Taxing income or consumption: Macroeconomic and distributional effects for Italy

D'Andria, Diego; DeBacker, Jason; Evans, Richard W.; Pycroft, Jonathan; Zachlod- Jelec, Magdalena Working Paper Taxing income or consumption: Macroeconomic and distributional effects for Italy JRC Working Papers on Taxation and Structural Reforms, No. 13/2021 Provided in Cooperation with: Joint Research Centre (JRC), European Commission Suggested Citation: D'Andria, Diego; DeBacker, Jason; Evans, Richard W.; Pycroft, Jonathan; Zachlod- Jelec, Magdalena (2021) : Taxing income or consumption: Macroeconomic and distributional effects for Italy, JRC Working Papers on Taxation and Structural Reforms, No. 13/2021, European Commission, Joint Research Centre (JRC), Seville This Version is available at: https://hdl.handle.net/10419/252329 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Taxing income or consumption: macroeconomic and distributional effects for Italy JRC Working Papers on Taxation and Structural Reforms No 13/2021 d'Andria Diego, DeBacker Jason, Evans Richard W., Pycroft Jonathan, Zachlod-Jelec Magdalena November 2021 This publication is a Technical report by the Joint Research Centre (JRC), the European Commission’s science and knowledge service. It aims to provide evidence-based scientific support to the European policymaking process. The scientific output expressed does not imply a policy position of the European Commission. Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use that might be made of this publication. For information on the methodology and quality underlying the data used in this publication for which the source is neither Eurostat nor other Commission services, users should contact the referenced source. The designations employed and the presentation of material on the maps do not imply the expression of any opinion whatsoever on the part of the European Union concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Contact information Name: Magdalena Zachlod-Jelec Address: Edificio EXPO, C/ Inca Garcilaso, 3, E-41092 Seville/Spain. Email: [email protected] Tel.: EU Science Hub https://ec.europa.eu/jrc JRC127016 Seville: European Commission, 2021 © European Union, 2021 The reuse policy of the European Commission is implemented by the Commission Decision 2011/833/EU of 12 December 2011 on the reuse of Commission documents (OJ L 330, 14.12.2011, p. 39). Except otherwise noted, the reuse of this document is authorised under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence (https://creativecommons.org/licenses/by/4.0/). This means that reuse is allowed provided appropriate credit is given and any changes are indicated. For any use or reproduction of photos or other material that is not owned by the EU, permission must be sought directly from the copyright holders. All content © European Union, 2021 How to cite this report: d'Andria D., DeBacker J., Evans R. W., Pycroft J., Zachlod-Jelec M. (2021), Taxing income or consumption: macroeconomic and distributional effects for Italy, JRC Working Papers on Taxation and Structural Reforms No 13/2021, European Commission, Joint Research Centre, Seville, JRC127016. Executive summary Reform proposals of the tax and benefits system are often at the centre of political debates. Taxes affect incentives to work, save and consume. They significantly modify the disposable income of households and thus address or exacerbate equity concerns, and are needed to fund public expenditure. Especially with the effects of the Covid-19 pandemic, governments face the necessity of boosting economic recovery and growth, while taking into account equity concerns and public budget constraints. When looking for a new design of the tax and benefits system that aims at enhancing both efficiency and equity, a consensus emerges to lower the tax burden on labour income. This is due to the fact that tax rates on labour income are high compared to the rates on consumption and the empirical literature suggests that labour and corporate income taxation are associated more often with poorer economic performance, compared to consumption and property taxation (e.g. Arnold et al., 2011). While the idea of a reduction of labour income taxes via a “tax shift” onto other, supposedly more efficient tax types seems to enjoy widespread consensus among practitioners and possibly among the general population in Italy, it is not yet clear what such a reform should look like. A revenue-neutral reform that would reduce personal income tax (PIT) rates and compensate lost revenues via an increase in the general value-added tax (VAT) rate can hardly preserve progressivity and will likely affect relevant groups of taxpayers differently. Also, reductions in the PIT can be achieved both by changing the tax rates or the no-tax allowance (i.e. a minimum income threshold not subject to PIT), which also brings different impacts in terms of equity and of the distribution of work incentives across the income quantiles. Finally, such reforms may cause general equilibrium and dynamic effects which should also be taken into account. The contribution of this paper is to build an analysis of potential reforms in Italy which jointly accounts for general equilibrium effects, effects across time, heterogeneous taxpayers who are differentiated by age and income levels with high granularity, and taking into account as much as possible the complex details of the real Italian tax and benefits system. We achieve this by means of an overlapping-generations computable general-equilibrium model paired with a microsimulation model of the tax and benefits system. We are thus able to overcome the limitations of the existing literature which either provides a purely microeconomic static analysis of reforms (thus disregarding any general equilibrium or dynamic effect), or an analysis based on DSGE modelling techniques, which is unable to account for the existence of many heterogeneous taxpayers and relies on stylized representations of the tax system (thus missing many of the complexities and subtle interactions of real-world tax and benefits systems). The presence of the overlapping generations on the household side breaks the Ricardian equivalence and enables a more realistic modelling of fiscal policy in the long run. Our analysis focuses on two hypothetical reform proposals that reduce PIT and obtain budget parity by increasing consumption taxes. The two studied reforms differ in the way PIT reductions are achieved: via a cut of statutory tax rates across the board or via an increase of the no-tax allowance. Our results suggest that a tax shift reform in Italy should prioritize cutting personal income tax rates, rather than extending the no-tax allowance. More importantly and perhaps counterintuitively, they point to the possibility that behavioural reactions may make the reform only mildly regressive, after accounting for dynamic and general equilibrium effects due in particular to increased labour supply of low-income households and overall savings. This result challenges a recurrent objection to such kind of tax shift policies, namely that they are necessarily regressive. While the latter may be true when limiting the analysis to a static representation of a national economy, our results point to large efficiency gains which are heterogeneous both across age and income and compensate for a large part of the reduction in progressivity of the tax schedule in the lower income deciles. i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 1 — #1 i i i i i i Taxing income or consumption: macroeconomic and distributional effects for Italy Diego d’Andriaa, Jason DeBackerb,d, Richard W. Evansc,d, Jonathan Pycroftdand Magdalena Zachlod-Jelec * e aInstitute for Employment Research (IAB), Nuremberg bDarla Moore School of Business, University of South Carolina cBaker Institute for Public Policy, Rice University dOpen Research Group eEuropean Commission Joint Research Centre, Seville Abstract We study a set of tax reforms introducing a budget-neutral tax shift in Italy, from labour income to consumption taxes. To this end we use a microsimulation model to provide the output with which to estimate the parameters of tax functions in an overlapping-generations computable general equilibrium model. In doing so we make marginal and average tax rates bivariate non-linear functions of capital income and labour income. The methodology allows for the representation of the non-linearities of the tax and social benefit system and interactions between capital and labour incomes. The linked macro model then simulates labour supply, consumption and savings in a dynamic setting, thus accounting for behavioural and general equilibrium effects within a life-cycle optimization framework. Our simulations show that a tax shift made by cutting personal income tax rates might bring significant efficiency gains in Italy, with limited regressive effects, notwithstanding the revenue-compensating increase in consumptions taxes. JEL classification: H24, H31, D15, D58. Keywords: computable general equilibrium, overlapping generations, taxation, microsimulation, Italy, tax shift.  The authors would like to thank Salvador Barrios, Ana Ag´undez Garc´ıa, Adri´an Hern´andez Mart´ın, Edlira Narazani, Alberto Tumino, and Wouter van der Wielen for valuable comments and clarifications, and seminar participants at the ZEW Public Finance Conference 2019, the International Institute for Public Finance Annual Congress 2019, the International Conference on Economic Modeling and Data Science (Eco- Mod2019) and the JRC.B2 Workshop on Fiscal Policy Modelling 2020. Errors are our own. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They should not be attributed to any of the affiliated institutions. * Corresponding author; authors’ emails: [email protected]; [email protected]; rwev[email protected]; [email protected]; magdalena.zachlo[email protected] 1 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 2 — #2 i i i i i i 1 Introduction Reform proposals of the tax and benefits system are often at the centre of political debates. Taxes affect incentives to work, save and consume. They significantly modify the disposable income of households and thus address or exacerbate equity concerns, and are needed to fund public expenditure. Especially with the effects of the COVID-19 pandemic, governments face the necessity of boosting economic recovery and growth, while taking into account equity concerns and public budget constraints. When looking for a new design of the tax and benefits system that aims at enhancing both efficiency and equity, a consensus emerges to lower the tax burden on labour income. This is due to the fact that tax rates on labour income are high compared to the rates on consumption and the empirical literature suggests that labour and corporate income taxation are associated more often with poorer economic performance, compared to consumption and property taxation (e.g. Arnold et al., 2011). Specifically in the context of Italy, international organizations like the IMF and the European Commission have repeatedly recommended to the national authorities a reduction in labour taxation through an increase in property and consumption taxes (see for example Andrle et al., 2018, European Commission, 2019). Workers in Italy face a larger tax wedge than other Eurozone members (see e.g. Cammeraat and Crivelli, 2020), when the wedge is computed also accounting for social security contributions and regional taxes on labour income. Italy is one of the European countries with the lowest employment rates, the lowest female participation to the workforce, and the highest unemployment rates among the young and in lagging-behind regions. Total factor productivity in Italy has also been stagnating since mid-1990s (Andrle et al., 2018, OECD, 2019). Consequently, a reform that would lower marginal tax rates on labour income might spur employment and bring significant efficiency gains. While the idea of a reduction of labour income taxes via a “tax shift” onto other, supposedly more efficient tax types seems to enjoy widespread consensus among practitioners and possibly among the general population in Italy, it is not yet clear what such a reform should look like. A revenue-neutral reform that would reduce personal income tax (PIT) rates and compensate lost revenues via an increase in the general value-added tax (VAT) rate can hardly preserve progressivity and will likely affect relevant groups of taxpayers differently. Also, reductions in the PIT can be achieved both by changing the tax rates or the no-tax allowance (i.e. a minimum income threshold not subject to PIT), which also brings different impacts in terms of equity and of the distribution of work incentives across the income quantiles. Finally, such reforms may cause general equilibrium and dynamic effects which should also be taken into account. The contribution of this paper is to build an analysis of potential reforms in Italy which jointly accounts for general equilibrium effects, effects across time, heterogeneous taxpayers who are differentiated by age and income levels with high granularity, and taking into account as much as possible the complex details of the real Italian tax and benefits system. We achieve this by means of an overlapping-generations computable general-equilibrium model 2 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 3 — #3 i i i i i i paired with a microsimulation model of the tax and benefits system. We are thus able to overcome the limitations of the existing literature which either provides a purely microeconomic static analysis of reforms (thus disregarding any general equilibrium or dynamic effect), or an analysis based on DSGE modelling techniques, which is unable to account for the existence of many heterogeneous taxpayers and relies on stylized representations of the tax system (thus missing many of the complexities and subtle interactions of real-world tax and benefits systems). The presence of the overlapping generations on the household side breaks the Ricardian equivalence and enables a more realistic modelling of fiscal policy in the long run. Our analysis focuses on two hypothetical reform proposals that reduce PIT and obtain budget parity by increasing consumption taxes. The two studied reforms differ in the way PIT reductions are achieved: via a cut of statutory tax rates across the board or via an increase of the no-tax allowance. Our results suggest that a tax shift reform in Italy should prioritize cutting personal income tax rates, rather than extending the no-tax allowance. More importantly and perhaps counter-intuitively, they point to the possibility that behavioural reactions may make the reform only mildly regressive, after accounting for dynamic and general equilibrium effects due in particular to increased labour supply of low-income households and overall savings. This result challenges a recurrent objection to such kind of tax shift policies, namely that they are necessarily regressive. While the latter may be true when limiting the analysis to a static representation of a national economy, our results point to large efficiency gains which are heterogeneous both across age and income and compensate for a large part of the reduction in progressivity of the tax schedule in the lower income deciles. Put in other words, the reform shows the potential to achieve a Pareto-improvement in the sense that all age groups and ability types see a rise in consumption with small cost in terms of increased inequality (a small social cost that, in principle, could be compensated by a simultaneous reform of social benefits, which we however did not attempt to design and simulate). The paper is structured as follows. Section 2 summarizes past literature from both the points of view of theory and applied economic analysis. Section 3 focuses on Italy, both its current economic situation and on research employing simulation tools to evaluate PIT reforms. Sections 4 and 5 describe in more detail our methodology by first presenting the main features of EDGE-M3 overlapping-generations macro model we employ and then explaining the way the EUROMOD microsimulation model is linked to it.1Section 6 describes the model baseline and Section 7 explains the two tax policy simulations performed. Section 8 presents the results from the simulations of our two reform scenarios. Section 9 summarizes the main conclusions and hints at prospects for future research. 2 Literature review Economic theory has long affirmed the concept that taxes on labour and capital income are less growth-friendly than the alternatives levied on immovable property and consumption 1EDGE-M3 is an abbreviation for European Dynamic General Equilibrium Micro-Macro Model. 3 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 4 — #4 i i i i i i (e.g. Mankiw et al., 2009). The intuition is that production factors such as labour and capital may be more reactive to changes in relative prices (such as those induced by tax reforms) and cause cumulative distortions in time, for instance in the case of a reduction in aggregate savings which would then also reduce labour productivity in the long run. An income tax burdens future consumption to a greater degree than current consumption (Auerbach, UC Berkeley 2006, retrieved from https://escholarship.org/uc/item/444479wh), thus it is intrinsically more distortionary compared to a consumption tax. A consequence is that any tax on the returns to factors subject to accumulation (i.e. capital, including human capital) should converge to zero in the long-run optimum (Milesi-Ferretti and Roubini, 1998, Judd, 1999). These theoretical results however hinge on several simplifying assumptions and, when complexity is added, some prescriptions may change, for instance if tax evasion is taken into account. The heterogeneity of the population of taxpayers may also affect optimal tax design. For instance (also relevant for the discussion to follow) Erosa and Gervais (2002) show that, in a setting with overlapping generations, the optimality of uniform taxation of consumption across lifetime depends on preferences and the way productivity changes with age. Empirical evidence based on macroeconomic data seems to confirm that from the perspective of economic growth, income taxes are less desirable, see: Kneller et al. (1999), Myles (2009), Arnold et al. (2011), Gemmell et al. (2014) (a study which partly challenges these results is Baiardi et al., 2019). Even accepting that taxes on capital and labour income should be reduced in favour of a tax shift onto consumption-based taxation, the question remains as to how to manage the equity trade-off arising from regressive taxes such as a uniform VAT. Because of the existence of bequests and possibly of other roles for accumulated wealth (e.g. as an insurance device against generic risks), savings cannot be fully considered as postponed consumption, hence the desirability for some degree of tax progressivity. Lehmann et al. (2016) argue that a more progressive tax schedule may increase overall employment, because low-income households have more elastic labour supply. Thus, it could prove efficiency-enhancing particularly in countries (like Italy) with low participation rates of the workforce. Starting from an existing tax system featuring a progressive PIT and a VAT, an important question is how to best design a tax shift from the former to the latter which brings the desired efficiency gains while also accounting for equity concerns. Shifting the burden away from labour taxation to more pro-growth taxes has been on the policy agenda of some EU countries for many years now. In light of its policy relevance, there has been a growing number of empirical and simulation studies on this topic. This area of research typically employs either microsimulation models coupled with structural models of labour supply (and more rarely, equilibrium models of labour demand), or general equilibrium models with some degree of agent heterogeneity. Microsimulation models allow to represent the complexity and full heterogeneity of the population of taxpayers in a given country at a given point in time. Thus, they are particularly powerful in providing analysis of the distributional impact of a reform. General equilibrium models are particularly suitable to study long-term effects of a reform and its potential for efficiency gains. In the remainder of this section, we provide an overview of empirical studies done with the use of microsimulation models followed by a literature overview of the general equilibrium macro 4 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 5 — #5 i i i i i i models in the area and papers employing linked micro-macro models. Similar studies having Italy as their focus will be reviewed in the next section. Using microsimulation analysis, Decoster et al. (2010) study the redistributive effects of fiscal devaluation2in five European countries (Belgium, Greece, Hungary, Ireland, UK) consisting in a cut in social security contributions financed by an increase in standard VAT rate. The simulation shows that less well-off groups in society are adversely affected while the richer ones benefit from the shift. O’Donoghue et al. (2004) also find a regressive impact in 12 OECD countries. Thomas and Picos-Sanchez (2012) simulate a revenue-neutral shift of 5 percent of the social security contribution burden to VAT and find increasing work incentives particularly for low-income earners across several European countries. Pestel and Sommer (2017) examine the equity-efficiency trade-off that arises in Germany from shifting taxes away from labour income to consumption. Stepwise increases in the VAT rate are compensated by revenue-neutral reductions in income-related taxes. They find, not surprisingly, a regressive impact of such a tax shift in the short run. In addition they prove that, when accounting for labour supply adjustments, the adverse distributional impact persists for PIT reductions, while the overall effects on inequality and progressivity become smaller when payroll taxes are reduced. This is partly due to increases in aggregate labour supply, resulting from higher work incentives. Due to the strongly progressive design of the personal income tax schedule, a compensated reduction of personal income taxes leads to a higher level of inequality. Low-income earners, pensioners and unemployed are found to be the main losers from the policy. Switching now to general equilibrium models, Nishiyama and Smetters (2005) study a reform in which a progressive income tax is replaced by a flat consumption tax. They use an overlapping-generations model in which agents face idiosyncratic wage shocks and mortality risk. They find that the effects of the tax reform crucially depend on the insurability of the wage shocks. Without wage shocks, adopting a flat consumption tax produces a positive and significant amount of extra resources. However and more realistically, with uninsurable wage shocks, adopting a flat consumption tax produces an efficiency loss. Lehmus (2011) analyses the effects of a tax reform that shifts tax burden from labour to consumption with the use of a dynamic general equilibrium model with heterogeneous agents for Finland. He studies the macroeconomic and income and wealth distribution effects of such reform, finding that a tax reform that replaces progressive labour taxes with a flat-rate consumption tax leads to a significant rise in capital accumulation, a negligible change in labour supply and gross labour income distribution, but a relatively considerable increase in wealth concentration. Lizarazo et al. (2017) assesses the macroeconomic and distributional impact of personal income tax reforms in the U.S. with the use of a DSGE model with household heterogeneity. Following other authors (e.g. Benabou, 2002, Heathcote et al., 2016 and Guner et al., 2016) federal income taxes are introduced in the model using a parametric tax function, which captures the effective tax rates paid at different levels of income. They find that the shift from direct 2“Fiscal devaluation” is a revenue-neutral shift in the tax structure (e.g. from employers’ social security contributions toward value-added and property taxes) with positive effects on output (see e.g. Andrle et al. (2021)) 5 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 12 — #12 i i i i i i 4.1 Earnings-ability Paths The model allows for agent heterogeneity across ages and lifetime earnings-ability profiles. This allows the model to capture the richness of the cross-sectional and intergenerational distributions over income, wealth, labour supply, and other endogenous variables. There are seven earnings-ability groups in the model. These groups refer to a deterministic lifetime earnings-ability paths, which are shown in Figure 1. New cohorts of agents in the model are randomly assigned to each group and there is no mobility between groups. The groups are not of equal size: the first group represents the earnings-ability path for up to the 25th percentile, the next for the 25th to 50th percentile, then for 50th to 70th, 70th to 80th, 80th to 90th, 90th to 99th, and finally, the top group is for those workers with the highest onepercent of earnings-ability. Splitting earning-ability groups in this way allows us to focus on the highest earners, especially the top one percent. The earnings-ability paths are estimated econometrically. As not all labour is equally productive, we estimate effective labour units, meaning the productivity of an earnings-ability type relative to the average. (Further details on the estimation procedure are given in d’Andria et al., 2020.) The resulting estimated earnings profiles are shown in Figure 1. Figure 1: Exogenous life cycle income ability paths log(ej,s) with S= 80 and J= 7 4.2 Demographics The model includes demographic projections from Eurostat on mortality rates, fertility rates, and immigration rates.6Taken together, these imply a population distribution that evolves over time according to the law of motion implied by these rates. Model agents are economically active for a maximum of Syears, facing a mortality risk that is a function of their 6Eurostat database: Population and social conditions — Population projections (proj) — Population projections at national level (2015-2080) (proj 15n) http://ec.europa.eu/eurostat/data/database, access 30/08/2018. 12 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 13 — #13 i i i i i i age, s. That is, agents can die within one year with the probability of dying given by the one-period mortality rates. It is assumed that agents live no longer than age 99. 4.3 Households Households are born each period and become economically relevant at age 20 (if they survive to that age). They live for a maximum of 100 years, and so are potentially economically active for 80 years. Households are subject to a budget constraint such that their consumption and new saving must match their labour and capital income plus transfers and bequests received, net of taxes paid. Households maximise their welfare by choosing lifetime consumption, labour supply and saving to maximise lifetime utility. Utility is received from consumption, reduced by labour and received by leaving bequests (a “warm glow” motive). It is a constant relative risk-aversion (CRRA) utility of savings, discounted by the mortality rate (to account for the probability that a household may not live to benefit from future consumption). 4.4 Firms Firms produce output using inputs of capital and labour according to a Cobb-Douglas production function. There is constant productivity growth, which is the rate of labouraugmenting technological progress. Firms seek to maximise profits (output less labour and capital costs). These features determine the optimal demand for labour and capital. 4.5 Government The government is not an optimizing agent in the model. The government levies taxes on households, provides transfers to households, makes other public expenditures, and engages in borrowing. All these operations influence households either directly through taxes and transfers the household budget constraint or indirectly through the effects government actions have on the equilibrium interest rate and wages. 4.5.1 Taxes We model three types of taxes: consumption taxes, a social insurance contribution, and income taxes. As households in the model consume only a composite consumption good, consumption taxes are modelled as the average tax paid on all goods and services. The consumption tax rate on this composite good is differentiated by age. This allows us to implicitly model variation in the basket of goods consumed by households as different points in the life cycle. For example, old ages consume more healthcare products, which are largely zero-rated for or exempt from VAT. The baseline rates of consumption tax range from around 18 percent down to around 13 percent for older ages as shown in Figure 2, which reflects this variation in the basket of goods and services over the lifecycle and it’s interaction with zero-rated or exempt goods and services. 13 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 14 — #14 i i i i i i Figure 2: Consumption tax rates by age Effective and marginal rates of social insurance contributions (SICs) are modelled as a function of labour income. Data on social contributions were obtained from the EUROMOD model which, as stated previously, employs EU-SILC survey data. To get the overall social insurance contribution we sum up the contributions paid respectively by employers, employees and self-employed workers. The overall SIC is then divided by gross labour income to get SIC rate. The SIC rate thus computed is regressed using OLS on gross labour income (GLI), its squared and cubic values: SIC rate =αi+β1GLIi+β2GLI2 i+β3GLI3 i+εi(1) By estimating a cubic polynomial we are able to capture common characteristics of the social security systems, namely the fact that SIC rates tend to be lower for low incomes (this is due to the existence of various allowances), then fairly constant for a large range of incomes, and then again lower for high incomes due to the existence of ceilings in contribution. The marginal SIC rates are then derived employing the coefficients obtained from the OLS regression, computing SIC rates at the current level of income and at a 3% larger income, finally dividing the difference in SIC rate by the difference in incomes. Finally, we model income taxes, which enter the OLG model as flexible, parametric functions. These functions are are estimated using output from the EUROMOD microsimulation model. These functions account for the interaction between labour and capital income on effective and marginal tax rates. This is our principal link between the micro- and macroeconomic models and is described in detail in Section 5. 4.5.2 Government budget Government spends a fixed share of GDP on general public expenditure and also on government transfers, which are uniformly distributed across all economically active households. The government can run surpluses or deficits in any given period. In our model, which is an open economy model, government bonds are purchased by domestic and foreign investors. We calibrate the share of new debt issues purchased by foreign investors to 32%, which is 14 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 15 — #15 i i i i i i in-line with recent purchases of Italian debt. To reflect the greater security of government bonds, the interest rate on government debt is below the rate paid on private capital. The difference between the interest rates varies over time, but it averages 2.1 percentage points in our model. Because our model is one with forward-looking agents, we need to be careful in considering how the government budget is satisfied in the long run. We cannot obtain an equilibrium in our model if the governments interest payments exceed GDP. We thus need to ensure that government budget deficits do not grow faster than GDP in the steady state. Any given income tax policy may produce structural budget deficits that do not satisfy this requirement. We therefore close the government budget by adjusting consumption taxes in all years. This closure is also a natural choice to simulate a shift from the income tax to the consumption tax. 4.6 Market Clearing Condition Three markets must clear in the OLG model—the labour market, the capital market, and the product market use.7We also present the law of motion for bequests, which, while not technically a market clearing condition, does have similar properties. Labour market clearing requires that aggregate labour demand equal the sum of household labour supplied (both measured in effective labour units). Capital market clearing requires that aggregate capital demand from firms equal the sum of capital savings and investment by households. The equation must account for the capital flows associated with immigration into or out of the country. It is assumed that immigrants have the same savings (and consumption) as natives of the same age.8 Product market clearing requires that aggregate output equals aggregate consumption, aggregate investment, and net exports. Total bequests are the collection of savings of household from the previous period who died at the end of the period. These savings are augmented by the interest rate because they are returned after being invested in the production process. 4.7 Equilibrium We solve for the rational-expectations equilibrium of the OLG model in the steady-state and along the entire transition path to the steady state. An equilibrium consists of agents having expectations that are consistent with equilibrium outcomes, households and firms acting optimally given prices and these expectations, and markets clearing in each period. The solution algorithm involves solving for the steady-state equilibrium first, via a fixed point algorithm, and then solving for the transition path through the methods of Auerbach and Kotlikoff (1987). 7In the model, only the labour market and capital market clearing condition are included. By Walras’ Law, the third market clearing condition is redundant. The product market clearing condition—also referred to as the resource constraint—is used as a check on the solution method. 8This assumption is necessary to constrain the dimensions of the model, as without it one would need to model immigrants separately from the rest of the population. As most immigrants are from the EU, it is not considered a strong assumption. 15 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 16 — #16 i i i i i i Note that our model has underlying growth in the population and in productivity through labour-augmenting technological change. In order to solve our model, we must make it stationary. All non-stationary variables (such as economic aggregates and wage rates, among other variables) are made stationary in order to solve the model. We present our results in terms of the stationarised values. 5 Mapping Reforms from the Micro- to the Macro- Level for Income Taxes The link between the EUROMOD microsimulation model and EDGE-M3 OLG macroeconomic model is established through parametric functions that represent average effective and marginal tax rates. These function capture tax progressivity and are functions of capital and labour income levels and age group. A representative agent in the OLG has labour and capital incomes that are function of the general equilibrium wages and interest rates and determined through optimal choices of the agent with respect to labour supply and savings. Marginal and effective tax rates affect these decisions through the agents’ budget constraints and first order conditions. Though the use of tax rate functions in the OLG model, the tax rates associated with agents decisions are endogenous. They are functions of the choices of labour supply and savings, which determine capital and labour income, which in turn affect the marginal and effective tax rates agents face. Importantly, we model tax rates as bivariate functions of capital and labour income, as well as age group. In this way, many tax-relevant characteristic of an individual that are not explicitly represented in the macro model are still indirectly captured by the estimated tax functions. For instance, if different sources of capital income face different rates of taxation (as is the case in Italy), then allowing tax rates to vary according to the mix of capital and labour income and by age may help to account for portfolio differences in capital income held by households of different ages with varying mixes of capital and labour income. A modelling strategy such as this allows one to account for the maximum degree of heterogeneity the OLG model can afford when modelling average and marginal tax rates from the EUROMOD microsimulation model, albeit implicitly. This section first outlines some key features of the EUROMOD microsimulation model followed by an outline of the methodology for mapping income taxes from the micro-model to the OLG macro-model. We then explain in detail the tax functions used and the estimation process. It is these tax functions that provide the key linkage between the macro results and the micro results. 5.1 The EUROMOD microsimulation model EUROMOD is the European Union tax-benefit microsimulation model (Sutherland (2007), Sutherland and Figari (2013)). The model is a static tax and benefit calculator that makes use of representative microdata from the harmonised EU Statistics on Income and Living Conditions survey (EU-SILC) and from national statistics on income and living conditions surveys, 16 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 17 — #17 i i i i i i to simulate individual tax liabilities and social benefit entitlements according to the rules in place in each Member State. Its main distinguishing feature is that it covers all EU countries within the same framework, allowing for flexibility of the analysis and comparability of the results. Starting from gross incomes contained in the survey data, EUROMOD simulates most of the direct tax liabilities and benefit entitlements.9EUROMOD represents most tax-relevant characteristics of individuals and households (including demographic and family characteristics, information on the type of labour activity, region of residence, and so on), it produces estimates of tax liabilities that take into account the full combined effects of allowances, tax credits, exemptions, additional tax rates and differential tax treatments. The model is able to represent all major tax credits and allowances, though some smaller ones are not computed due to data limitations (as an example, tax credits that are granted for very specific expenses incurred in case of home renovations improving energy efficiency cannot be tracked, as the data used to calibrate EUROMOD do not include such detailed breakdown of households’ expenditures). The effective tax rate on total income is calculated by simply taking income tax liabilities as a share of combined labour and capital income. These are obtained from the EUROMOD database, which is taken from the EU-SILC survey. Labour income is defined as earned income, which is the sum of wages, salaries, and self-employment income. Capital income is defined as the sum of income from investment, pension, and property.10 The microdata we use are at the individual level for main income earners in a household (we believe in this way we better capture the characteristics of the Italian tax system compared to household-level data) and come from the EUROMOD model.11 EUROMOD can also be used to compute marginal tax rates for each agent by assuming an increase of a fixed percentage of income and recalculating the labour or capital income tax liability.12 5.2 Mapping income taxes from micro to macro model As noted above, the micro-macro link is based on income levels and age group. In the overlapping generations model, the tax rates associated with this agent are determined by these endogenous income levels (as well as by age in line with age groups distinguished - see Section 9For more information on EUROMOD see the official website: https://euromod-web.jrc.ec.europa.eu/. 10We obtain labour income summing up EUROMOD ’s variables yem (wage employment income) and yse (self employment income), capital income summing up ypp (private pension), yiy (investment income) and ypr (property income), labour taxes summing up tinna s and tinrg s, and capital taxes summing up tinktcp s, tinktdt s,tinktdv s,tinktbd s,tinktgb s,tprmb s,tprob s and tinrt s (all the latter variables starting with the letter tare for taxes and are endogenously computed by the EUROMOD model). 11We find that there are several observations with extreme values for their effective tax rate. Since effective (marginal and average) rates are calculated as ratios, unrealistically large values might be obtained, for example when the denominator is a measure of income and this is very small. We omit such outliers by imposing the following restrictions upon the raw output of the microsimulation model. First, we exclude observations with an effective tax rate greater than 70% and observations with a marginal tax rate greater than 75% or less than 0%. Second, we drop observations from the microsimulation model where adjusted total income is less than 5 EUR. 12We used a 3% increase for this purpose. Sensitivity tests were performed by also computing marginal tax rates with a 0.1% increase instead, and the resulting figures were identical after winsorizing the 1% lowest and largest values. 17 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 18 — #18 i i i i i i 5.3). The effective income tax rates enter into the agents’ budget constraint and the marginal tax rates enter first-order conditions for the agents’ optimization problem, thus impacting on agent behaviour (see Section 4.3 for more details). Most characteristics of an individual that are tax-relevant but not explicitly represented in the macro model are anyway indirectly captured by the estimated tax functions, for example the presence of children in the household, marital status, or type of employment are not explicitly modelled in the OLG model but their impact on tax liabilities is still captured as an average effect by the tax function estimation process (see below). Such modelling strategy allows one to account for the full range of average and marginal effects of the tax system from the EUROMOD microsimulation model, albeit implicitly. 5.3 Income Tax Functions In order to represent the personal tax system, we follow the novel approach described in DeBacker et al. (2019), which make use of the microsimulation output to estimate tax functions used in the EDGE-M3 OLG model. The method enables not only the estimation of tax functions for current policy, but also for counterfactual tax policies, including tax policy levers that are difficult or impossible to model explicitly in a general equilibrium framework. Here we focus on the functional form and how it effectively translates the information from the microsimulation output into a function that can be entered into the OLG model. Inspection of the data indicates a clear difference between young-to-middle-aged adults and older adults. Therefore, in order to improve the accuracy of the estimation, we estimate separate tax functions for those aged 20 to 59 and for those aged 60 and over, which we refer to as the young and old tax functions, respectively. The split captures heterogeneity in tax liability that is correlated with the age of the taxpayer, beyond what is captured purely by the size of the incomes (for example, due to a different composition of assets or age-specific policies). Looking first at the young-to-middle-aged adults (ages 20-59), Figure 3 shows scatter plots of effective tax rates (ETR), marginal tax rates on labour income (MT Rx) and capital income (MT Ry) simulated using the EUROMOD model, each plotted as a function of labour income and capital income in the base year 2015. Labour and capital income are truncated at 6000 EUR and 3000 EUR per month in the plots for clarity. Figure 3(a) shows the scatterplot of the effective tax rates for each labour and capital income combination. Whilst noting some noise in the data, some key properties of the data can be clearly seen. First, those on low capital and labour incomes tend to face low ETRs. For those with low capital income, as labour income rises, a clear cluster of data is seen where the ET R rises but at a diminishing rate. From any level of labour income, higher capital income also raises one’s ET R for most individuals. These anticipated properties of the data lead us towards the use of a functional form that captures these key features. Following DeBacker et al. (2019) we fit to the data a Cobb-Douglas aggregator of two ratios of polynomials in labour and capital income (see eq. (2)) that we explain below. Important 18 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 19 — #19 i i i i i i Figure 3: Scatter plot of ETR,MTRx and MT Ry as functions of labour income and capital income (EUR per month) from microsimulation model, year 2015, ages 20-59 (a) Effective tax rates ETR (b) Marginal tax rates on labour income MT Rx (c) Marginal tax rates on capital income MT Ry 19 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 20 — #20 i i i i i i properties of the chosen functional form are that it produces the observed bivariate negative exponential shape and is non-decreasing in both labour income and capital income, which are consistent with the observed data. Turning to the data for the marginal tax rates on labour income (MTRx), Figure 3 (b), similar properties are displayed. In particular, the data display a negative exponential shape and are monotonically increasing in labour income; also visible are the different regimes for employees and the self-employed. However, the shape is less pronounced with respect to capital income. For the marginal tax rates on capital income, Figure 3 (c), the shape of the underlying function has a clear line at low capital income with levels rising for higher capital income, which can be captured by the Cobb-Douglas aggregator. For these reasons, we estimate the same function for ETR,MT Rx and MT Ry. As will be shown below, the function has sufficient flexibility to provide a good fit in each case. The equivalent scatterplots for ages 60 and over are shown in Figure 4. The data bear some resemblance to that for young ages, however capital income is more important in this age group.13 The estimation algorithm works as follows: let xbe total labour income, x≡wtej,s ˆnj,s,t, that is the product of the wage, w, the effective labour per unit of labour, e, and the labour supply, n, by age, sand earnings-ability type, jin time, t; let ybe total capital income, y≡rtˆ bj,s,t, that is the product of the interest rate, r, and the stock of savings, b, by age, s and earnings-ability type, jin time, t. Our tax rate function is a Cobb-Douglas aggregator of two ratios of polynomials in labour and capital income, and is expressed as follows: τ(x, y)=[τ(x) + shiftx]φ[τ(y) + shifty]1−φ+shift where τ(x)≡(maxx−minx)Ax2+Bx Ax2+Bx + 1+minx and τ(y)≡(maxy−miny)Cy2+Dy Cy2+Dy + 1+miny where A, B, C, D, maxx, maxy, shiftx, shifty>0 and φ∈[0,1] and maxx> minxand maxy> miny (2) The key building blocks of the functional form equation (2) as proposed by DeBacker et al. (2019) are the τ(x) and τ(y) univariate functions. The ratio of polynomials in the τ(x) function Ax2+Bx Ax2+Bx+1 with positive coefficients A, B > 0 and positive support for labour income x > 0 creates a negative-exponential-shaped function that is bounded between 0 and 1, and the curvature is governed by the ratio of quadratic polynomials. The multiplicative scalar term (maxx−minx) on the ratio of polynomials and the addition of 13Splitting the age groups into 59 and below and 60 and over was arrived at following extensive experimentation. Splitting the sample at an older or younger age was experimented with, but the tax function estimates were judged to be somewhat poorer in capturing the microsimulation data. Splitting within the 59 and below group was found to add little information. Splitting within the 60 and over group faces a problem with the sample size. 20 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 21 — #21 i i i i i i Figure 4: Scatter plot of ETR,MTRx and MT Ry as functions of labour income and capital income (EUR per month) from microsimulation model, year 2015, ages 60+ (a) Effective tax rates ETR (b) Marginal tax rates on labour income MT Rx (c) Marginal tax rates on capital income MT Ry 21 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 28 — #28 i i i i i i age 80. After this age, all ability types stabilise or reduce their stock of savings. At older ages, savings behaviour is mostly driven by households trading off utility from consumption and utility from leaving bequests. Note that it is never optimal to end life without savings, because households gain a very large marginal utility from leaving small bequests. Figure 7.d shows income taxes paid, which rises to a peak for those of age mid-to-late 50s, corresponding to the peak in labour supply and earnings. The top one percent of earnings-ability, group seven, has higher labour and capital income and hence, much higher income taxes. Table 6 in Appendix B details calibrated values and other exogenous parameters’ values of EDGE-M3 model used here. Figure 8 presents baseline levels of individual variables in the fifth year of a dynamic solution of the model. It shows level of labour supply, consumption, savings and tax revenues paid for the seven ability types and three age groups. The three age groups are defined as young for individuals aged 20-39, mid-age for individuals aged 40-59, and old for individuals aged 60-100. Similar broad shapes can be seen to those in the steady state. In addition one can also compare different age group with this figure. For instance, in line with intuition, the middle aged pay the highest income tax as they work the most hours. It can also be seen that the richest pay very high income tax due to having the highest income from both labour and capital (the latter due to having the largest accumulation of assets). 28 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 29 — #29 i i i i i i Figure 7: Baseline steady-state values for labour supply, consumption, savings and income tax paid for seven ability types, ages 20-99 (a) Labour supply nss (b) Consumption css (c) Savings bss (d) Income tax paid taxss 29 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 30 — #30 i i i i i i Figure 8: Labour supply, consumption, savings and income tax paid for seven ability types - 5th year of the dynamic solution (a) Labour supply npath (b) Consumption cpath (c) Savings bpath (d) Income tax paid taxpath 7 Simulations We describe here the simulated policy scenarios. Each simulation involves a change in the personal income tax (PIT) schedule, which is first performed in the microsimulation model and then, using the methodology described in Section 5, the income tax function for the macro-model is re-estimated, thus incorporating the micro-level information. Two income tax simulations are performed which we label as “2pp-cut” and “Thres-rise”:  2pp-cut: A 2 percentage point cut in all PIT rates  Thres-rise: Raising the PIT threshold by EUR 2320 The reason for the choice of EUR 2,320 is that in the microsimulation model, this change in threshold has exactly the same revenue cost as the 2 percentage point cut in PIT rates. 30 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 31 — #31 i i i i i i Thus, the two reform scenarios are equivalent ex ante in terms of their reduction in average personal tax liability, where ex ante here means before considering behavioral reactions and general equilibrium effects. The reforms are described in greater detail in Tables 2 and 3. Table 2: Statutory thresholds and marginal tax rates for personal income tax: baseline vs. 2pp-cut reform PIT bracket Baseline 2pp-cut reform (annual income in EUR) up to 15,000 0.23 0.21 15,000 to 28,000 0.27 0.25 28,000 to 55,000 0.38 0.36 55,000 to 75,000 0.41 0.39 75,000 and above 0.43 0.41 Source: EUROMOD and authors Table 3: Statutory thresholds and marginal tax rates for personal income tax: baseline vs. Thres-rise reform PIT bracket PIT bracket Rates (annual income in EUR) (annual income in EUR) (Baseline and Baseline Thres-rise reform reform) n/a up to 2,320 0.00 up to 15,000 2,320 to 15,000 0.23 15,000 to 28,000 17,320 to 28,000 0.27 28,000 to 55,000 28,000 to 55,000 0.38 55,000 to 75,000 55,000 to 75,000 0.41 75,000 and above 75,000 and above 0.43 Source: EUROMOD and authors Note that both these reforms constitute a PIT cut for all income taxpayers. Also it should be noted that reforms such as these will interact with other elements of the tax system, which are captured in the microsimulation model with a high degree of granularity. The changes due to the re-estimated effective tax rate (ETR) function in the two tax reforms are shown in Figure 9. The estimation is carried out separately for younger and older agents in the model. The figure shows the difference between the re-estimated function and the one in the baseline. Figure 9a shows the 2pp-cut for young agents; one sees that those with a high labour income receive the greatest reduction in ET R, which is close to the 2 percentage points. Low-income taxpayers (the young and/or low-ability types) receive less benefit, as they were paying less income tax. In contrast, under the Thres-rise reform, Figure 9.b, the greatest benefit goes to those earning around 1000 euros per month of labour 31 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 32 — #32 i i i i i i income, as they benefit from the threshold rise and this constitutes a large share of their income tax. Older taxpayers receive a reduction of between 1.0 and 1.8 percentage points in their ET R function in the 2pp-cut reform, Figure 9.c, with the variation present only in the capital income dimension, which is where most of their income is derived (pension income is included as capital income). The Thres-rise reform for older ages, Figure 9.d, has a similar pattern, however, the largest reduction is for those earning around 1000 euros per month of capital income. Figure 9: Change in effective tax rate (ETR) for the two reforms (reform less baseline, EUR 1000s per month) (a) 2pp-cut, ages 20-59 (b) Thres-rise, ages 20-59 (c) 2pp-cut, ages 60-99 (d) Thres-rise, ages 60-99 In a similar fashion, the effect of the reforms on the marginal tax rate on labour income function is shown in Figure 10. The reduction in the marginal tax rate for the 2pp-cut reform, Figures 10a and 10c, are reasonably consistent across income levels, ranging from a reduction of 1.1 to 1.5 percentage points. The variation that does exists is almost entirely in the labour income dimension. Changes in marginal tax rates are less pronounced in the Thres-rise reform, Figures 10b and 10d, with near-zero impacts apart from for young ages on low incomes. This is consistent with the nature of the reform, which directly affects the marginal rates for the first 2320 euros per year of taxable labour income, which is only marginal for low-income workers. 32 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 33 — #33 i i i i i i Figure 10: Change in marginal tax rates on labour (MTRx) for the two reforms (reform less baseline, EUR 1000s per month) (a) MTRx, 2pp-cut, ages 20-59 (b) MTRx, Thres-rise, ages 20-59 (c) MTRx, 2pp-cut, ages 60-99 (d) MTRx, Thres-rise, ages 60-99 The consequences for the marginal tax rate on capital income, MT Ry, are concentrated on lower labour income and high capital income earners (see Figure 11). The figures show how the consequence of a tax cut has different effects by income levels, but also depends on the source of income and other characteristics of the individual, which are incorporated into the EUROMOD output and then captured by the income tax function. The figures for young ages, Figures 11a and 11b, show that capital income levels have little impact on the reduction in marginal rates on capital income. Those with low labour income receive the largest reduction. As labour income rises, falls in the MT Ry from the reform become smaller, with the 2pp-cut reform showing larger benefits for high labour-income earners. For old ages, Figures 11c and 11d, some variation in the capital income dimension in seen, as pension income is typically subject to personal income tax and so would be impacted by the reforms. 33 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 34 — #34 i i i i i i Figure 11: Change in marginal tax rates on capital (MTRy) for the two reforms (reform less baseline, EUR 1000s per month) (a) MTRy, 2pp-cut, ages 20-59 (b) MTRy, Thres-rise, ages 20-59 (c) MTRy, 2pp-cut, ages 60-99 (d) MTRy, Thres-rise, ages 60-99 Generally speaking a reduction across the board of tax rates, like the ones here simulated, decreases marginal tax rates on labour income. This alone implies a substitution effect such that labour supply will increase. At the same time, income effects would imply less labour supply. Also due to the general equilibrium design of the model, gross wages and capital formation will be affected and this in turn will impact ability groups differently. The different composition of labour versus capital incomes also implies different effects by age. Overall, as will be shown, substitution effects dominate income effects in the 2pp-cut reform scenario and income effect is more pronounced in the Thres-rise reform scenario. Both reforms have different intensities across ability groups and ages. Both the simulated reform scenarios are budget neutral for the government in the steady state and along the transition path. Given the fall in income tax revenue, we achieve budget neutrality by raising consumption taxes pro-rata across all age groups. (Recall that consumption taxes vary by age in the baseline as shown in Figure 2.) This allows us to focus on a realistic possibility for tax reform (rather than expanding the public debt further): a tax shift from income to consumption taxes. 34 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 35 — #35 i i i i i i 8 Results We now present and discuss the main results obtained from the simulated policy reforms. Figures 12 and 13 report the changes in labour supply (as change in the share worked out of total time endowment), consumption, savings and disposable income (as percent deviations from the baseline solution). We also report the change in income tax paid (as absolute changes, obtained as the value under the reform minus the value under the baseline) and the percentage change in consumption tax paid. These results are for the simulated tax changes in the steady-state, in comparison to baseline values. We interpret the steady-state results as long-run results of the reform, which we address first, turning to the short-run effects later in this section. As can be seen from the graphs the effects of tax rate cuts differ based on age and ability type. The observed changes for labour supply are substantial for all working ages in the 2pp-cut reform, Figure 12a, as predicted by our choice for the functional forms for agents’ utility. The reduction in marginal tax rates on labour income causes an increase in the labour supply, particularly for the low-ability agents (which is coherent with the empirical literature discussed in previous sections, e.g., Meghir and Phillips, 2009, and Blundell, 2016). In contrast, the Thres-rise reform, shown in Figure 13a, by leaving marginal tax rates on labour unchanged but raising consumption taxes, induces an overall decrease in labour supply which is stronger for low- and middle-income and younger agents. There is also some decrease in labour supply due to the income effect, as the tax cut results in higher disposable income (see Figures 12d and 13d).17 The impact on consumption, shown in Figures 12b and 13b, differs across the reforms: it increases for all agents in the 2pp-cut reform (also thanks to increases in labour supply) and more so for high-ability agents. In this respect, the 2pp-cut reform is Pareto improving. In contrast in the Thres-rise reform, consumption decreases and generally decreases more with age and ability type. This is due to the large increase in consumption tax which more than offsets the additional after-tax income income from the PIT cut. The effect is stronger for higher earners, who spend more relative to the size of the income tax cut from the rise in the threshold. The changes for saving are generally positive for both reforms. In the 2pp-cut reform, Figure 12c, the percentage rise in savings is especially strong for middle and old ages. There is a reduction in savings for the lowest ability group in young adulthood, which saves less in this age group to smooth (increased) consumption across their lifetime. In the Thres-rise reform, Figure 13c, there are increases in savings for most groups, though these tend to be smaller than for the 2pp-cut reform. The lowest ability type again reduces saving in young adulthood, but then shows the largest percentage rises in middle and old ages. This rise is partly driven by the difference in the marginal utility of savings, which decreases with income. 17We define disposable income here as labour income plus capital income minus income taxes and social security contributions paid. We abstract from social transfers as they are modelled in a simplified way in the analysis presented here. They are assumed as constant percent of GDP in all periods and are distributed uniformly to all individuals. In this simplified set-up accounting for transfers would not change the conclusions in terms of the distributional aspect of analysed tax reform. 35 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 36 — #36 i i i i i i Figure 12: Effect of the 2 pp. tax rate cut reform by age groups in the steady state (all % deviation except for income tax that is absolute deviation) (a) Labour supply nss (b) Consumption css (c) Savings bss (d) Disposable income disp incss (e) Income tax taxss (f) Consumption tax ctaxss 36 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 37 — #37 i i i i i i Figure 13: Effect of the 2320 EUR threshold rise reform by age groups in the steady state (all % deviation except for income tax that is absolute deviation) (a) Labour supply nss (b) Consumption css (c) Savings bss (d) Disposable income disp incss (e) Income tax taxss (f) Consumption tax ctaxss Figures 12e and 13e report the change in tax liabilities. Income tax revenues decrease for the whole population in both reforms. The income tax paid shows the results of interactions between the rate changes and the consequent changes labour supply and savings decisions. 37 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 44 — #44 i i i i i i equilibrium effects, a cut in tax rates across the board, compensated by increases in VAT rates, as shown by many microsimulation studies, would obviously produce a clearly regressive tax reform. Thus, such a reform would face an important trade-off between efficiency gains (particularly those in the form of labour supply gains) and equity, and predictably, political resistances as well. 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Sutherland, Holly, “Modeling our Future: Population Ageing, Social Security and Taxation, Vol. 15, International Symposium in Economic Theory and Econometrics,” in Ann Harding and Anil Gupta, eds., EUROMOD – The Tax-Benefit Microsimulation Model for the European Union, Elsevier, Amsterdam, 2007. 49 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 50 — #50 i i i i i i and Francesco Figari, “EUROMOD – The European Union Tax-Benefit Microsimulation Model,” EUROMOD Working Paper No. EM8/13, 2013. Thomas, A. and F. Picos-Sanchez, “Shifting from Social Security Contributions to Consumption Taxes: The Impact on Low-Income Earner Work Incentives,” OECD Taxation Working Papers, 2012, (No. 11). 50 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 51 — #51 i i i i i i Appendices A Household Problem A measure ω1,t of households is born each period, become economically relevant at age s=E+1 if they survive to that age, and live for up to E+Speriods (Seconomically active periods), with the population of age-sindividuals in period tbeing ωs,t. Let the age of a household be indexed by s={1,2, ...E +S}. At birth, each household age s= 1 is randomly assigned one of Jability groups, indexed by j. Let λjrepresent the fraction of individuals in each ability group, such that Pjλj= 1. Note that this implies that the distribution across ability types in each age is given by λ= [λ1, λ2, ...λJ]. Once a household member is born and assigned to an ability type, he remains that ability type for his entire lifetime. Thus, it is the deterministic ability heterogeneity as an agent cannot change his ability type (for more details see Section 4). Let ej,s >0 be a matrix of ability-levels such that an individual of ability type jwill have lifetime abilities of [ej,1, ej,2, ...ej,E+S]. The budget constraint for the age-shousehold in lifetime income group jat time tis the following: cj,s,t 1 + τc s,t+bj,s+1,t+1 = (1 + rt)bj,s,t +wtej,snj,s,t +ζj,s BQt λjωs,t +ηj,s,t TRt λjωs,t −TI j,s,t −TP j,s,t ∀j, t and s≥E+ 1 where bj,E+1,t = 0 ∀j, t (8) where cj,s,t is consumption, τc s,t is consumption tax rate, bj,s+1,t+1 is savings for the next period, rtis the interest rate (return on savings), bj,s,t is current period wealth (savings from last period), wtis the wage, and nj,s,t is labour supply. The next term on the right-hand-side of the budget constraint (8) represents the portion of total bequests BQtthat go to the age-s, income-group-jhousehold. Let ζj,s be the fraction of total bequests BQtthat go to the age-s, income-group-jhousehold, such that PE+S s=E+1 PJ j=1 ζj,s = 1. We must divide that amount by the population of (j, s) households λjωs,t. d’Andria et al. (2020) detail how to calibrate the ζj,s values from consumer finance data. The penultimate term on the right-hand-side of the budget constraint (8) represents the portion of total transfers T Rtthat go to the age-s, income-group-jhousehold. Let ηj,s,t be the fraction of total transfers TRtthat go to the age-s, income-group-jhousehold, such that PE+S s=E+1 PJ j=1 ηj,s,t = 1. We must divide that amount by the population of (j, s) households λjωs,t. Section 4 details how transfers are distributed among households. The last two terms on the right-hand-side of the budget constraint (8) represent income taxes paid by households, TI j,s,t, and payroll tax, TP j,s,t. Households choose lifetime consumption {cj,s,t+s−1}S s=1, labour supply {nj,s,t+s−1}S s=1, and savings {bj,s+1,t+s}S s=1 to maximise lifetime utility, subject to the budget constraints and non negativity constraints. The household period utility function is the following: 51 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 52 — #52 i i i i i i u(cj,s,t, nj,s,t, bj,s+1,t+1)≡(cj,s,t)1−σ−1 1−σ+egyt(1−σ)χn s(b1−nj,s,t ˜ lυ1 υ)+ χb jρs (bj,s+1,t+1)1−σ−1 1−σ∀j, t and E+ 1 ≤s≤E+S (9) The period utility function (9) is linearly separable in cj,s,t,nj,s,t, and bj,s+1,t+1. The first term is a constant relative risk aversion (CRRA) utility of consumption. The second term is the elliptical disutility of labour.19 The constant χn sadjusts the disutility of labour supply relative to consumption and can vary by age s, which is helpful for calibrating the model to match labour market moments. It is necessary to multiply the disutility of labour in (9) by egy(1−σ)because labour supply nj,s,t is stationary, but both consumption cj,s,t and savings bj,s+1,t+1 are growing at the rate of technological progress. The egy(1−σ)term keeps the relative utility values of consumption, labour supply, and savings in the same units. The final term in the period utility function (9) is the “warm glow” bequest motive. It is a CRRA utility of savings, discounted by the mortality rate ρs.20 Intuitively, it represents the utility a household gets in the event that they don’t live to the next period with probability ρs. It is a utility of savings beyond its usual benefit of allowing for more consumption in the next period. This utility of bequests also has constant χb jwhich adjusts the utility of bequests relative to consumption and can vary by lifetime income group j. This is helpful for calibrating the model to match wealth distribution moments. Note that any bequest before age E+Sis unintentional as it was bequeathed due an event of death that was uncertain. Intentional bequests are all bequests given in the final period of life in which death is certain bj,E+S+1,t. The household lifetime optimisation problem is to choose consumption cj,s,t, labour supply nj,s,t, and savings bj,s+1,t+1 in every period of life to maximise expected discounted lifetime utility, subject to budget constraints and upper-bound and lower-bound constraints. max {(cj,s,t),(nj,s,t),(bj,s+1,t+1)}E+S s=E+1 S X s=1 βs−1ΠE+s u=E+1(1 −ρu)u(cj,s,t+s−1, nj,s,t+s−1, bj,s+1,t+s) (10) s.t. cj,s,t 1 + τc s,t+bj,s+1,t+1 = (1 + rt)bj,s,t +wtej,snj,s,t +ζj,s BQt λjωs,t +ηj,s,t TRt λjωs,t −TI j,s,t −TP j,s,t (8) and cj,s,t ≥0, nj,s,t ∈[0,˜ l],and bj,E+1,t = 0 ∀j, t, and E+ 1 ≤s≤E+S The non-negativity constraint on consumption does not bind in equilibrium because of the Inada condition limc→0u1(c, n, b0) = ∞, which implies consumption is always strictly positive in equilibrium cj,s,t >0 for all j,s, and t. The warm glow bequest motive in (9) also has an Inada condition for savings at zero, so bj,s,t >0 for all j,s, and t. This is an implicit 19Advantages of modelling labour disutility with the elliptical funtional form are discussed in Evans and Phillips (2018). 20See d’Andria et al. (2020) for a detailed discussion of mortality rates in EDGE-M3 . 52 i i “Journal˙OLG˙paper˙25112021” — 2021/11/26 — 11:52 — page 53 — #53 i i i i i i borrowing constraint.21 And finally, as discussed in Evans and Phillips (2018), the elliptical disutility of labour supply functional form in (9) imposes Inada conditions on both the upper and lower bounds of labour supply such that labour supply is strictly interior in equilibrium nj,s,t ∈(0,˜ l) for all j,s, and t. The household maximisation problem can be further reduced by substituting in the household budget constraint, which binds with equality. This simplifies the household’s problem to choosing labour supply nj,s,t and savings bj,s+1,t+1 every period to maximise lifetime discounted expected utility. The 2Sfirst order conditions for every type-jhousehold that characterise the its Soptimal labour supply decisions and Soptimal savings decisions are the following. wtej,s −∂TI j,s,t ∂nj,s,t −∂TP j,s,t ∂nj,s,t !(cj,s,t)−σ1 1 + τc s,t =egy(1−σ)χn sb ˜ lnj,s,t ˜ lυ−1"1−nj,s,t ˜ lυ#1−υ υ ∀j, t, and E+ 1 ≤s≤E+S (11) (cj,s,t)−σ1 1 + τc s,t =e−gyσχb jρs(bj,s+1,t+1)−σ+β1−ρs1 + rt+1 −∂T I j,s+1,t+1 ∂bj,s+1,t+1 (cj,s+1,t+1)−σ 1 1 + τc s+1,t+1  ∀j, t, and E+ 1 ≤s≤E+S−1 (12) (cj,E+S,t)−σ=χb j(bj,E+S+1,t+1)−σ∀j, t and s=E+S(13) where the marginal income tax rate with respect to labour supply ∂Ts,t ∂nj,s,t is described in equation (6). ∂T P j,s,t ∂nj,s,t is the marginal rate of payroll tax with respect to labour supply. B Exogenous Parameters and Calibrated Values All exogenous parameters that are inputs to the model are listed in Table 6. 21It is important to note that savings also has an implicit upper bound bj,s,t ≤kabove which consumption would be negative in current period. However, this upper bound on savings is taken care of by the Inada condition on consumption. 53