Microreg: A traditional tax-benefit microsimulation model extended to indirect taxes and in-kind transfers

The first phase of a microsimulation model is the choice of micro-data. In Italy many microsimulation models use the Survey on Household Income and Wealth of Bank of Italy (SHIW), which provides accurate information on income and household wealth². MicroReg uses the EUROSTAT Survey on Income and Living Conditions (EU-SILC), since it is more representative at regional level with respect to SHIW. In this paper we describe the model built on EU-SILC 2013 (year of income 2012). However, some important information is missing in EU-SILC. Indeed, gross income and cadastral value of buildings need to be estimated.

This procedure is performed to make estimates of gross income more similar to real data of the MEF and therefore to tackle the problem of tax evasion. Usually in a survey under the guarantee of anonymity, people are more honest than when the counterparty is the tax authority. The calibration binds the original sample weights to the joint distribution of individuals by income class (taken from the MEF) and by socio-demographic variables derived from ISTAT. The total income considered for the calibration is the one used in the grossing up procedure, plus incomes from buildings obtained after the estimation of cadastral values.

In literature two types of calibration methods can be found: i) independent calibration and ii) integrative calibration. The independent calibration allows calibrating weights with households’ variables independently from individual’s variables. The convergence procedure is generally fast, but it generates different weights for households and individuals. Integrative calibration takes into account households’ and individuals’ variables together. It converges more slowly, but households’ and individuals’ weights are the same (as requested by the European Commission Regulation for the SILC). In MicroReg an integrative calibration is performed with the following constraints: taxpayers by income classes and prevailing source of income; population by age, sex, gender and level of education; population by region of residence and by number of family members.

After having imputed missing information (see Section 2.1) and calibrated sample weights (see Section 2.2) we simulate all fiscal rules that every taxpayer follows to pay PIT in the following way:

1. According to Italian fiscal rules, every taxpayer can deduct the value of the main residence⁶ and other expenses (such as expenditure for disabled family members or for donations) from gross income. Since EU-SILC does not collect detailed information about deductible expenses, we impute their value to each taxpayer by applying a coefficient equal to the ratio between deductions and gross income by gross income classes calculated on official data from the MEF⁷. Taxable income is then simulated by subtracting deductions from gross income tax for each taxpayer.

2. Gross PIT is simulated by applying the legal tax rates to the simulated taxable income.

3. Each taxpayer can subtract different types of tax credits from gross PIT: i) tax credits by income source, ii) tax credits for family members and iii) other tax credits (for health expenditure, housing works, etc.). Tax credits by income source and for family members are simulated in the model since detailed information on income and household components are collected in EU-SILC. The other tax credits, similar to tax deductions, are estimated by applying to each taxpayer a coefficient given by the ratio of tax credits and gross income by gross income classes registered by MEF⁸.

4. Finally, the net PIT is simulated by detracting simulated and imputed tax credits from gross PIT. When PIT is positive, regional additional income tax is simulated by applying the different fiscal rules of each region.

In order to validate the model, the results of our simulations are compared with data from the MEF. Table 3 compares the distribution of the total number of taxpayers by prevailing income source resulting from the model with respect to official statistics. The total number of taxpayers in the model is in line with the real one and the composition is very similar to the one of the MEF. These satisfactory results are expected given that one of the constraints of our calibration procedure (see Section 2.2) is the distribution of taxpayers by source of income and gross income classes.

Table 4 compares aggregate fiscal amounts simulated by the model with official data from the MEF⁹. The model is able to simulate quiet gross income, taxable income, gross and net PIT well. A little less accurate is the simulation of tax credits for family members. Results are in line with other microsimulation models. In Ceriani et al. (2016) the model over-estimates gross income by 3% and PIT by 1%. In Pellegrino et al. (2011) the average gross income is 97.5% of the real one. Models that also use administrative data obtain better results. In Di Nicola et al. (2015) a microsimulation model is built on a dataset that matches EU-SILC with administrative data on PIT and real estate datasets. Their results are very close to official statistics,except for municipal taxes, where the difference in amounts between the model and the MEF is lower than 1%.

Figure 1 shows the density function by gross income classes simulated by MicroReg and registered by MEF¹⁰. The overall distribution of gross income simulated by the model is close to the real one with some specific limits. The model under-estimates the number of taxpayers under 1,000 euro and over-estimates between 7,500 and 10,000 euro. The under-estimation in the first class depends on a typical problem of under-reporting on small amounts of income in EU-SILC¹¹. We do not correct for this under-reporting problem since taxpayers under 1,000 euro represents a small part of the total that do not pay PIT. The over-estimation of taxpayers between 7,500 and 10,000 euro is partially offset by a small under-estimation of taxpayers between 6,000 and 7,500 euro.

Figure 1

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Figure 2 reports the distribution of taxpayers with positive net PIT by gross income classes¹². The distribution of simulated PIT is quite similar with respect to official statistics. The number of taxpayers with positive PIT is 32.3 million in MicroReg against 31.2 million in official data of the MEF.

Figure 2

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Table 5 finally shows the main redistributive indexes calculated at the taxpayer level. The pre-tax Gini coefficient is about 0.42. After the PIT the Gini becomes 0.38 with a decreasing of 0.05. The strong redistribution is given by the combination of an average tax rate of 0.19 and a strong progressive tax (Kakwani index of 0.22). As expected, the redistributive effect of regional additional income tax is lower with respect to PIT. Indeed, several regions apply a proportional additional tax and others impose a less progressive system of tax rates than PIT.

One of the recent developments of MicroReg is the simulation of indirect taxes after a matching of EU-SILC with a database on consumption. An integrated database can be used with many aims: to analyse saving and consumption behaviour; to study consumption of durable or not durable goods; to make multidimensional analysis of poverty; and to study the impact of fiscal policies.

Despite the large availability of sample surveys, it does not exist a unique survey which collects information both on income (y) and consumption (z with a minimum level of accuracy and details. Basically, given the variables x,y,z,, where x is a set of households ‘characteristics, the database lacks completely or partially, the joint observation of all three. The only way to integrate the two datasets is to assume that information in x is sufficient to jointly determine both y and z. Literature suggests many solutions to integrate the two datasets (Decoster et al., 2007). Basically, at least two approaches can be distinguished and they are explained in the following.

One, the so called explicit approach, uses Engel curves to impute expenditure to the income database. According to this approach a regression of each expenditure share variables common to the consumption and the income database (usually disposable income and socio-demographic characteristics) is estimated on the consumption database. Then, the estimated coefficients are applied to records in the income database to impute expenditure shares for each good. An application of this procedure in Italy is in O’Donoghue et al. (2004). The survey which collects information on income is the SHIW, while the consumption database is the Italian Household Budget Survey (HBS). In the latter a variable on disposable income is collected (even if underestimated), so a regression of total consumption on income and socio-demographic characteristics is estimated. The estimated coefficients are then applied to SHIW to impute total consumption. Budget shares of total consumption are subsequently estimated in HBS trough Engel curves and applied to the imputed total consumption in SHIW. The explicit approach is more recently applied in Taddei (2012), where the income database is EU-SILC and the consumption one is HBS. The procedure is made in two steps. Taddei (2012) first applies a statistical matching to impute income from EU-SILC to HBS. Once imputed income to HBS by following the explicit approach, it estimates Engel curves to associate to each observation in EU-SILC a vector of budget shares for each consumption good.

The second approach, called implicit approach, tries to find for each household of the income database the most similar in the consumption database. This approach is not based on a statistical model or on theoretical assumptions that explain consumption behaviour, but on a statistical matching (D’Orazio et al., 2002). The matching links similar units through a distance function that should be minimized. Units are compared according to a set of socio-demographic characteristics, common to the two databases. The matching can be done only if the two surveys are random samples extracted from the same population. In Italy a statistical matching between the Bank of Italy Survey of Households Income and Wealth and HBS is in Battellini et al. (2009), in which the integrated database is mainly used to compile Social Accounting Matrices (SAM). More recently, in Pisani and Tedeschi (2014) a matching technique is applied to build an integrated dataset useful for direct and indirect tax benefit microsimulation models¹³. The income database is the Bank of Italy Survey of Households Income and Wealth and the consumption one is HBS. Before doing the matching, Pisani and Tedeschi (2014) estimate a propensity score to synthesize in one scalar all the different variables common to the two databases. The propensity score is indeed the estimated probability to belong to SHIW conditioning on the common set of characteristics. Then, they apply two different matching procedures. In the first one they associate to each observation in SHIW the one in HBS with the closest propensity score (nearest neighbour within calliper). In the second they use a function (called Mahalanobis) to measure for each unit in SHIW the distance to all units in HBS in the common variables (included the propensity score). The unit in HBS with the lower distance is then associated to each unit in SHIW. According to Pisani and Tedeschi (2014) the Mahalanobis distance function performs better than the nearest neighbour method.

In MicroReg an implicit approach based on a matching between EU-SILC and HBS is implemented. Therefore, our method is not parametric as the ones used in O’Donoghue et al. (2004) and Taddei (2012), but it is more similar to Pisani and Tedeschi (2014). The objective of the matching is to link each family in EU-SILC to the most similar in HBS, given the set of common observable variables. The matching is shown in detail in the following three steps:

1. Preliminarily a comparison between the common variables is made by using a T-test for the mean difference and a X²test for equality of distribution (results are reported in appendix, Tables A.4 and A.5). After, variables are standardized with the same classifications and encodings and aggregated at household level.

2. Secondly, we select the conditioning variables for the matching. We do not estimate a propensity score, as in Pisani and Tedeschi (2014), but we select among the distinct common variables. The common set of variables is selected by making a regression of consumption on socio-demographic characteristics (see results for the Centre of Italy in appendix, Table A.6). Some variables refer to households characteristics (such as residence area, number of components, number of rooms, presence of loan to pay, personal computer and dishwasher ownership, access to internet). Other variables refer to sociodemographic characteristics of household components (number of children, number of adults, type of work, number of earners).

   In order to improve the matching, for each EU-SILC household an estimation of total consumption is added to the set of common variables. More precisely, a regression of total consumption on household income is estimated for income quintiles in the Bank of Italy Survey of Households Income and Wealth. Indeed, SHIW collects detailed information on income, but also an aggregate measure of consumption. Then, estimated coefficients are applied to EU-SILC households to find the imputed total consumption that can be used in the matching.

3. Similarly to Pisani and Tedeschi (2014) we define a proximity function to integrate household by household information collected from both surveys. Our matching is made in two steps. A first exact matching for a selection of common variables (geographical area and number of components) is implemented. The exact matching allows linking each EU-SILC household with the corresponding HBS household, given the two selected variables. For the other variables the following proximity function is defined:

   (3) $s(x,y)=\max {\displaystyle \sum {}_{j=1}^N}{{{\displaystyle \sum }}^{\text{}}}_{i=1}^P{s}_i(x_{\text{ij}},y_{\text{ij}})\forall j\in N$
   (4) $s_i(x_{ij},y_{ij})=\{\frac{1\text{if}{\text{x}}_{\text{ij}}=y_{ij}}{0\text{otherwise}}$

Basically, the distance function counts for every household in EU-SILC, the number of variables with the same value in EU-SILC and in HBS. The total consumption is considered equal if the difference is lower than 1,000 euro. Finally, for each EU-SILC household the HBS household with the higher number of variables with the same value is associated. When two HBS household have the same number of equal variables the household with the lower difference of total consumption is linked.

In the integrated database the Value Added Tax (VAT) rates by type of expenditure are inversely applied to find the production price (HBS collect retails prices which include indirect taxes). Given the tax base VAT can subsequently be simulated.

The following statistics are used to validate the matching procedure and the VAT simulation. In line with expectations, the food share is higher in the South of Italy than in the North-Centre (Table 6) and the propensity to consume decreases by income deciles (Table 7).

The total VAT base is about 419 billion euro while tax revenue is 58 billion¹⁴ (Table 8). The validation of the simulation of VAT is not an easy task, as Taddei (2012) underlines, since official statistics about the revenue deriving from households are not available. As expected, our simulated tax revenue is lower with respect to the official data estimated by ISTAT (2016)¹⁵ (about 94 billion euro). Indeed, the official data includes the tax paid from public administration, no-profit institutions and others that, on the contrary, is not included in our simulation on final consumption of households. According to Taddei (2012) the percentage of total revenue that derives from households is about 70%. D’Agosto et al. (2012) estimates that about 68% of the potential tax revenue depends on final consumption of households. By applying these percentages to the total tax paid estimated by ISTAT (2016) a value around 64–66 billion is obtained, not very far from our result (58 billion euro). Further, our simulated tax revenue is in the middle between the one obtained by Taddei (2012), about 72 billion euro, and the one simulated by Gastaldi et al. (2014), around 49 billion euro.

Finally, Table 9 shows redistributive indexes, calculated at household level, for each VAT rate. Not surprisingly, VAT has a negative redistribution role. Indeed, the Gini of disposable income increases after the tax. Among the different rates, it is easily to see that the reduced rate (4%) has the most regressive impact with a negative Kakwani of 0.21. The reduced rate is applied to those essential goods that each household needs and, consequently, the fiscal burden is higher for lower incomes. Despite this, the ordinary rate shows the strongest negative redistributive effect owing to the highest average tax rate.

In conclusion, the matching results and the simulation of VAT are satisfactory and in line with expectations. The indirect tax module of MicroReg can then be used to simulate different scenarios of VAT reforms.

The second extension of MicroReg concerns in-kind transfers¹⁶. Many empirical studies about inequality and poverty do not consider benefits from public expenditure in in-kind transfers like education, health, transport and so on. The monetary disposable income is, however, only a part of the household welfare, which depends also on the public subsidies for the production and the financing of services. The inclusion of in-kind transfers in a microsimulation model allows: i) to compare their distributive impact with respect to in-cash transfers, ii) to make a more correct comparison between countries which have a different composition of in-cash and in-kind transfers, iii) to monitor the effects of cuts in services and spending reviews.

In order to estimate the distributive effects of in-kind transfers many methodological issues should be addressed (Gigliarano & D’Ambrosio, 2009). The first issue refers to the imputation of a monetary value to in-kind transfers. Usually the monetary value is quantified by estimating the average production cost of the public sector, even if this approach has several limits. For example, it does not take into account that differences in production costs could depend on differences in the quality of services, in inefficiency or on different costs of inputs.

Once quantified the monetary value, in-kind transfers should be imputed to the individuals/households of the sample (in our case EU-SILC). In literature, two approaches have been used, the actual consumption approach (AA) and the insurance value approach (IA).

The AA imputes the monetary value of in-kind transfers only to individuals who actually use the service. The advantage of this approach is that it considers the true usage of services and it takes into account individuals’ differences. Disadvantages are many. First, the attribution is not independent on the time interval considered, during which the use of services could be entirely random. Second, it does not consider different needs of families. For example, it can impute a large monetary value to old people who need many health services with a consequent strong re-ranking (old people become richer than people with more income who do not use services).

The IA imputes to every individual an average monetary value of in-kind transfers by demographic characteristics (usually age and gender), without taking into account the actual use of services. In health, for example, a sort of insurance premium against diseases is imputed to all individuals by demographic characteristics. According to the IA, the use of health services should not depend on random reasons (as in the AA), but on demographic differences. Also this approach, however, has some disadvantages. The possibility to have a re-ranking is still present (even if less likely than in the AA) and it does not take into account individuals’ differences.

In literature the AA is often applied for education. In health the debate is more open. In studies that compare both the approaches, it has been noticed a higher distributive impact of IA than AA (Baldini et al., 2007).

In evaluating the distributive impact of in-kind transfers further methodological issues must be addressed. Usually the long run effects of in kind-transfers (like education returns) are not considered in empirical studies. Further, there is no consensus about the correct counterfactual (the starting income) that should be used to evaluate the distributive effect of in-kind transfers and about the equivalence scale that should be used. Moreover, studies about in-kind transfers typically neglect externalities. In other words, by imputing the benefit only to students or to patients they under-estimate the positive externalities of education and health on the entire population.

In MicroReg the monetary value of in-kind transfers is quantified with the cost of production of the public sector. The monetary value is imputed to individuals through the AA approach, both for education and for health. The equivalence scale is not used for in-kind transfers, but a per-household member in-kind value is attributed to each individual. The modified OECD scale is used only for the monetary disposable income. In what follows methodological choices and data used for education and health are described in details. The simulation of in-kind transfers is performed only for the Region of Tuscany, both for education and health¹⁷.

3.2.4 The distributive impact of in-kind transfers

The incidence of simulated in-kind transfers on income by quintiles of equivalent disposable income shows the important distributive role of public expenditure, both in education and health (Figures 3 and 4).

Figure 3

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In education, the incidence clearly decreases with income and it is particularly high in the first quintile for high and middle school. The incidence is lower for pre-school even if still decreasing with income (Figure 3). Also health expenditure seems to affect more low income quintiles. Among the different services considered hospital ones tend to have a stronger impact (Figure 4).

Figure 4

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These descriptive results are confirmed by the redistributive indexes (Table 10) calculated at the individual level. All in-kind transfers in education have a positive redistributive impact like in Baldini et al. (2007). Further, similarly to Baldini et al. (2007) the stronger redistribution derives from primary, middle and high school. The progressivity index is particularly elevated for middle and high school. The reduction in the post-transfer Gini index is lower for pre-school and university. Pre-school has a high progressivity, but a low incidence. University is the less progressive education in-kind transfer.

Table 10

	Pre-transfer Gini	Post-transfer Gini	Avg. tax rate	Reynolds-Smolensky net redis. effect	Kakwani Progressivity index	Re-ranking
Pre-school	0.2838	0.2825	0.0050	0.0013	0.3186	0.0002
Primary school	0.2838	0.2808	0.0113	0.0030	0.3268	0.0006
Middle school	0.2838	0.2814	0.0068	0.0024	0.4062	0.0004
High school	0.2838	0.2776	0.0134	0.0062	0.5221	0.0007
Total school	0.2838	0.2712	0.0365	0.0126	0.4122	0.0019
University	0.2838	0.2824	0.0127	0.0014	0.2165	0.0014
Pharmaceutical services	0.2838	0.2802	0.0147	0.0036	0.2585	0.0001
Outpatient services	0.2838	0.2806	0.0129	0.0032	0.2544	0.0001
Hospital services	0.2838	0.2792	0.0305	0.0047	0.3250	0.0050
Total health services	0.2838	0.2731	0.0582	0.0107	0.2924	0.0054

1. Source: MicroReg.

According to our simulation, as in Baldini et al. (2007), but different with respect to Sonedda and Turati (2005)²⁰, health services decrease inequality. Inequality diminishes especially thanks to hospital services that have the higher incidence and progressivity. Different with respect to pharmaceutical and outpatient services, hospital services are concentrated on old people and their cost of production can be very high. Consequently, as in Baldini et al. (2007), hospital services have a strong re-ranking effect.

Due to data availability the model is extended to in-kind transfers only for the Region of Tuscany.

However, also in SHIW households’ wealth is highly under-estimated.

Second homes (when more than one) are considered together in the tax paid that remains after the dwelling house. This simplification should not be a problem since second homes are basically subjected to the same taxation, independently on their number.

The small difference depends on the sequence of the phases of the model. Indeed, the imputation of cadastral value precedes the sample weights calibration.

The data of Dipartimento delle Finanze and Agenzia del Territorio (2012) is a projection.

Actually in 2012 the cadastral value of the dwelling house is not included in gross income so it does not be deducted.

The imputation is made for each taxpayer, so in our model the number of taxpayers with positive gross income is equal to the number of taxpayers with positive taxable income.

Consequently, each taxpayer has a positive tax credit.

Results for each Italian Region can be found in appendix (Tables A.1 and A.2).

The comparison on the average value of gross income by gross income classes can be found in appendix (Figure A.1).

The problem is detected also in Di Nicola et al. (2015). They can recover the small amounts of income within PIT and real estate datasets.

The average value of PIT by gross income classes can be found in appendix (Figure A.2).

Gastaldi et al. (2014) evaluate some VAT reforms on the integrated database built in Pisani and Tedeschi (2014).

Tax base and tax revenue for each Region is reported in appendix (Table A.3). In appendix it is also shown the distribution of tax revenue by income and expenditure deciles (Figure A.3).

Table 10 “Imposte indirette prelevate dalle Amministrazioni pubbliche e dall'Unione europea per tipo di tributo. Anni 1995 - 2015 (milioni di euro correnti)”.

See Bianchini et al.(2013) for a previous application.

The education module can be easily extended to the rest of Italy. For health data are available only for Tuscany.

Data are taken from Comitato Nazionale di Valutazione del Sistema Universitario (CNVSU).

The services for which regional data are available do not cover the entire public health expenditure. Prevention, homecare, assistance against addiction, mental health assistance, primary and district care are excluded.

Sonedda and Turati (2005) find a regressive but weak and not highly significant impact of health expenditure. They follows the insurance value approach.

1. Version of Record published: April 30, 2017 (version 1)

© 2017, Maitino

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