Microsimulation and non parametric estimation - CiteSeerX

Microsimulation and non parametric estimation: is their combination useful? An application to Italian data Carlo V. Fiorio∗ London School of Economics and STICERD Preliminary version February 14, 2002

Abstract In this paper we present a novel combination of a microsimulation model (MSM) and non-parametric density estimation using Italian household data. With counterfactual analysis, we showed that overall decrease of inequality was due to a movement of part of the density mass from upper to lower levels of income. The sample was decomposed and the differential effects of the reform on various groups of the population analysed. Finally, studying the difference between a counterfactual after-tax and the actual 1998 after-tax income densities, we showed that changes in income brackets were much more effective in increasing income concentration than changes in tax allowances. These results were tested using the bootstrap.

JEL codes: C14, C15, H2, I32 ∗

I am grateful to Frank Cowell, Conchita D’Ambrosio, Emmanuel Flachaire and Fabrizio Iacone for helpful comments and fruitful discussions. I am indebt to Roberto Artoni and Luigi Bernardi for their support. Finally I gratefully thank the Bank of Italy for providing the SHIW data and Prometeia, and in particular Daniela Mantovani, for allowing me to use the Dirimod95 model. All remaining errors are my own responsibility. E-mail: [email protected]

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1

Introduction

At the beginning of the last decade, Italian national accounts were characterised by a dramatic level of public debt which had constantly increased since the early eighties. While other European countries took advantage of positive economic trend during the late eighties for stabilizing public debt over GDP ratio, Italy “missed the chance” entering the nineties with a public debt which was nearly 10% bigger than GDP. The turning point of Italian public finance management came with the monetary and currency crisis of 1992, which caused the recovery process to be started with no further delay. During the 90’s several tax policies were undertaken regarding both direct and indirect taxation. In particular, two clearly different periods could be distinguished: the first up to 1996 and the second starting from 1996. The first of these periods was characterized by constant political instability and frequent changes of the Minister of Finance, with several temporary taxes without a clear overall design, while during the second higher political stability favoured the design of a comprehensive tax reform. We will focus here on some aspects of the 1997-98 tax reform, and in particular on the effects caused on the distribution of income and inequality on Italian households caused by the Personal Income Tax (Irpef) reform. These topics have been analysed by other authors. Among others, Bosi et al. [7], Cer [9] and [10] and Birindelli et al. [5] analysed in detail the 1998 reform compared with the previous year legislation, while Giannini and Guerra [17] compared 1999 taxation system with the 1990 one. All these contributions use the Bank of Italy Survey on Household Income and Wealth (SHIW), updating the more recent database with CPI if necessary and using a microsimulation model (MSM) to recover the beforetax income, since all data in SHIW are net of taxes. Even though different MSMs are employed, the results are usually presented using the same methodology, namely, presenting an analysis of income variation per deciles decomposing the sample in many different subgroups, i.e. per income recipient, type of income, household head occupation, region of residence, gender and age of income recipient. All the mentioned contributions conclude that the reform caused an overall increase of Irpef liability on Italian households but there is less agreement in detecting the most and least affected group dividing the sample by area of residence and household head occupation. Moreover the results are at times numerically quite different. There are a few reasons why we are not completely satisfied with the analysis of microsimulation results provided in the mentioned works. With 2

regard to inequality, we think that it is necessary to consider the household, and not the income recipient, as unit of analysis for assessing the redistribution effects of taxation, using an equivalence scale to compare incomes of individuals belonging to household with different characteristics (Cer [9] and [10], in particular, do not introduce any equivalence scale). Moreover, the analysis of inequality and redistribution effects, when present is very sketched or not completely satisfactory (i.e. Bosi et al [7] and Giannini and Guerra [17] use the concentration coefficient while Birindelli et al. [5] use the Atkinson index neither of them explaining the reasons for their choice). With regard to analysis of distributions, we think that abundance of tables of results provided in the papers mentioned often results in an unclear picture of the effect of tax policies, expecially when confidence intervals are not computed. We feel that other methodologies ought to be investigated to increase access of these results and some test to our conclusion should be performed. Our claim is that microsimulation models are a great source of information and once built they have to be better exploited. In this paper we are not adding our own estimates to the effects of the Irpef reform but we are suggesting to use non-parametric density estimation for increasing access and draw conclusions out of MSM’s results. In Section 2 we describe the data set and the microsimulation model used. In Section 3 we build up the methodology we propose here and then present the results we obtained. Some other simulation are then performed and results commented and tested. In Section 4 we conclude.

2

The data set and the microsimulation model

The dataset we use in the present paper is the Survey of Household Income and Wealth (SHIW) published by the Bank of Italy and based on intrerviews run in 19981 . It collects detailed microdata about 7,147 households and 20,901 individuals regarding disposable income, consumption, labor market, monetary and financial variables. The sample was drawn in two stages (municipalities and households) with the stratification of the primary sampling units (municipalities) by units and size. Within each stratum, the municipalities in which interviews would be conducted were selected by including all municipalities with population of more than 40,000 and randomly selecting smaller towns. Household were then collected randomly and a sample 1

For the nineties the available issues are 1991, 1993, 1995, 1998.

3

weight has been attached to each observation, defined as the inverse of the probability of inclusion of each household in the sample. Since all SHIW data about income are net of taxes a microsimulation model is necessary for fiscal policy analysis. We limit our analysis to 1998 Personal Income Tax (Irpef) net of social and pension contributions. Irpef is the more relevant tax levied on personal income: together with Company Income Tax (Irpeg) it accounts for more than 85% of total Italian revenues from direct taxation. Given the disposable income declared by each unit of all households interviewed, before-tax income is derived estimating evasion and aggregating different income sources in a slightly different way from that used in the aggregation by the Bank of Italy. We built and developed our microsimulation model starting from the Dirimod95 model, built by Prometeia, Bologna. In particular we followed quite strictly the Dirimod95 model for reconstructing the before-tax (BT) income and tax evasion while we built by ourselves the algorithm for obtaining after-tax (AT) income. Anyway, so many were the changes we made on Dirimod95 that the final version is quite different from the original and all responsibilities for possible mistakes can only be attributed to us. Following Dirimod95, estimation of evasion is obtained making use of the “Analysis of 1992 Income Revenue”, published by the Ministry of Finance. Unfortunately it was not possible to use a more recent publication since the Ministry of Finance publishes these reports with great delay. The evasion estimation was performed in more stages, first imputing the AT income given the hypothesis of no evasion and then estimating the difference with data provided by the Ministry of Finance. The evasion was consequently estimated with a coefficient applied to disposable income dependent on the category of workers, from a minimum of zero evasion for dependent work income to a maximum of about 75% of evasion for imputed rents. We than obtained AT income using our algorithm and considering considering the fiscal legislation for 1998 and all available information about the characteristics of the household and its members.

3

Estimation of income densities and of their counterfactuals

Using U.K. data, Cowell et al. [12] among others showed the value of non parametric technique to detect irregular patterns of income distribution and the emergence of bimodality in income distribution and to provide explana4

tion for a particular evolution through time. They showed that UK income distribution during the 1980s presented a bi-modal character the nature of which changed substantially in the decade after 1979. From their subgroup breakdowns it appeared that the driving forces behind the aggregate changes were the shifts to higher levels of working households incomes, combined with an increase in the relative size of non-working household together with substantial immobility of its distribution. For Italy, D’Ambrosio [14] described the increase in polarization of the Italian households income distribution from 1987 to 1995, combining non parametric density estimation with polarization indices and showing it was caused by a movement apart of the southern and northern area of the country. Many other contributions could be mentioned in income distribution literature which proved the utility of the non parametric methods, but they usually present the common characteristics of just referring to disposable income while nothing is said about the role of the taxation system in the evolution of the distribution. In this paper we suggest combining microsimulation models and the descriptive power of non parametric density estimation both to increase the access of the microsimulation results and to facilitate the detection of unusual movements in income distribution, due to the recent fiscal reforms undertaken in Italy.

3.1

The density estimation technique

We use a non parametric techniques of density estimation to obtain a representation of the income density without excluding a priori any bimodality or irregularity in the income distribution. The non-parametric method we use here is derived from a generalization of the adaptive kernel density estimator to take into account the sample weights attached to each observation. The adaptive kernel is built with a two-step procedure. An initial estimate is used to get a rough idea of the density and this estimate is then used to obtain a pattern of bandwidths corresponding to the various observations and these bandwidths are than used for the construction of the adaptive kernel itself. In detail the procedure is as follows: e such that f(y e i ) > 0, ∀i defined as: 1. Find a pilot estimate, f(y)

5

¶ µ n X − y 1 y j i e i) = , ∀yj K f(y nhn hn

(1)

i=1

where n is the number of observations of the sample, hn is the fixed bandwidth parameter and K(.) is the kernel function. In this paper the kernel function used is the normal. 2. Define a local bandwidth factor λ(yi ) :

λ(yi ) =

Ã

e i) f(y g

!α

(2)

where α is the sensitivity parameter, such that 0 ≤ α ≤ 1, and g is e i ), i.e. e.: the geometric mean of f(y ´1/n ³ e i) g = Π f(y

(3)

3. The final estimation is given by: n

1 1X K fba (yi ) = n hn λ(yi ) i=1

µ

¶ yj − yi , ∀yj hn λ(yi )

(4)

where in addition to a global bandwidth parameter hn a local one is included in the estimating procedure λ(yi ). The adaptive kernel can than be modified to take into account the sample weights, θ i , associated with each observation. As a consequence every observation is weighted by θi and not by n1 implying that (1) becomes: b i) = f(y

µ ¶ n X θi yj − yi K , ∀yj hn hn i=1

while (4) becomes:

6

(5)

fba (yi ) =

n X i=1

θi K hn λ(yi )

µ

¶ yj − yi , ∀yj hn λ(yi )

(6)

where the sample weight are normalised to sum to one. Some remarks can be made at this point. Without going too much into the estimation technique properties we can just point out that the construction of the pilot estimate in the first step could be performed using also other density estimation technique even though the general view in the literature2 is that the method is insensitive to the fine detail of the pilot estimate. Making the local bandwidth factor dependent on a power of the pilot density gives flexibility in the design of the method so that, the larger the power α, the more sensitive the method will be to variations in the pilot density, and the more difference there will be between different bandwidth. In this paper we will set α = 12 . The definitions (4) and (6) of the adaptive kernel estimate ensures that, provided the kernel function is non-negative, the estimate will be a differentiable estimate without excessively heavy tails differently with what is frequent to have with the nearest neighbour method.

3.2

The non parametric density estimation and the microsimulation models combined

The combination of microsimulation and non-parametric density estimation we suggested here is developed in two stages. In the first stage, using the disposable income 1998 SHIW sample data and the fiscal legislation for 1998, we use the microsimulation model to obtain the element (yijt | ynjt , taxjt ), for each individual j belonging to the sample, where yijt is the AT income for individual j at time t, yn is his/her BT income (including estimated evasion) and taxjt is the amount of taxes j paid in year t. The element (yijt | ynjt , taxjt ) belongs to the conditional distribution density ft (yit | ynt , taxt ), which will be estimated with a non parametric technique. In the second stage, starting from (yijt | ynjt , taxjt ) obtained at the first stage, for any j belonging to the sample, we will use the same microsimulation model, properly modified to take into consideration differences in fiscal legislation, to get (ynjt | yijt , taxjz ), with z 6= t, belonging to the distribution ftz (ynt | yit , taxz ), where ftz is the counterfactual density and taxz is the tax system of year z at year t prices. This distribution can be 2

For details, see Silverman [23] and Abramson [2] among others.

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described as the “distribution of income that would have prevailed if taxes had remained at the z level”3 . We should say better that density is the density that would have prevailed at time t if taxes had remained at z level and income recipient had obtained exactly the same income, before state intervention”. Since we are concerned with household welfare we had to adopt an equivalence scale. Given the impossibility of obtaining a unique equivalence scale (see Cowell and Mercader-Prats [13] and Blundell and Lewbel [6]) we decided to adopt the Italian Poverty Commission approach, which is derived from the Engel methodology. The elasticity of total consumption on family magnitude is estimated by a weighted regression where, as dependent variable, we consider the proportion of food expenditure on total expenditure (ca ) and, as independent variable, the log of total household expenditure (C) and the log of the number of the member of the household (N): ca = a + b ln C + c ln N + u

(7)

The elasticity estimate is consequently obtained as ε = (−c/b) and the equivalent income of each member of household j can be estimated as: yh =

xh Nε

(8)

where xh is the household income and N is the number of household members4 . From the regression we performed on 1998 SHIW data, we got an elasticity equal to 0.757. The two main novelties of the 1998 Irpef reform with respect to previous years Irpef regard the modification of the tax brackets and of the tax allowances structure, while no relevant change in income base definition has been introduced. As shown in the Appendix, the number of fiscal brackets were reduced, from seven to five, with the reduction of the highest tax rate (from 50% of 1991, increased to 51% from 1992 onwards, to 46% of 1998), the increase of the first tax rate (from 10% of 1991 to 19% of 1998) and a substantial change of the others. The tax allowances for dependent work and self employment were increased in amount and in number, tax allowances for “family burdens” were increased, a new tax allowance for pension recipient where introduced depending on income and other few attributes. 3

Of course, if z = t we would get the net income back from our microsimulation model. For a detailed discussion for the equivalence scale choice by the Poverty Commission, see De Santis [15]. 4

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As we can see from Figure 1, the reduction of dispersion induced by the fiscal system is clearly depicted: the 1998 BT income distribution reaches a higher maximum than the after-tax one, while the former presents a thinner tail than the latter showing that the fiscal system is very effective in reducing the density at medium-high level of income. Moreover, in both distribution there is no clear evidence of bimodality. Given this pattern we can reasonably expect that the inequality indexes will show a decreasing trend from BT income to after-tax income and will checked later. More interesting is the comparison between the two after-tax distribution, the actual and the counterfactual one. The latter was estimated after simulating for each individual in the 1998 sample what would have been his income had he received the same income BT that he received in 1998 and had the tax schedule been equal to that of 1991 (the 1991 tax brackets and the amount of tax allowances were updated to 1998 prices using the CPI)5 . We can clearly see that the counterfactual after-tax density reaches a lower maximum, than the actual after-tax income density. Moreover, the estimated modes are basically the same for the two densities and no clear bimodality is appearing6 . We omit the estimation in logs since they are not much more informative than the case in levels while the latter allows me to keep the income scale on the horizontal axis, without any transformation. For assessing inequality dynamics in the different situations we computed the Lorenz curves before starting any consideration about which inequality index to choose. Since we estimated the density function for the different kind of incomes, we computed the continuous version of the Lorenz curve (Lambert [21]). Provided that the density function is non zero throughout the range [x1 , xn ], where n is the number of observation, and x1 < xn , then for each p ∈ (0, 1), there is just one income level p, which satisfies R y p = F (y), the income of the first 100p percent of income recipients is n 0 xf(x)dx and the total income R∞ is n 0 xf(x)dx = nµ, where µ is the mean income. Hence, using fb for the density estimation of income, we can define the Lorenz curve L(p) by p = F (y) ⇒ L(p) =

Z

0

y

xfb(x)dx ,0 < p < 1 µ

5 We have considered the 1991 as the comparison year since 1992 is regarded as the year before “turning point” of Italian public finance managment. The year 1991 is the last year before the recovery process. 6 Even though a polarization index may be recommendable, we are not considering it here.

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In Table 1 we provide the Lorenz curve for BT income, counterfactual after-tax income and actual after-tax income. Since the Lorenz curve do not cross, we can consequently say that 1998 after-tax income Lorenz-dominate (i.e. is more equally distributed of) the counterfactual after-tax income, which Lorenz-dominates the BT income. This results will be confirmed by a large class of inequality indices satisfying axioms of anonymity, mean independence and the transfer principle (Cowell [11]). We report in Table 2 some inequality indices which coherently with what stated before show that equality is increased by 1991 Irpef and even more by 1998 Irpef. Table 1: Lorenz curve for different type income. Pop. share 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 1

BT income. 0.0117 0.0396 0.0811 0.1363 0.2066 0.2936 0.3997 0.5308 0.6986 1

count. AT y 0.0161 0.0560 0.1146 0.1920 0.2880 0.4015 0.5282 0.6631 0.8086 1

AT y 1998 0.0176 0.0611 0.1247 0.2093 0.3123 0.4315 0.5615 0.6939 0.8313 1

Table 2: Some inequality indices for different type of income. AT income count AT y AT income rel. mean deviation 0.306 0.288 0.285 coeff. of variation 0.923 0.826 0.818 Gini index 0.429 0.404 0.401 Theil entropy meas. 0.325 0.283 0.279 Theil mean log dev. 0.359 0.315 0.312 Let’s now see what additional insights can we get from the non-parametric density estimation. In Figure 2, the difference between the counterfactual and the actual after-tax density is depicted. This figure makes even more clear the shift of density mass from high to lower levels of income and increase of concentration around the mode. The negative values reached by the difference means that there are more individuals with equivalent income 10

levels nearby the mode of the distribution and that, to the contrary, there are less with equivalent income higher than 180 millions lire. Decomposing the sample by occupation of the household head (Figures 3, 4, 5, and 6) and by size (Figures 7 and 8) other interesting observations can be made. Looking at the sign of the difference between the counterfactual and the actual after-tax income density, all decompositions presented show that the difference is negative at first and becomes positive at higher levels of income. This pattern is in particular clear for household whose head is either selfemployed (Figure 4) or not employed, excluding pensioners (Figure 6) and for different size of households (Figures 7 and 8). Observing the level of the difference at zero income level we can in particular notice that while household with dependent worker head (Figure 3) and household with four or more components (Figure 8) do not present a negative jump, this is present in the other cases. A negative difference at zero equivalent income means that introducing a personal income tax such as the 1998 Irpef in substitution of the 1991 Irpef causes an increase of density of people whose income is nil or almost nil. In particular, the jump is significantly negative for household whose head is not employed (Figure 6). For the SHIW dataset is not employed both the unemployed (i.e. a person who is not working but is looking for a job) and who is not part of the labour force (wealthy person, housewife, student, military servant). The negative value of the densities difference for this group of people means that the probability of experiencing poverty is much higher after the reform than before. This result probably comes from the fact that for this group of people the marginal tax rate is much increased (from 10% to 19%) while they cannot properly take advantage of the increase in tax allowances since they are neither dependent, self-employed worker nor pension receivers.

3.3

A revenue-neutral reform simulation

Since the 1998 Irpef reform induced a relevant increase of revenue compared to 1991 system we performed a revenue-neutral simulation. We assumed two different revenue-neutral simulations. In the first the eccess of revenue is distributed equally to each individual in the population, in the second the eccess revenue is distributed to each individual proportionally to BT income. In reality we can equally think of redistribution as happening in cash or in kind or in reductions of other taxes liability. Being the difference of the densities in the first simulation positive at low level of income (Figure 9) it is clear that such a policy, if compared to 1998 11

counterfactual AT income, would induce a reduction of the density at lower level of income and an increase in the mode of the distribution basically due to a shifting of the former distribution to the left. Since the transfer is pro capite, it would benefit more the larger households. In the second simulation instead the proportional redistribution is greately reducing the effect of the reform to income distribution, the difference being much smaller than in the previous cases (Figure 10). If the difference was not significantly different from zero we could conclude that the eccess revenue is due to an increase of tax liability proportional to BT income. Given the nature of the proportional redistribution simulated, there is no reranking issue involved here.

3.4

Decomposing the fiscal reform

In order to investigate the aggregate relevance of the tax allowances compared with the change in income brackets structure for reducing total inequality, we have pushed further the combination of microsimulation and non parametric density estimation. In particular, we decomposed the difference between the counterfactual densities and the actual one we have estimated so far (see Figure 2 , and bottom parts of Figures 3, 4, 5, 6, 7 and 8), in such a way that the more effective element in the reform and the point in the distribution where it had more influence can be clearly detected. Indicating with td = 98 the set of tax allowances from gross tax liability in 1998 and with tirp = 98 the tax bracket structure of 1998 and analogously for 1991, we can represent the difference between the two densities we mentioned before as in (9) and decompose this difference in several other differences of interest. In (11), for example, we have the difference between a counterfactual after-tax income density, which was obtained using the 1998 tax allowance system and the 1991 gross Irpef and the actual 1998 after-tax income density. f(yn | yi98 ; td = 91, tirp = 91) − f(yn | yi98 ; td = 98, tirp = 98) =

(9)

[f(yn | yi98 ; td = 91, tirp = 91) − f (yn | yi98 ; td = 98, tirp = 91)]

(10)

+[f(yn | yi98 ; td = 98, tirp = 91) − f(yn | yi98 ; td = 98, tirp = 98)]

(11)

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In the last part of this paper we simulate two alternative Scenarios, both on 1998 data. Scenario 1 is characterised by a tax allowance system from gross tax liability equal to the one actually in use in 1998 but with an income bracket structure and tax rates as in 1991 (i.e. the difference in (11)). On the other hand, Scenario 2 considers the case in which the tax allowance system is like that in 1991 and the income brackets structure and tax rates as in 1998. Results are shown in Figures 11 and 12. It is evident that the Scenario 1 density approaches the actual after-tax one more clearly in Scenario 1 than in Scenario 2. This is evident both from the kernel density estimation and from the performed differences (which, are plotted keeping the same reference level on the vertical axis). While the difference between the counterfactual Scenario 1 and the actual densities is well about the zero difference line, the difference between the counterfactual Scenario 2 and the actual densities shows an increase of concentration around the mode (i.e. a negative difference) and a decrease of concentration at the higher tail (i.e. a positive difference) for higher level of income. To provide more evidence about this conclusion, we use some of the summary indices which have been suggested in the statistical literature7 . These indices are built considering two probability distributions F1 and F2 , with corresponding densities f1 and f2 , absolutely continuous with respect to Lebesgue measure and with respect to each other. The Jeffreys measure of divergence is:

J12 (y) =

Z

∞

0

[f1 (y) − f2 (y)] ln

f1 (y) dy f2 (y)

(12)

The Kolmogorov measure of distance is: 1 K= 2

Z ³p ´2 p f2 (y) − f1 (y) dy

(13)

The Komogorov measure of variation distance is: 1 Kov = 2

Z

|f2 (y) − f1 (y)| dy

(14)

7 For details about a general class of measures of divergence of distributions, see Ali and Silvey [1].

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Calling f1 the density of 1998 actual after-tax income and f2 the density of one of the two scenarios considered, the results of computation can be seen in Table 3. Table 3: Indices of divergence of distribution J K Kov

act.AT-count.AT 0.5287 ∗ 10−2 0.0442 ∗ 10−2 2.2138 ∗ 10−2

Actual - Scen1 0.0237 ∗ 10−2 0.0020 ∗ 10−2 0.4290 ∗ 10−2

Actual - Scen2 0.4523 ∗ 10−2 0.0378 ∗ 10−2 2.1335 ∗ 10−2

The distance between the actual density and the counterfactual Scenario 1 is significantly smaller than the distance between the actual density and the counterfactual Scenario 2, confirming that the reduction in inequality of equivalent income induced by Irpef reform for 1998 income was mainly due to the new structure of income brackets and in particular to the increase of the tax rates, while is only marginally due to the change of the structure of tax allowances. Focussing on the Kolmogorov measure of variation distance, we finally test if the difference in distributions is statistically bigger for Scenario 2 with respect to Scenario 1. Defining Tb(1) and Tb(2) the Kolmogorov measure of variation between the actual and Scenario 1 (second column of Table 3) and the distance between the actual and Scenario 2 distributions (third column of Table 3) respectively, we define the statistic: τ = (Tb(2) − Tb(1) ) b

(15)

b τ ∗ ≡ (Tb(2)∗ − Tb(1)∗ ) − (Tb(2) − Tb(1) )

(16)

and test H0 : τ = 0, H1 : τ > 0. Since we do not know the true distribution of b τ , we estimate it through bootstrap resampling. The main problem with this test is the dependency of F1n , F2n on F3n since the former are obtained from a MSM using two different tax schedule but the same sample, whose density is F3n . Consequently, to compute the critical values, we pooled the datasets keeping dependency obtaining S = {(x1 , y1 , z1 ), ..., (xn , yn , zn )} and then we bootstrapped B new samples of the same dimension Si∗ = {(x∗1 , y1∗ , z1∗ ), ..., (x∗n , yn∗ , zn∗ )}i , with i = 1, ...B. Since our new samples are obtained from S, whose statistic τ is as in (15) the bootstrap statistic which will provide us with the empirical distribution function will be, as discussed in the introduction of Hall [19],

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Our test will consist in counting how many times b τ >b τ ∗ . The bootstrap p-value, using I as indicator function, p* is p∗ =

B 1 X I(b τ ∗i > b τ) B i=1

(17)

If the bootstrap test rejected H0 , we would conclude that the Komogorov measure of variation distance Tb(2) is significantly bigger than Tb(2) and the difference shown in Table 3 is not only due to chance. [Results of bootstrap to be completed]

3.5

Pros and cons of this methodology

We believe that the approach we have taken in this paper is successful to show the results of MSMs in a more effective way than generally used in the literature, where table of numerical results and histogram are commonly used. While numerical results are often difficult to interpret, expecially if no confidence interval is provided, histogram has the relevant drawback of suffering of the discretisation of the income range: easy excercises of changing the bin width and origin show that histogram estimates are highly unrobust (see for example Silverman [23]). Given the speed of modern calculators, density estimation can be quickly estimated and compared with the difference of alternative distribution providing many insights about the evolution of the distribution. A non parametric density estimation can also allow tests of distance of distribution after a reform has been undertaken without being alternative to stochastic dominance analysis for ranking distribution. This approach does not give any insight about the reranking of the population but just a picture of overall distribution of income in the total population or in a subgroup of it.

4

Conclusions

In our paper we proposed a methodology consisting in a combination of microsimulation and non parametric density estimation for public finance policies analysis. We showed that this combination can greatly increase the understanding and access of microsimulation results and provide useful insights regarding income distribution profiles.

15

Simulating after-tax income for 1998, we showed the higher concentration induced by taxation system. The combination of microsimulation and nonparametric density estimation allowed us to show that the 1998 Irpef system increased the concentration around the mode with respect to the updated 1991 Irpef system. The higher concentration was obtained with a movement of part of density mass from upper level of income to lower levels, resulting in an overall decrease of inequality. Decomposing the sample into different subgroups, the loss incurred in households with non-employed head has been shown in terms of an increased probability of being in the lower levels of income and experiencing poverty for households belonging to this group. Finally, decomposing the difference between the counterfactual aftertax density estimate (1998 BT income with 1991 Irpef) and the actual 1998 after-tax income we showed clearly that changes in income brackets were much more effective in increasing concentration than changes in tax allowances. This result was verified both graphically and numerically using some measure of distance between distributions and a bootstrap test has been suggested. All these results showed that the use of non-parametric density estimation technique can significantly improve the analysis and understanding of MSM’s results.

5

Appendix: 1998 Irpef vs. counterfactual 1991 Irpef

Here are the details about the difference between the 1991 and the 1998 legislations. The counterfactual density has been simulated updating 1991 Irpef tax brackets and tax allowances to 1998 price.

5.1

Income brackets and tax rates

Income brackets were reduced from seven to five (income brackets in millions Italian lire):

16

1991 Irpef* Counterfactual* 0-6,800 0-8,786 6,800-13,500 8,876-17,442 13,500-33,700 17,442-43,540 33,700-67,600 43,540-87,339 67,600-168,800 87,339-218,090 168,800-337,700 218,090-436,308 over 337,700 over 436,308 * amounts in thousands Italian lire

5.2

% 10 22 26 33 40 45 50

1998 Irpef* 15,000 15,000-30,000 30,000-60,000 60,000-135,000 over 135,000

% 19 27 34 40 46

Tax allowances for “family burdens”

For a fiscally dependent partner, tax allowance depends on BT income: 1991 Irpef* any income

tax all.* 675

Counter. tax all.* 872.1

1998 Irpef* 0-30,000 30,000-60,000 60,000-100,000 over 100,000

tax all.* 1,057.552 951.552 889.552 817.552

* amounts in thousands Italian lire 1991 tax all.* depend. child 78 other dep. relative 108 * amounts in thousands Italian lire

17

counterf tax all.* 101 139.5

1998 tax all.* 336 336

5.3

Tax allowances for dependent workers

1991 Irpef* 12,400 12,400-12,659 over 12,659

Fisc.all.* 851 750** 648

count. brack.* 16,021 16,021-16,355 16,355

t.a.* 1,099 969 837

1998 brack.* 0-9,100 9,100-9,300 9,300-15,000 15,000-15,300 15,300-15,600 15,600-15,900 15,900-30,000 30,000-40,000 40,000-50,000 50,000-60,000 60,000-60,300 60,300-70,000 70,000-80,000 80,000-90,000 90,000-90,400 90,400-100,000. over 100,000

t.a.* 1,680 1,600 1,500 1,350 1,250 1,150 1,050 950 850 750 650 550 450 350 250 150 100

* in thousands lire. ** is an average. The actual tax allowance (in thousands Italian lire) was computed as 851-[(yi-12,400)*0.78], where yi is BT income. If the individual receives only a pension income which is less than 18 million lire, and he is not owner of other building apart from the principal dwelling , there is an additional tax allowance equal to 70,000 lire in 1998 while he did not receive anything in 1991..

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5.4

Tax allowances for self-employed workers

’91 inc. brack* 0-6,800 6,800-7,000

tax.all.* 168 90**

Counterf.* 0-8,786 8,876-9,044

t.a.* 217 116

New Irpef* 0-9,100 9,100-9,300 9,300-9,600 9,600-9,900 9,900-15,000 15,000-30,000 30,000-60,000

t. a.* 700 600 500 400 300 200 100

* in thousands lire. ** is an average. The actual tax allowance (in thousands Italian lire) was computed as 168-[(yi-6,800)*0.78], where yi is BT income.

References [1] Ali, S.M. e S. D. Silvey (1966), “A General Class of Coefficients of Divergence of One Distribution from Another, Journal of the Royal Statistical Society, Serie A, 1, 131-142; [2] Abramson, I. S. (1982), “On bandwidth variation in kernel estimates a square root law”, 10, 1217-1223; [3] Bernardi, L. (1989), “Per un’introduzione al dibattito sul sistema tributario italiano e alle proposte di riforma”, in Antonio Pedone, La questione tributaria, Il Mulino, Bologna; [4] Bernasconi, M. e A. Marenzi (1998), “Il deficit pubblico al 3%. Linee interpretative del processo di risanamento”, in L. Bernardi (ed.), La finanza pubblica italiana. Rapporto 1998, Il Mulino, Bologna; [5] Birindelli L., L. Inglese, G. Proto e L. Ricci (1998), “Gli effetti redistributivi della politica economica e sociale” in N. Rossi (ed.), Il lavoro e la sovranit` a sociale, 1996-1997, Quarto rapporto CNEL sulla distribuzione e redistribuzione del reddito in Italia, pp. 147-200, Il Mulino, Bologna; [6] Blundell, R. W. e A. Lewbel (1991), ”The information content of equivalence scales”, Journal of Econometrics, 50, 49-68;

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[7] Bosi, P., D. Mantovani e M. Matteuzzi (1999), “Analisi degli effetti redistributivi della riforma IRAP-IRPEF”, Nota di lavoro, 2, Prometeia, Bologna; [8] Brandolini, A. and L. Cannari (1993): “Methodological appendix: The bank of Italy’s Survey of Household Income and Wealth”, in Savings and the Accumulation of Wealth. Essays on Italian Households and Government Saving Behaviour, ed. by A. Ando, L. Guiso and I. Visco, Cambridge University Press, Cambridge; [9] C.E.R. (1998), La riforma fiscale: una simulazione con il modello macroeconomico del C.E.R., April, Centro Europa Ricerche, Roma, mimeo; [10] C.E.R (1998), La manovra IRAP-IRPEF. Effetti microeconomici sui percettori di reddito e sui bilanci familiari, June, Centro Europa Ricerche, Roma, mimeo; [11] Cowell, F. A. (1995), Measuring Inequality, (second ed.), Harvester Wheatsheaf, Hemel Hempstead; [12] Cowell, F., S. P. Jenkins, J. Litchfield (1996), “The changing shape of the UK income distribution: Kernel density estimates”, in J. Hill (ed.) New inequalities, Cambridge University Press; [13] Cowell, F. e M. Mercader-Prats (1997), “Equivalence of Scales and Inequality”, Distributional Analysis Discussion Paper, 27, STICERD, London School of Economics, London; [14] D’Ambrosio, C. (2000), “Household characteristics and the distribution of income in Italy: an Application of Social Distance Measures”, forthcoming in Review of Income and Wealth; [15] De Santis, G. (1998), “Le misure della povertaa in Italia: scale di equivalenza e aspetti demografici”, Commissione di indagine sulla povertaa e sull’emarginazione, Presidenza del Consiglio dei Ministri, Dipartimento per gli affari sociali, Roma; [16] Gerelli, E. and A. Majocchi (1984), Il deficit pubblico: origini e problemi, Franco Angeli, Milano; [17] Giannini, S. e M. C. Guerra (1999), “Il sistema tributario verso un modello di tassazione duale”, in L. Bernardi, La finanza pubblica italiana: Rapporto 1999, Il Mulino, Bologna; 20

[18] Grilli, V. D. Masciandaro and G. Tabellini (1991), “Political and Monetary Institutions and Public Finance Policies in Industrial Countries, Economic Policy, 6, 342-392; [19] Hall, P. (1992), The Bootstrap and Edgeworth Expansion. Springer series in Statistics, Springer Verlag, New York; [20] Jenkins, S.P. (1994), “Did the middle class shrink during the 1980s? UK evidence from kernel density estimates”, Economics letters, 407-413; [21] Lambert, P. J. (1993), The distribution and redistribution of income (Second Edition), Manchester University Press, Mancester; [22] Redmond, G., H. Sutherland and M. Wilson (1998), The arithmetic of tax and social security reform, Cambridge University Press, Cambridge; [23] Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.

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Figure 1: Estimated densities compared

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Figure 2: Differences in densities

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Figure 3: The household head is dependent worker

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Figure 4: The household head is self-employed worker

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Figure 5: The household head is pension receiver

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Figure 6: Household head is not employed

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Figure 7: Household with 3 or less members

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Figure 8: Household with 4 or more members

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Figure 9: Lump sum redistribution of eccess revenue

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Figure 10: Redistribution proportional to BT income

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Figure 11: Counterfactual Scenario 1 vs. actual after-tax income densities

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Figure 12: Counterfactual Scenario 2 vs. actual after-tax income densities

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