Abstract
This paper studies the effects of several tax reforms in an economy where taxes are partially evaded by means of undeclared work. To this purpose, we consider a twosector dynamic general equilibrium model calibrated to Italy which explicitly accounts for underground production. We construct various tax reform scenarios, such as ex ante budgetneutral tax shifts from direct to indirect taxes, and tax cuts on labor and business financed by decreases of government spending. Our results indicate that neglecting the existence of the underground sector may lead to severely miscalculating the macroeconomic effects of tax reforms. Further, the dimension of the underground sector is permanently and considerably reduced by changes in the tax mix that diminish the labor tax wedge. Reductions of the business tax prove to be highly expansionary in the presence of a sizable informal sector.
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Notes
 1.
Of course there are other factors playing an important role, such as the possibility of tax avoidance, which affects the extent of tax evasion and, therefore, the size of the underground economy. See, e.g., Neck et al. (2012).
 2.
Along this line of research, see Feltenstein and Shamloo (2013).
 3.
A laudable exception is given by the recent contribution of Pappa et al. (2015) who study the effects of fiscal consolidation accounting for the presence of tax evasion and corruption. In their analysis, conducted for Greece, Italy, Portugal and Spain, they unambiguously show that the recent consolidation plans introduced in these economies tend to increase tax evasion.
 4.
In doing so we enrich the analysis of Busato et al. (2012) who focus on the effects of tax reductions on labor and income, with public spending being determined endogenously so as to preserve the balance of the public budget constraint at all times.
 5.
In this respect, through the use of a macroeconomic model embodying an underground sector, this paper contributes to the vast literature studying the effects of tax distortions and measuring the impact of tax reforms involving tax shifts or changes in public spending met by adjustments in taxes (see e.g. Baxter and King 1993, Mendoza and Tesar 1998, Leeper and Yang 2008).
 6.
See the OECD Tax Database available online at https://data.oecd.org/tax/taxwedge.htm. The tax wedge is measured as the ratio between the amount of taxes paid by a single worker at 100% of average earnings without children and the corresponding total labor cost borne by the employer.
 7.
This value arises when considering only the market economy, that is excluding the nonmarket services provided by Public Administrations. When the latter are included, the estimate of the underground economy reduces to 17.5% of GDP. See ISTAT (2010).
 8.
This discrepancy of estimates can be partly explained by the fact that different definitions of the shadow economy entail different measurements. For instance, Buehn and Schneider (2016) claim that explicit shadow activities—that is, shadow activities from ‘black’ hours worked—only account for about one third of the shadow economy. See also Zizza (2002) for further details.
 9.
The model abstracts from international mobility of productive factors. Yet illegal immigration and the size of the informal sector in the destination country are strongly intertwined, as shown by Dell’Aringa and Neri (1987) for the Italian economy. For a comprehensive analysis on Southern Europe, see BaldwinEdwards and Arango (1999). For a nice theoretical model dealing with this unexplored aspect and the implied economic policy implications, see Camacho et al. (2017).
 10.
On the contrary the final good sector can only operate formally. Since production of the final good sector utilizes domestic and foreign intermediate inputs a value added tax scheme could be introduced into the model, so allowing for tax evasion also in this sector. Notably, being based on a creditandrefund scheme, the VAT is strongly vulnerable to evasion, fraud and tax avoidance. For instance, over the period 2009–2013, Italy reported an average VAT gap of 33%. See European Commission (2015a). For an analysis of revenueneutral tax shifts accounting for the existence of a VAT creditandrefund scheme, see Paz (2015).
 11.
As is common practice in new open economy macroeconomics, we assume that the elasticity of substitution between varieties in the tradable sector is the same for the domestic and the imported bundle.
 12.
Perfect competition can be rejected for almost all sectors in all countries and Italy is not an exception. See Christopoulou and Vermeulen (2012).
 13.
The existence of price stickiness is fully supported by empirical evidence. See, e.g, Alvarez et al. (2006) and Dhyne et al. (2006). In general, a marked heterogeneity in the frequency of price adjustment is found across sectors. Further, prices seem to change less frequently in Europe than in the United States.
 14.
For instance, Gallaway and Bernasek (2002) and Marcelli et al. (1999) show that, at least in urban settings, low skilled workers are more likely to work in the irregular sector compared to those workers who attained a higher level of education. Amaral and Quintin (2006) link the presence of lowskill workers in the underground sector to the fact that informal managers have access to less outside finance than their formal counterpart, and they substitute part of physical capital with lowskill workers. Further, Paz (2014) points out that small firms are more likely to hire informal workers. Since capital intensity tends to increase with firm size, this stylized fact is consistent with the assumption we make that in the informal sector firms are less capital intensive.
 15.
On the notion of ‘moonlighting production’, see e.g. Bajada (1999) and Cowell (1990). This scheme allows us to capture the fact that firms operate simultaneously in the official and in the unofficial sectors. Several causes have been listed in the literature to explain the coexistence of formal and informal production within the same firm in contrast to a ‘ghost’ type production scheme, where firms opt to operate only in the informal sector. For instance, participation in the official market facilitates access to credit and public sector services and grants property right protection. Official production may also represent a valuable shield against fiscal audits for firms engaging in underground production. Moreover, openness to trade implies that export products should meet the requirements of the destination country, which looks in principle less likely for ‘ghost’, unregistered, firms. Our choice is also supported by the empirical evidence showing the predominance of this scheme of informality for Italian firms (see Mantegazza et al. 2014).
 16.
This property, together with homogeneity and the fact that both \(Y_{i,t}^{m}\) and \(Y_{i,t}^{u}\) can be both used in the final good production function with no additional costs, suggests that this model with underground economy could be more appropriately defined a twotechnology model rather than a twosector model.
 17.
For evidence of habit formation in consumption of Italian households, see Rossi (2005).
 18.
Despite the absence of adjustment costs on shifting labor supply or demand from one market to another, each labor market has its own specific characteristics that this extra term tries to represent.
 19.
 20.
The price at time t of a riskfree asset that pays one unit of currency in period \(t+1\) has to be equal to the inverse of the riskfree nominal (gross) interest rate \(R_{t}\), that is \(Q_{t}=R_{t}^{1}\).
 21.
In other words, there is a premium on foreign bond holdings which is a function of the aggregate net foreign asset position of the domestic households. The existence of this debt elastic risk premium is necessary to induce stationarity of the equilibrium dynamics. For details, see SchmittGrohé and Uribe (2003).
 22.
This assumption implies that all the observed changes in the terms of trade are to be ascribed to changes in the price level \(P_{t},\) since \(P_{t}^{*}\) is also kept constant. See Eq. (31). This is due to the fact that we assume perfect passthrough, therefore any change in the price of domestic varieties is fully reflected in the price of exportations.
 23.
This assumption allows us to switch off any possible feedback channels coming from monetary policy.
 24.
These estimates have been obtained on the sample period 1982–2006.
 25.
 26.
Deterministic simulations are carried out when studying the effects of structural and/or policy interventions involving permanent changes in some structural parameters and/or tax rates.
 27.
Recently many EU Member States have been attempting to strike the balance between economic recovery and fiscal soundness by reducing the tax burden on labor and by narrowing the tax base of corporate income taxation, while increasing consumption taxes. Lower tax wedges on labor, in fact, ought to lead to a significant rise in labor utilization and, thereby, to a higher level of economic activity. Similarly, alleviating the tax burden on business may stimulate investment. However, given the risk for public finance, lower labor and business taxes need to be compensated by increases in other sources of revenue, such as consumption taxes, or by public spending cuts. For further details, see European Commission (2015b).
 28.
Moreover, in the last years, personal income tax has also been reduced for those starting a new business and to the benefits of those embarking on home renovation works. Other sectors involved regard art, sport, and tourism.
 29.
See the note available from Italian Ministry of Economics and Finance website at http://www.mef.gov.it/inevidenza/article_0190.html and the information made available from the spending review working group at http://revisionedellaspesa.gov.it/.
 30.
We have also conducted a more standard analysis in which we vary the marginal tax rates by 1 p.p. in isolation. This analysis is useful to uncover the forces at work in each combined policy scenario. See Appendix 2.
 31.
This could be interpreted as a reduction in the sum of the tax on labor income and workers’ SSC, reflecting the fact that these two wedges isomorphically affect households decisions.
 32.
As shown in Appendix 3, similar results emerge after a fiscal policy envisaging a reduction of the business tax base, rather than a cut of the tax rate.
 33.
Similar qualitative results are obtained in response to a reduction of SSC bearing on firms financed by a cut in government spending. See Appendix 3.
 34.
It should be noted that the model is calibrated and solved on a quarterly basis. We do not show the full transition dynamics, rather we report the effects of tax reforms over a 20quarter horizon.
 35.
See Appendix 1 for details.
 36.
It can been shown that in closed economy and, therefore, of external competition, the tax reforms induce firms to expand their production by more by decreasing the markup immediately. This effect tends to be stronger, the smaller the dimension of the underground sector, so exacerbating the shortrun differences in the reaction of output under different sizes of the informal sector. These results are available from the authors upon request.
 37.
In Appendix 4 we investigate the role played by nominal and real rigidities in determining the speed of adjustment toward the new steady state.
 38.
Given the parametrization of the model, the term \(1ps\tau _{t}^{y}\) is always larger than zero. This rules out the possibility that \(H_{i,t}^{u}=0\).
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Acknowledgements
We thank the editor and two anonymous referees for their excellent comments. This paper has also benefited from the comments and suggestions of Amedeo Argentiero, Andrea Costa, Fabio Di Dio, Edgar L. Feige, Giammario Impullitti, Elisabetta Marzano, Libero Monteforte, Alessandra Pelloni, Lorenza Rossi, Emilio Zanetti Chini, seminar participants at the Università degli Studi di Roma “Tor Vergata” and participants at the Shadow Conference 2015, University of Exeter and at the 56th Annual Conference of the Italian Economic Association, Università Parthenope, Naples.
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Appendices
Appendix 1
Marginal costs of production in the intermediate good sector
This appendix derives the expression for firms’ marginal costs in order to show that they are equal for all producing firms. To see this, take the intermediate producers’ firstorder conditions with respect to regular labor, underground labor, and capital, respectively Eqs. (12), (13), and (14)^{Footnote 38}
and use the first two to substitute for \(\hbox {MC}_{i,t}^{N}Y_{i,t}^{m}\) and \(\hbox {MC}_{i,t}^{N}Y_{i,t}^{u}\) into (14), to obtain
Now, use again Eqs. (12) and (13) after having substituted in them for \(Y_{i,t}^{m}\) and \(Y_{i,t}^{m}\) from Eqs. (7) and (8), respectively, and rearrange them as to have expressions for \(\frac{H_{i,t}^{m}}{K_{i,t}}\) and \(\frac{H_{i,t}^{u}}{K_{i,t}}\). By substituting these two ratios into (36), we obtain
which solved for \(\hbox {MC}_{i,t}^{N}\) shows how the latter does not depend on firm specific variables, that is, it is equal for all firms.
Complete set of equilibrium conditions

\(P_{t}^{F}Y_{t}^{F}=P_{t}Y_{t}^{H}+S_{t}P_{t}^{M}M_{t},\) equilibrium condition in the final good sector

\(Y_{t}^{H}=(1\alpha _{M})\left( \frac{P_{t}}{P_{t}^{F}}\right) ^{\sigma _{M}}Y_{t}^{F},\) demand for domestic intermediate goods

\(M_{t}=\alpha _{M}\left( \frac{S_{t}P_{t}^{M}}{P_{t}^{F}}\right) ^{\sigma _{M}}Y_{t}^{F},\) demand for foreign intermediate goods (imports)

\(Y_{t}=Y_{t}^{H}+X_{t},\) equilibrium condition in the intermediate good sector good sector

\(X_{t}=\alpha _{X}\left( \frac{P_{t}}{S_{t}P_{t}^{F^{*}}}\right) ^{\sigma _{X}}Y_{t}^{F^{*}},\) foreign demand for domestic intermediate goods (exports)

\(Y_{t}^{m}=\Delta _{t}^{1}A^{m}\left( H_{t}^{m}\right) ^{\alpha } K_{t}^{1\alpha },\) legal production of intermediate goods

\(Y_{t}^{u}=\Delta _{t}^{1}A^{u}\left( H_{t}^{u}\right) _{u}^{\alpha }K_{t}^{1\alpha _{u}},\) underground production of intermediate goods

\(Y_{t}=Y_{t}^{m}+Y_{t}^{u},\) total production of intermediate goods

\((1+\tau _{t}^{f,s})W_{t}^{m}=\frac{\alpha \hbox {MC}_{t}^{N}Y_{t}^{m}}{H_{t} ^{m}},\) demand for legal labor

\((1+ps\tau _{t}^{f,s})W_{t}^{u}=\frac{\alpha _{u}\hbox {MC}_{t}^{N}Y_{t}^{u} }{H_{t}^{u}},\) demand for illegal labor

\(R_{t}^{k}=\hbox {MC}_{t}^{N}\left[ (1\alpha )\frac{Y_{t}^{m}}{K_{t}} +(1\alpha _{u})\frac{Y_{t}^{u}}{K_{t}}\right] ,\) demand for capital

\(\widehat{p}_{t}=\frac{\theta }{\theta 1}\frac{E_{t}\sum _{j=0}^{\infty }\psi ^{j}Q_{t,t+j}^{R}\hbox {MC}_{i,t+j}\left( \frac{P_{t+j}}{P_{t}}\right) ^{\theta _{Y}}Y_{t+j}}{E_{t}\sum _{j=0}^{\infty }\psi ^{j}Q_{t,t+j}^{R}\left[ (1\tau _{t+j}^{y})+\tau _{t+j}^{y}(1ps)\frac{Y_{i,t}^{u}}{Y_{i,t}}\right] \left( \frac{P_{t+j}}{P_{t}}\right) ^{\theta _{Y}1}Y_{t+j}},\) optimal price setting condition (where \(Q_{t,t+j}^{R}=\beta \frac{\lambda _{t+j}}{\lambda _{t} }\))

\(1=\psi \varPi _{t}^{\theta 1}+\left( 1\psi \right) \widehat{p} _{t}^{1\theta },\) PPI inflation

\(\Delta _{t}=\left( 1\psi \right) ^{\theta }+\psi \varPi _{t}^{\theta } \Delta _{t1},\) price dispersion

\(\lambda _{t}=\frac{\left( C_{t}\eta \bar{C}_{t1}\right) ^{\sigma } }{1+\tau _{t}^{c}}\frac{P_{t}}{P_{t}^{F}},\) firstorder condition of the representative household with respect to consumption

\(\,H_{t}^{m}+H_{t}^{u}=\lambda _{t}^{\frac{1}{\xi }}\left[ \frac{(1\tau _{t}^{h}\tau _{t}^{h,s})W_{t}^{m}/P_{t}}{\varGamma _{0}}\right] ^{\frac{1}{\xi }},\) total labor supply

\({H_{t}^{u}\!=\! {\left\{ \begin{array}{ll} \lambda _{t}{}^{\frac{1}{\varphi }}\left( \frac{\left[ 1ps(\tau _{t}^{h} +\tau _{t}^{h,s})\right] \frac{W_{t}^{u}}{P_{t}}(1\tau _{t}^{h}\tau _{t}^{h,s})\frac{W_{t}^{m}}{P_{t}}}{\varGamma _{1}}\right) ^{\frac{1}{\varphi } }\!\!, &{} \text {if} \; \left[ 1ps(\tau _{t}^{h}+\tau _{t}^{h,s})\right] \frac{W_{t}^{u}}{P_{t}}\\ &{}\quad \quad \ge (1\tau _{t}^{h}\tau _{t}^{s,h})\frac{W_{t}^{m} }{P_{t}},\\ 0, &{} \text {otherwise,} \end{array}\right. }} \) supply of illegal labor

\(Q_{t}=\beta E_{t}\frac{\lambda _{t+1}}{\lambda _{t}}\frac{P_{t}^{F} }{P_{t+1}^{F}},\) Euler equation (nominal riskfree asset)

\(K_{t+1}=(1\delta )K_{t}+\left[ 1S\left( \frac{I_{t}}{I_{t1} }\right) \right] I_{t}\) with \(S\left( \frac{I_{t}}{I_{t1}}\right) =\frac{\phi _{I}}{2}\left( \frac{I_{t}}{I_{t1}}1\right) ^{2}\), accumulation of physical capital

\(q_{t}=\beta E_{t}\frac{\lambda _{t+1}}{\lambda _{t}}\left[ (1\tau _{t+1}^{k})\frac{R_{t+1}^{k}}{P_{t+1}}+q_{t+1}(1\delta )\right] ,\) firstorder condition of the representative household with respect to capital where \(q_{t}\) is the Tobin’s q

\(1=q_{t}\frac{P_{t}}{P_{t}^{F}}\left[ 1\phi _{I}\left( \frac{I_{t} }{I_{t1}}1\right) \frac{I_{t}}{I_{t1}}\frac{\phi _{I}}{2}\left( \frac{I_{t}}{I_{t1}}1\right) ^{2}\right] +\beta E_{t}q_{t+1}\frac{\lambda _{t+1}}{\lambda _{t}}\frac{P_{t}}{P_{t}^{F}}\phi _{I}\left( \frac{I_{t+1}}{I_{t}}1\right) \left( \frac{I_{t+1}}{I_{t}}\right) ^{2},\) firstorder condition of the representative household with respect to investment

\(\frac{\lambda _{t}S_{t}}{P_{t}}=\beta \frac{E_{t}\lambda _{t+1}S_{t+1} }{P_{t+1}}R_{t}^{*},\) Euler equation on foreign asset

\(R_{t}^{1}B_{t+1}=B_{t}+P_{t}^{F}G_{t}T_{t},\) public debt

\(T_{t}=(\tau _{t}^{h}+\tau _{t}^{h,s}+\tau _{t}^{f,s})W_{t}^{m}H_{t} ^{m}+ps(\tau _{t}^{h}+\tau _{t}^{h,s}+\tau _{t}^{f,s})W_{t}^{u}H_{t}^{u}+\tau _{t}^{c}P_{t}^{Y}C_{t}+\tau _{t}^{y}P_{t}\left( Y_{t}^{m}+psY_{t}^{u}\right) +T_{t}^{ls},\) total tax revenues

\(S_{t}F_{t+1}=R_{t}^{*}S_{t}F_{t}+P_{t}X_{t}S_{t}P_{t}^{M}M_{t},\) foreign asset equation

\(R_{t}^{*}=\tilde{R}_{t}^{*}\varphi ^{F}(e^{f_{t}f}1),\) riskadjusted interest rate on foreign asset

\(Y_{t}=\frac{P_{t}^{F}}{P_{t}}C_{t}+\frac{P_{t}^{F}}{P_{t}}G_{t} +\frac{P_{t}^{F}}{P_{t}}I_{t}+X_{t}\frac{S_{t}P_{t}^{M}}{P_{t}}M_{t},\) resource constraint of the economy

\(\hbox {ToT}_{t}=\frac{P_{t}}{P_{t}^{M}}=\frac{P_{t}}{S_{t}P_{t}^{*}}\), terms of trade
The (average) markup is given by \(P_{t}/\hbox {MC}_{t}^{N}.\) Trade balance as a fraction of output is measured as \(\left( X_{t}\frac{S_{t}P_{t}^{M}}{P_{t} }M_{t}\right) /Y_{t}.\)
The model is solved under the two following monetary and fiscal policy hypotheses:

\(S_{t}=S,\)

\(T_{t}^{ls}\) adjusts so that \(B_{t}/P_{t}\) is constant over time.
Welfare computation
This appendix describes the welfare measure we use to evaluate the effects of the envisaged tax reform scenarios. Let a and b be two alternative generic policies that can be implemented by the government. Then, the present discounted value of the utility flow under policy a is:
where \(C_{t}^{a}\), \(H_{t}^{m,a}\), and \(H_{t}^{u,a}\) respectively denote consumption, regular hours, and irregular hours under policy a, and T is the time horizon we are interested in evaluating the welfare effects of the reform. Similarly, the present discounted value of the utility flow under policy b is:
where clearly, \(C_{t}^{b}\), \(H_{t}^{m,b}\), and \(H_{t}^{u,b}\), respectively, denote consumption, regular hours, and irregular hours under policy b. The welfare cost of adopting policy a instead of policy b is defined as the constant fraction of consumption, \(\omega \), that individuals have to give up under policy b in order to be indifferent between the two policies. Formally, \(\omega \) represents the solution to the following identity:
If computed in this way, \(\omega \) allows to capture the transitional welfare effects of different fiscal reforms. Another broadly used measure of welfare only looks at the steady state effects of policy reforms. Similarly to (40), the steady state welfare cost \(\omega _{ss}\) solves
The distinction between transitional and steady state welfare effects is important since it might be the case that a policy is welfare improving in the steady state, whereas it generates negative effects in transition (and vice versa).
Appendix 2
In what follows we report the transition dynamics and the steadystate effects of marginal changes in the tax rates and in public expenditure. We consider each policy intervention in isolation. Of course in this case the policy experiments are not fully comparable, since the tax bases are different. As in the case of revenueneutral policy combinations, we observe that the stronger effects on output are recorded in case of a small underground sector. The terms of trade effect operates, as in the combined experiments, by diminishing the differences across economies in the shortrun (Figs. 6, 7, 8, 9, 10; Table 11).
Appendix 3
In this appendix we show the effects of two additional fiscal experiments, namely (1) 0.5% of output reduction of the business tax base achieved by introducing a partial deductibility of labor cost and financed by an increase in the consumption tax (Table 12); (2) 0.5% of output cut in SSC bearing on firms financed by an equal size reduction of public spending (Table 13). For each variable and dimension of the underground sector we report a vector of three elements, where the first two elements refer to 1 and 5 years, while the third element refers to the impact of the reform on the longrun (steadystate) levels of economic activity.
Appendix 4
In this appendix we explore the role of frictions in shaping the response of the economy. For each variable, scenario and dimension of the underground sector, we report a vector of three elements, where the first two elements refer to 1 and 5 years, while the third element refers to the impact of the reform on the longrun (steadystate) levels of economic activity.
In Table 14 all the fiscal experiments are conducted by removing the adjustment costs on investments, consumption habit and nominal rigidities. In the absence of any frictions all variables adjust immediately to the new fiscal system. We observe major reactions of consumption and investment, as a result of the absence of habit and of real adjustment costs, while the markup reaches immediately its long run level since prices are fully flexible and price setters can immediately adjust them so as to maximize current profits.
Table 15 shows the impact of the tax reforms in an economy featuring real frictions but not nominal rigidities, while Table 16 presents the results for an economy displaying only habit formation, but neither adjustment cost on investments, nor nominal frictions. Under flexible prices, but with real frictions on investment and consumption, the 1 year response of the economy to the fiscal reforms envisaging a cut of the business tax is minor, since the average markup does not overshoot its long run level, as observed in the benchmark case. On the contrary, in \(S_{2}\), \(S_{3}\) and \(S_{5}\) the markup does not jump up excessively, therefore the initial impact on output is higher than in the benchmark case. Under the assumption that the only friction characterizing the economy is given by habit persistence, as expected, investments are shown to be more reactive in the shortrun than in the benchmark case.
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Annicchiarico, B., Cesaroni, C. Tax reforms and the underground economy: a simulationbased analysis. Int Tax Public Finance 25, 458–518 (2018). https://doi.org/10.1007/s1079701794507
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Keywords
 Dynamic general equilibrium model
 Underground economy
 Tax reforms
 Italy
JEL Classification
 E62
 O41
 O52