector in the welfare implications of optimal redistribution policy. Informality among high-productivity workers harms the government’s ability to redistribute and finance public expenditures. The removal of such informality should thus be a priority in policy considerations. In contrast, tax evasion by low-productivity individuals can lead to welfare gains from a redistributive perspective.

Extending this view to tax enforcement or audit design, efforts should aim to make it more costly for high-productivity workers to participate in the shadow sector. For example, penalties could be highly progressive concerning the amount of income concealed in the shadow sector and could further increase based on any signals of high productivity, such as formal income.

Our quantitative exercise with the model calibrated to Colombian data illustrates how the balance between the gains and costs of the informal sector can shift depending on the strength of a government’s preferences for redistribution. For a government with weak redistributive desires, the presence of the shadow economy can lead to better outcomes, characterized by minimal redistribution costs and significant efficiency gains. However, as the desire to redistribute increases, the efficiency gains are overshadowed by the redistribution costs.

Regarding tax enforcement and audits, if targeting enforcement across the productivity distribution is costly, then for a government with ambitious redistribution objectives, enforcement is highly complementary to a progressive tax scheme. Conversely, for a government with more moderate redistribution objectives, low enforcement, even if it has low cost, can be optimal.

This nuanced approach suggests that policy measures should be tailored to the specific redistributive goals of the government. High enforcement costs may necessitate targeted strategies that maximise compliance among high-productivity individuals, while more moderate goals might be achieved with a less aggressive enforcement stance. This flexibility allows for a more effective balance between efficiency and equity in tax policy.

Finally, our analysis reveals that the relationship between the size of the shadow economy and redistribution capacity is more complex than it appears. The impact of the shadow economy on redistribution is not solely a function of its size but also of the demographic and economic characteristics of those who participate in it. Understanding which parts of the population are overrepresented in the shadow sector is crucial to grasping the extent to which it limits redistribution.

Studies have shown that the composition of the shadow economy varies widely across countries and even within regions of a country. For instance, Schneider and Enste (2000) highlight that in many developing countries, the shadow economy often includes a large proportion of low-skilled workers, whereas in some developed countries, high-skilled professionals tend to engage more in informal activities. According to our analysis, it is the latter scenario—where high-skilled professionals are more involved in the shadow economy—that poses a greater threat to redistribution.

An important caveat is that this discussion focuses on the taxation aspect of informality. It does not address potential regulatory avoidance, such as food safety standards, which could increase the costs of informality, or dynamic concerns related to differences in human capital acquisition between the informal and formal markets.

6. Conclusions

This work studies the welfare implications of the informal sector, introducing a novel approach to decomposing the change in social welfare into ‘efficiency gain’ and ‘redistributive gain’. Traditional methods, such as evaluating the social welfare function or examining the Pareto frontier, conflate efficiency with redistribution, obscuring the specific drivers of welfare changes. Our decomposition method clarifies this ambiguity, distinguishing between welfare improvements due to more efficient labour allocation and those arising from equitable tax redistribution.

Applied to the Colombian context, our findings reveal that the shadow economy strengthens efficiency of labour supply at the expense of possible redistribution. When preferences for redistribution are weak, the former channel dominates and the existence of the shadow economy is welfare improving. These results highlight the non-trivial welfare implications of informality.

Looking forward, our analysis opens several pathways for extending this research. First, considering government interventions like audits and penalties could refine our understanding of how differentiated enforcement strategies influence the shadow economy’s welfare effects. Such measures could potentially align tax evasion opportunities with welfare optimisation rather than merely curbing evasion (Cremer and Gahvari, 1996). Moreover, our welfare decomposition technique can illuminate the efficiency and redistributive outcomes of various economic changes, from structural shifts to educational advancements, independent of informality’s context.

Funding

Funding support for this article was provided by the European Research Council under the European Union’s Horizon 2020 research and innovation progra 788547-APMPAL-HET (788547-APMPAL-HET), MICIU/AEI/10.13039/501100011033 and FEDER, UE PID2023-147183NB-I00 (PID2023-147183NB-I00).

Footnotes

Acknowledgements

Luis E. Rojas acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation program (788547-APMPAL-HET). We are grateful for the useful comments of Árpád Ábrahám, Charles Brendon, Antoine Camous, Hal Cole, Mike Golosov, Piero Gottardi, Ramon Marimon, Wojciech Kopczuk, Dirk Krueger, Humberto Moreira, Erwin Ooghe, Wojciech Paczos, Evi Pappa, Dominik Sachs, Julia Schmieder, Jon Temple, and Yanos Zylberberg. All errors remain our own.

References

Appendix A

Proof from Section 2 

To see that the planner optimally distorts the labour supply of type i, notice that a marginal adjustment of $yif$⁠, starting from the undistorted level $yif∗$⁠, has no direct impact on welfare of type i by the Envelope Theorem. However, the distortion in a correct direction will reduce the payoff of –i from misreporting, relax the incentive constraint and, hence, allow for more redistribution. In particular, if $wif<w−if$ (⁠$wif>w−if$⁠), a marginal decrease (increase) of $yif$ will relax the incentive constraint. □ 

Define a function $Ψ(w)≡U(wv′−1(w),v′−1(w))$⁠, equal to the utility level of an individual with productivity w who supplies labour efficiently and receives no transfers. The efficiency term can be restated as $λiμi(Ψ(wis)−U(wifniM,niM))$⁠. Since $Ψ$ is an increasing function, the efficiency gain is increasing in $wis$ and changes sign at $w¯is≡Ψ−1(U(wifniM,niM))$⁠. To see that $w¯is<wif$⁠, note that since $niM$ is distorted, $Ψ(wif)>U(wifniM,niM)$⁠.

Combining it with (A.2), we find that $TiM−TiSE=μ−i(U(wifniM,wifniM/w−if)−Ψ(w−is)).$ It implies that the redistribution term is decreasing in $w−is$ and changes sign at $w¯−is≡Ψ−1(U(wifniM,wifniM/w−if))$⁠. $w¯−is<w−if$ holds, since $U(wifniM,wifniM/w−if)<Ψ(w−if)$ due to the optimal distortion of $niM$⁠. □