Dealing with Residents and Cross-borders in a Tax-benefit Model for Luxembourg

When the resident population alone is at stake, EUROMOD may be run on the classical “European Union Statistics on Income and Living Conditions” (EU-SILC) data.⁷ Unfortunately, EU-SILC data are not covering cross-borders.

Alternatively, a EUROMOD model is running on the “Household Finance and Consumption Survey” (“HFCS”) data for residents.⁸ HFCS data are also available in Luxembourg for active cross-border households,⁹ that is residing in the Greater Region and involving at least one member working in Luxembourg, hence not embedding all persons covered through the LU social security or fiscal systems.¹⁰ This last survey “is specifically designed to complement the Luxembourg Household Finance and Consumption Survey” initially set up for residents only (Chen et al., 2021). The overall coverage of both residents and active cross-border households induces us to adopt this HFCS-based framework for the present analysis, yet some comparison with SILC-based outcomes can be maintained sometimes.

Hereafter we use “EUROMOD/SILC”, “EUROMOD/HFCS-R” and “EUROMOD/HFCS-XB” to refer either to the EUROMOD models based on SILC or HFCS data, or to the EUROMOD input databases built from the same datasets, depending on the context. For simplicity reasons, we are also referring to “XBs” (cross-borders) as to “active commuter cross-border households” or “all cross-border households”, indifferently and depending on the context.

Three waves have been collected up to now for HFCS in Luxembourg: 2013 (income reference year), 2017 and 2020 (not available yet at date of the present analysis). The present analysis is building on the most recent wave available when the microsimulation tools were designed (2022), that is 2017. Therefore and given our objective to involve the XBs in the analysis as well, we have to update a former version of the EUROMOD/HFCS-R model, to take into account a more recent wave for the HFCS data for residents, namely the 2017 one (income reference year), and more recent policy systems in the EUROMOD model as such, up to 2017. And we build a new version of the EUROMOD/HFCS-XB model targeting that additional population.

Note that for dealing with missing information resulting from the HFCS surveys, “a multiple stochastic imputation strategy has been chosen [by the designers of the surveys]. The dataset provides five imputed values (replicates) for every missing value corresponding to a variable entering the composition of household wealth, consumption or income”.¹¹

Practically, this implies that an input created for the purpose of microsimulation from HFCS microdata is composed of 5 datasets, each of them involving the whole sample. Those 5 inputs are simulated and analyzed in turn, generating altogether 5 outputs. Finally, all outcomes shown up in the present paper are, for each variable and unless otherwise mentioned, output means resulting from those multiple outputs.¹²

Finally and for comparative reasons, the EUROMOD/SILC model may be used as well, building here on wave 16 (income reference period: 2017).

Most outcomes in this paper resulting from the “EUROMOD/SILC and EUROMOD/HFCS models for Luxembourg resident and cross-border populations, version I4.62+ Beta release (3.4.10), in combination with the author’s computations”, we are considering this piece of information as implicit for all tables and Graphs where no other mention of sources is explicitly provided.

Table 1 below is showing up some basic information about the samples retained for the different EUROMOD models, directly depending on the microdata those are grounding on (HFCS-R 2017/wave 3 and HFCS-XB 2017/wave 3). For comparative concerns, we also add some information derived from the EU-SILC data, hence the well-established EUROMOD/SILC model.

The discrepancy between the weighted number of persons covered through the EU-SILC data, on one side, and HFCS-R data, on the other side, are partially explained only by the international civil servants’ households being embedded to a more comprehensive extent in EU-SILC.¹³

Another remarkable information in Table 1 is about the dimension of the samples. The number of persons and households interviewed through the HFCS-R survey being lower than under the EU-SILC environment, we may expect by principle outcomes less accurate in terms of background confidence intervals.¹⁴ This could become more noticeable when looking into sub-groups of population, taking into account income deciles, levels of wages, types of households etc.

Even if essential topics like outcomes for higher income deciles and wealth-related concerns and transfers are deeply examined in HFCS-R compared to alternative datasets, some (monetary) variables are sometimes aggregated or missing, compared to EU-SILC. Fortunately, the EUROMOD/SILC model can be adapted anyway to run EUROMOD/HFCS-R.

HFCS-XB data deserve some additional comments as well. Less information is collected, compared to HFCS-R, especially for non-“reference/FKP” household members (for example about the economic activity). Moreover, some variables are missing or have been aggregated in HFCS-XB (for example in relation with Luxembourgish versus non-Luxembourgish origin of revenues).¹⁵ This last limitation matters as we need some idea about that part of income leading to social contributions and taxes specifically due to Luxembourg (see Section 2.3).

Therefore, we have to impute some missing information in HFCS-XB, which is reported in Appendix A.

The outcomes from EUROMOD/HFCS-XB are primarily based on total household incomes, whatever originated from Luxembourg or other countries.

For total revenue regarding Luxembourg, a main concern in case of a change in socio-fiscal rules, we stick to the Luxemburgish tax authority’s 2-step computation. Firstly, a global tax rate is derived from EUROMOD for each XB household, considering its total taxable income (whatever the geographical origin of revenues) and Luxembourgish fiscal rules only. Secondly, this rate is applied to income originated from Luxembourg only, to fix the tax due to Luxembourg.

Therefore, we are neither considering foreign socio-fiscal rules nor dealing with separate bilateral fiscal agreements between Luxembourg and surrounding countries,¹⁶ what we refer to as “hypothesis H1” (through the present paper, we emphasize strong or prominent hypotheses regarding XBs by this type of “Hx” marker signal, essentially in Appendix B). Such a simplifying approach, out of being easily applicable, seems also sufficiently close to real practice and acceptable as a prior step.

Leaving aside XB households which do not presently involve any active worker in Luxembourg, for example a couple of Belgian pensioners, may reduce the total public revenue seen as due to Luxembourg. Some social contributions or personal income taxes are then ignored by the present exercise. Therefore, the information is partial and a comparison to other more comprehensive official statistical sources might be difficult.

Therefore, we show in Appendix B how, building on outcomes from the EUROMOD/HFCS-R and EUROMOD/HFCS-XB platforms, how we choose to roughly complete the picture to add to social contributions and personal income taxes revenue from those XB households ignored up to now. Such a “macro adjustment” leads, for the reference year 2017, to a supplement of 1.1% for social contributions ([VI]/[IV], Table B1) and 2.7% for the tax on income ([XV]/[TAX/HFCS+], Table B2).

These amounts deserve to be taken into account −and they are− without fundamentally altering the overall picture, given our objectives. But the distributional effects derived from EUROMOD/HFCS-XB are not entirely relevant and are therefore only marginally addressed in this document.

Table 2 is gathering such a rich information in the context of our benchmark “STD” which is a picture available for Luxembourg in 2017 (income year), as derived from several microsimulation platforms and additional macro adjustments.

The top lines of Table 2 are reminding the populations covered by the data and simulation models and show the total taxable income before tax allowances (based on EUROMOD variables tinty_s for residents, tinty_lu_s for the XBs) available for Luxembourg. Active XB households are providing an amount that is 40% of the taxable income coming from residents: 7.95 billion € as computed through microsimulation (hence an aggregation of individual results), against 20.04 billion € for residents in 2017 (based on EUROMOD/HFCS-R and XB, see also Footnote 20).

Then comes information about the total public revenue for Luxembourg in terms of social contributions (3.71 billion € from residents if HFCS data; 2.03 billion € from XBs), with several sources participating in this total, and taxes on personal incomes (3.44 billion € for residents; 824 million € from XBs), taking into account several tax credits reducing the tax after a prior application of the tax schedule to the tax base. It appears that the overall tax rate on XB income is 824/7,947=10.4%, much lower than for residents (17.2%). We will come back to that downstream.

The next section in Table 2 is reporting several “well-being” and “inequality indices” for residents, all dimensions genuinely embedded in an approach undertaken through microsimulation. As seen from Table 2 for residents, the usual sub-groups of households like “Single with dependents” or “Couple with 3 dependents or more” are facing a well-being much lower than other categories of population. This is complementarily illustrated for those sub-groups by a higher level of poverty (18% and 21%, if EUROMOD/HFCS-R environment). The poverty risk represented here is the share of population below 60% of the median equivalent income, a threshold called the “poverty line”, also shown in Table 2.

Another indicator is telling something about the unequal distribution of well-being throughout the population: the inequality Gini coefficient. As summarized in Vergnat et al. (2022), this coefficient is an index with a value between 0 and 1 (0.2993 in Luxembourg in 2017, based on EUROMOD/HFCS-R). It increases if inequalities in equivalent incomes become greater (zero would indicate perfect equality; the same income for all). It is equal to the absolute Gini index (the average absolute difference between incomes, 2,103 EUR/month) divided by twice the average equivalent income (3,513 EUR/month).¹⁸

We are not commenting the levels of well-being, poverty and Gini resulting from the EUROMOD/HFCS-XB platform for XB active households. This population is partial only, compared to the usual reference involving a whole (resident) population, hence comparisons more hazardous, as already mentioned earlier. And what will be at stake at that moment will be the changes in several indicators, on top of absolute values given here as basic references.

In the same vein but for other reasons, we are not commenting outcomes from EUROMOD/SILC, also for the resident population (international civil servants’ households included). Differences may be important in comparison to results obtained through EUROMOD/HFCS-R, especially when having a look on sub-groups, less numerous in terms of survey observations (see for example the risk of poverty for Single with dependents, quite high through SILC). Those gaps might deserve a deeper analysis in future times.

However, we note that total public revenue, as derived from the two platforms, are close each other, embedding a lower level of social contributions through EUROMOD/HFCS-R (-5%), partially compensated by more income taxes (+5%).

Finally, Table 2 is embedding some additional information related to the macro adjustment for XBs uncovered through HFCS data as introduced in Section 2.4.

Figure 1 shows how the resident and active XB populations of Luxembourg are spread based on their so-called “employment” status in 2017, that is their socio-economic status at large as referenced to in the EUROMOD environment.

Figure 1

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As mentioned earlier, “active” XBs are gathering all XB households embedding at least one worker presently active in Luxembourg. Therefore, the active XB population cannot be compared as such with the resident one. A more appropriate basis for comparison might be to concentrate, on the resident side, to households reporting some labor income only. This sub-resident population is also shown up in Figure 1 as a matter of comparison.

The employees and pensioners represent altogether a little less than 60% of the whole resident population. Therefore, we can expect larger effects of changes when these groups are affected. On the contrary, an alternative targeting the self-employed is likely to show smaller overall effects (this group is still lighter in HFCS-XB).

Obviously, the share of pensioners is much more limited when considering the active XB households (2%, against 17%), even if we compare “active” sub-groups (2%, against 6%). Let’s also mention that observed differences may also result from some kind of misclassification, the information we are building on through HFCS-XB being limited, as mentioned earlier. An indication of that is the share of “other” statuses in HFCS-XB, much larger than in HFCS-R (10%, against 4% to 6%).

Figure 2 examines the share of employees, employers/self-employed and pensioners, the most prominent categories in the employment statuses (out of students and “others”), based on their gross labor and public pension earnings compared to the Minimum Social Wage (MSW = 1998.59 EUR per month in 2017), a key social parameter in Luxembourg. We consider here thresholds at 2*MSW, 5*MSW and above, which may play an important role in some alternatives. Self-employment and pension incomes are both examined for residents only, those categories being less represented in HFCS-XB (cf. Figure 1).

Figure 2

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Unsurprisingly, self-employed residents enjoy higher average incomes from work than employees.¹⁹ They more often exceed the 5*MSW essential threshold (18% compared with 7%). Pensions of residents, on the other hand, are rarely as high, due in particular to the rules governing the capping of pensions in Luxembourg.

Finally, we underline higher wages for XBs, when generated through their activity in Luxembourg compared to all sources taken together: 3,881 €/month, on average from Luxembourg, against 3,442 €/month when all wages considered (Figure 2A). Nevertheless, despite average wages from Luxembourg being 13% higher than the general mean for XBs, those Luxembourgish-based salaries remain 16% lower than the residents’ ones.²⁰ In the same vein, 64% of the XB employees benefit from a Luxembourgish salary less than twice the MSW, what is the situation for 55% of the resident employees only.

We can now go a step further in the derivation of the total taxable income (simulated EUROMOD/HFCS variables “tinty_s”, or “tinty_lu_s” if considering Luxembourgish revenues only). Those amounts can be examined at the individual or fiscal household level.

Table 3 describes the components of the total taxable income in Luxembourg. Note that figures in Table 3 can hardly be compared horizontally between residents and XBs. Those figures involve the whole population and are most often means per person, hence with an impact of the structure of households on outcomes, whereas previous results were given by worker or pensioner at stake, like in Figure 2.

For residents, the salaries and pensions are by far the most prominent sources for the taxable income tinty_s. Remarkably, incomes from capital (interest, dividends, etc.) and property are reported at a level similar to the one from self-employment (4.6% of the taxable income from capital and property, against 5.5% for self-employed). This deviates from classical outcomes from EUROMOD/SILC data which are showing up a much lower proportion for those incomes (Liégeois et al., 2011). In the same vein, given the objectives of HFCS surveys, pensions from private plans are now visible with a participation to the taxable income by 1.4% (close to 0% in SILC).

On the XB-side, the taxable income composed from the survey is mainly attributable to wages (92.3%). Other components, often “0”, are in line with both some limitations in survey data and imputations operated as reported in Table A1. Table 3 is also showing which part of the taxable income is composed of Luxembourgish revenues: 77% on average (1,581 € / 2,054 €).

However and given the relative dimensions of residents and XB populations shown in Table 1, we have already an indication from Table 3 that the macro or total taxable income prevailing for XBs (and Luxembourgish revenue) is about 40% of the one for residents,²¹ as reported more precisely through the in Table 2 (7,947 millions € / 20,041 millions €, when ignoring macro adjustment).

Grounding on the taxable income, we are now in position to derive the personal income tax for Luxembourg through microsimulation. What are the main ingredients for that?

At the level of a tax household, the tax deducted from the taxable income of fiscal households depends on i) the tax base, i.e. the taxable income EUROMOD variable “tinty_s” from which are deducted the tax allowances “tinta_s” (including social security contributions themselves), ii) the tax brackets to which are allocated specific tax rates (discussed in Section 4 below) and iii) the “class of tax” prevailing for that household.

The classes of tax can be identified as “0” (basically, single with dependents or aged ≥ 65), “1” (single without dependents and aged < 65) and “2” (couples). Table 4 tells more about the share of fiscal households across those classes. Still, the populations covered through HFCS-R and HFCS-XB surveys differing structurally, we can hardly compare figures horizontally. However, we can partially explain the relatively high proportion of “class 0” fiscal households in the resident population by the presence of many single households aged 65 or more see Figure 3), hence classified in “class 0”.

Figure 3

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Finally, we show in Figure 4 the share of fiscal households across several fiscal brackets, under EUROMOD/HFCS-R and EUROMOD/HFCS-XB. We focus on class-1 and class-2 households only, the most frequent types encountered (see Table 4).

Figure 4

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To fix the ideas, we select the brackets available in the EUROMOD models for the income year 2017 and that may play a prominent role in alternatives examined downstream: brackets [1-9], that correspond to [0€-26,457€, yearly]; [10-19] ⇒ [26,457€-45,897€]; 20 ⇒ [45,897-100,002]; 21 ⇒ [100,002-150,000]; 22 ⇒ [150,000-200,004]; and 23 ⇒ ≥ 200.004 (for the original tax brackets, see Islam et al., 2020).

As was expected based on an examination on gross incomes behind the scene (see Figure 2), tax bases are more concentrated on lower brackets in the XB population. We can show that this statement remains true even if comparing only to Luxembourgish fiscal households experiencing a positive labor income (either from employment or self-employment).

On the other side of the income spectrum, the highest brackets (more than 100.002 EUR for the gross taxable earnings) are gathering a little part of the fiscal households: 5.7% if considering resident couples ; 0.4% for (active) XBs.

Let’s first examine the role of each fiscal bracket in the total funding, whoever is concerned by this bracket.

With such a perspective in mind, Table 5 [A] (Upper Part) is showing up how deriving an approximation of the overall tax rate for class-2 resident fiscal households. For sake of illustration, we focus here on this category of households which generates by far the largest proportion of income tax in Luxembourg.

Starting from the classification of those households across the fiscal brackets (copied from Figure 4) in column [a], we derive for each bracket the share of fiscal households concerned by this specific bracket (column [b], obviously 100% for the lowest bracket) and, subsequently, the sum of tax bases specifically impacted by that bracket, in column [f].

Note that the “27%” seen in column [a] for the bracket [26,457-45,897] should be understood as 27% of class-2 resident fiscal households experiencing a tax base situated between 52,914 €/year (twice 26,457) and 91,794 €/year (see the “note to reader” in Figure 4).

The 0.5% of fiscal households belonging to the highest bracket (≥ 200,004 €/year, hence an original tax base exceeding 400,008 €/year) generate (405,658-200,004) * 0.5 = 102,827 € of income to be taxed based on the highest rate (42%, [g]), for 100 fiscal households and on average, hence an income tax of 43,187 € coming from that highest bracket for 100 households (46,297 € if avoiding rounding factors).²³

The reasoning is similar for the second highest bracket [150,000-200,004], but the sum of taxable incomes here concerned is 1.0 * (167,270-150,000) from those households belonging to the 2^nd highest bracket + 0.5 * (200,004-150,000) from those households belonging to the brackets above the present one (hence here the 1^st highest bracket) = 42,272 € (43,312 € in [f], without rounding errors), hence a marginal income tax from that bracket equal to 17,758 € ([h]). Going on with the lowest brackets, we finally get a total income tax of 871,521 € ([k]), which drives to an overall tax rate of 871,521 € / 4,433,421 € = 19.7%.

This general outcome may be compared to the figure shown up in Table 2 and coming from the microsimulation, which is 20.9% (tax rate after tax allowances, but before tax credits). Taking into account that this latter value incorporates some participation to the unemployment fund (7% to 9%, depending on the level of gross tax base; cf. Islam et al. (2020), Section 2.6), our approximate value of 19.7% is not that far from the one observed for all fiscal households: 19.5%, after a rough evaluation of the contribution to the unemployment fund (cf. [‡] in Table 5).²⁴

A lesson to keep in mind from that exercise is that the lowest brackets play a prominent role in the accumulation of income tax. In our example, 48% of the income tax are generated through fiscal brackets below 45,897 €/year. We are specifically mentioning “fiscal bracket” and not “income bracket” as those lowest brackets are concerned with households benefitting from higher incomes as well. The first level retained here, below 26,457 €/year, yet facing the lowest marginal rate, is dealing with a large tax base, hence a return which remains appreciable (17% of the total).

Therefore, an average increase of 1 percentage point for the tax rates applicable to the fiscal brackets below 45,897 €/year would provide 4% of additional taxes from class-2 fiscal households: 1% * (2,330,900 € + 950,689 €) = 32,816 € per year for 100 fiscal households, derived from variations in [f] * [g] = [h]).

On the other side of the distribution, 7% of the tax are coming from the brackets above 150,000 €/year (*2 for original tax bases).

Table 5 [B] (Lower Part) is performing the same kind of approximation, but for the class-2 active XB fiscal households.²⁵

Starting from the share of fiscal households across the fiscal brackets mentioned in Figure 4 we are reaching a total income tax of 413,469 € in 2017 ([k] in Table 5, for 100 class-2 households, on average), out of a tax base of 3,160,620 € ([j]), hence an overall implicit tax rate approximated to 13.1% for class-2 households. This is close to the 12.9% resulting from the microsimulation (roughly corrected for the unemployment fund, cf. [§] in Table 5).

The conclusion is here straightforward: the distribution of incomes, more concentrated on the lower brackets for XBs, compared to residents, drive to a reduced average tax rate: 13.1% against 19.7% for residents, that is 6.6 p.p. lower. On top of this, the lowest brackets, below 45,897 € (*2), are now concentrating 77% of the income tax (48% for residents).

Let’s now turn to the role of the fiscal households themselves (gathered by sub-groups, depending on their tax base) in the total funding, taking into account all the fiscal brackets these households are concerned with.

Table 6 are summarizing the exercise in the same vein as for Table 5, for class-2 resident fiscal households, then active XB fiscal households. The derivation of total income taxes being more common and made explicit through the table headers, we are not detailing this path anymore.

Let’s just remind that some outcomes, if directly computed from the tables as shown up here, may deviate from what is visible, due to rounded values in the presentation. For example, the second line in column [e] in Table 6A would lead, based on figures made visible in the table, to 26,457 * 7.5% = 1,984 €, and not 1,975 €. This results from the rate applicable in the background, which is 7.465% rather than 7.5% as shown up for clarity in the table. The total amount of tax could also show some differences compared to outcomes in Table 5, again explained by other kinds of approximations implemented while deriving all those tables.

We can see from Table 6A that the class-2 resident fiscal households whose yearly tax base is greater than 100,002 EUR (*2), representing about 6% of the class-2 fiscal households (column [a]), are providing 33% of the total personal income tax coming from class-2 ([i]). And the tax due to the brackets above 100,002 EUR represents only about 14% of that total amount (Table 5A). This is a classical expression of the progressive nature of the personal income taxation which is also emphasized through column [j].

We are providing Table 6B, dealing with class-2 active XB fiscal households (and total incomes, not limited to LU-ones), just for illustration and will not comment it.

We are finally briefly illustrating that analytical framework through an application in Table 7 provided for class-2 resident fiscal households.

Let’s consider an alternative to the fiscal policy in force in 2017, with fiscal brackets unchanged but higher rates applied for the highest brackets: 40% over [45,897€-100,002€] (rather than 39%), 42% over [100,002-150,000] (rather than 40%), 44% over [150,000-200,004] (rather than 41%), and 46% for the bracket above 200,004€ (rather than 42%). The role of fiscal households in the total fiscal revenue is here at stake (similarly to Table 6).

We derive through the Table 7 an approximation of the average tax on personal income as resulting from the EUROMOD/HFCS-R framework for class-2 resident fiscal households (gathered by sub-groups, depending on their tax base). This approximation (20.2%, to be compared to 19.8% in Table 6A for the benchmark STD), despite partial compared to fiscal households taken altogether, is quite close to what is more precisely derived from the microsimulation model for all resident households: 21.4% (see [***]), downsized here to 20.0% if the unemployment fund contribution is deducted.

This represents an increase by 0.5% (21.4%-20.9%) if building on more precise microsimulation outcomes, including the contribution to the unemployment fund, 0.4% (20.2%-19.8%) through the present approximation for class-2 resident households, without the contribution to the unemployment fund.

As is expected given the nature of the alternative fiscal policy, we can see that high income households are now contributing more intensively to the whole funding than before the change. This intensity of contribution is 0.35 and 0.41 for class-2 resident fiscal households earning more than 150,000 EUR (*2) /year (Table 7, column [j]), rather than 0.33 and 0.38 in the benchmark STD (Table 6B). The progressivity of taxation is obviously reinforced through such an alternative.

The conclusions (not developed here) are qualitatively similar for class-2 active XB fiscal households. However, the effects of the alternative fiscal policy are quite lighter, in line with a distribution of gross tax base less concentrated on higher tax brackets for XBs (see Figure 4). We can show that the approximate average tax rate is now 13.4%, to be compared to 13.3% in Table 6B for the benchmark STD.

Finally, Table 8 is partly replicating Table 2 for a more general overview of outcomes, separately for residents and for active XB households. We are not commenting here this table. Let’s mention only higher total revenue and tax rates, with social contributions logically unchanged. The well-being is reduced for highest deciles (see the 9^th Decile) and the reinforced progressivity of the fiscal schedule evoked earlier is driving to lower inequalities (Gini). However, the poverty line and rate are quite stable, under such a change in fiscal policy affecting the highest income brackets. The XBs being less represented in those higher levels of gross incomes (see Table 9 Figure 4) are also marginally affected only by the change.

https://www.csl.lu/en/

CSL – LISER Project « Alternative Ways for Funding the Luxembourgish social security system, with distributional effects ». The full reports by both Liégeois (2023a) and Liégeois (2023b) are confidential, the present paper grounding on, and developing, some aspects to be made accessible to a larger audience.

STATEC (2019), page 14, for 2017; STATEC (2023), page 18, for 2022

For detailed explanations on the model, see Sutherland and Figari (2013).

HFCS results from a joint project of EU national central banks and national statistical institutes, providing data improving outcomes for higher income deciles and wealth-related concerns and transfers (https://www.ecb.europa.eu/stats/ecb_surveys/hfcs/html/index.en.html).

Collected via a separate survey organized by the Banque Centrale du Luxembourg (https://www.bcl.lu/en/index.html) in collaboration with LISER (Chen et al., 2021).

https://ec.europa.eu/eurostat/web/microdata/european-union-statistics-on-income-and-living-conditions

Kuypers et al. (2016); Kuypers et al. (2020); , see Chen et al. (2020) and Household Finance and Consumption Network (2020).

Collected via a separate survey organized by the Banque Centrale du Luxembourg (https://www.bcl.lu/en/index.html) in collaboration with LISER (Chen et al., 2021) (.

The “Greater Region” is covering the territories of Lorraine in France, Wallonia in Belgium, Saarland and Rhineland-Palatinate in Germany as well as the Grand Duchy of Luxembourg (https://www.granderegion.net/en/The-Greater-Region-at-a-Glance).

See Household Finance and Consumption Network (2020), page 7.

In particular, if a Gini coefficient is derived, with values 0.2903, 0.2905, 0.2897, 0.2901 and 0.2899 resulting from the 5 runs of a EUROMOD model we report 0.2901 as an outcome. Alternatively, we could have gathered or averaged ex ante the 5 values outputted from EUROMOD/HFCS for the equivalent income, then computing ex post the “overall” Gini. But we rather chose to build on procedures available ex ante the present study for saving time, what might deserve some deepening ex post the study, yet probably not fundamentally changing the outcomes.

EU-SILC 2018 data are embedding households involving international civil servants/ICS, what HFCS data do not (unless some ICS being a member of a household selected on another basis).

This remark does not refer to the “quality” of the survey, which is not at stake here. HFCS data are also involving questions and information about essential topics like wealth-related items which are much more deeply examined in this survey, a clear and useful innovation compared to other studies. For an analysis of confidence intervals in EUROMOD/SILC data for Luxembourg, see Liégeois et al. (2011).

During the interview, a person who is the “most knowledgeable with the financial situation of the household”/FKP is designated. This FKP is providing more detailed personal information, needed for an efficient microsimulation exercise, than the other members of the households for whom, therefore, such a useful information may not have been collected.

See Clément et al. (2023), page 20.

This so-called OECD-modified equivalence scale is attributing a weight of 1 to the first adult, 0.5 to additional persons (aged fourteen or more), and 0.3 per child (aged under fourteen).

These two indicators are not concerned with the same notion of inequality; the first measures the relative differences in equivalent income between members of a population, while the second refers to the absolute differences in equivalent income between them. The relative Gini index will not change if equivalent income increases in the same proportion for all (scale invariance), even though this increase would change the absolute gap and thus the absolute Gini. Conversely, if equivalent income increases by the same absolute amount for all, the absolute Gini will not change (translation invariance); the gap in income between individuals remains constant, while the relative Gini will change.

Nevertheless, such comparisons may be biased. Let’s remind that for self-employed, part of the employer’s social contributions are considered as incorporated in the gross incomes as reported in the raw microdata, whereas they still have to be added-up to such gross levels for employees (to reach sometimes called “gross-gross” levels).

Such a disequilibrium between labor earnings for XBs and residents, at the advantage of the latter, is confirmed in Chen et al. (2020), page 44. Clément et al. (2023), chapter 2, are also giving an insight about the underlying determinants (education attainment, nature of jobs, etc) that can explain those discrepancies between the residents and XB workers.

For residents through HFCS-R data: 535,897 persons * 3,116 €/month * 12 = 20,04 billions €/year; for XBs as covered through the HFCS-XB data: 418,997 * 1,581 €/month * 12 = 7,95 billions €/year (see also Table 2 for totals).

More applications can be found in Liégeois (2024).

The figure “110,230 €” shown up in column [f], rather than 102,827 € roughly computed here, comes from rounding errors in presentation, “0.5” in [a] being indeed in the background “0.536”.

Note that during this approximation exercise, we had to fix marginal tax rates for the several brackets shown up here, sometimes gathered compared to the real tax schedule. For such a bracket as [150,000-200,004], this is obvious given that this bracket is incorporated as such in the real tax schedule. For an intermediate one like [26,457-45,897], we had to combine “manually” several marginal rates (see [†] in Table 5), building on the marginal rates observed, the ranges of incomes considered in the real tax schedule and the mean tax base corresponding to households belonging to that specific bracket ([c]).

We can mention a specificity for that population, compared to the resident one. The exercise undertaken here is based on total incomes for XBs, whatever coming from Luxembourg or from other countries, given that the tax rate is fixed on that basis by principle (and as a first approximation, probably the only one possible at this stage), before being applicable on a fiscal household level to the income originated from Luxembourg to derive the income tax due to this country specifically (see Section 2.3). Therefore, our reference of 13.8% mentioned below Table 5B in [§] results from the tax on total XB income and differs a little from the 14.4% reported in Table 2 for XBs, valid for LU-incomes only.

A priori, the HFCS “HXG0100x” variables (total gross household income, all sources) could serve as a basis for deriving some information related to pension incomes. However, many inconsistencies were observed between those variables and incomes derived separately from several sources during the same survey, hence the choice to not build on HXG0100x at that level.

Islam et al. (2020) for some information about the data with regard to the EUROMOD/SILC model, for HFCS-R data, Chen et al. (2021) for HFCS-XB, all for Luxembourg. For EUROMOD/HFCS-R more generally (2^nd Wave), the reader can refer to Kuypers et al. (2016) and for HFCS-R, see also “Household Finance and Consumption Network” (2020).

OECD (2023).

Islam et al. (2020), Section 4 for classical validation outcomes of EUROMOD/SILC.

Some information is missing in the second wave of HFCS-XB (income year 2017), compared to HFCS-R and what seems necessary for the microsimulation exercise. The present Appendix is summarizing the imputations resulting from such missing variables.

Logically, a household member’s labor income (which is not separated between employment or self-employed income in HFCS-XB), if this person is by elsewhere identified as an employee (resp. self-employed), is considered as employment income “yem” (resp. “yse”). Other income variables were imputed based on averages derived from the resident population, or even simply set to “0” if either limited in size or when no relevant information is available by elsewhere.

Departing from those simple treatments, a more sophisticated imputation is implemented for pension incomes, which are not reported as such in HFCS-XB.²⁶ We remind that those pensioners are not that numerous in HFCS-XB which are targeting active XB households. If a household member is identified as a retired person, we attribute to this inactive person an amount of pension income in proportion of the total work income in the household. Those proportions are those observed for the resident population (HFCS-R), in households with working members, and depending on the number of pensioners in the residence household.

Finally, a decision about the share of incomes coming from LU-sources and from other countries has to be made.

Table A1 is summarizing the adaptations undertaken to complete the HFCS-XB original survey data with information relevant for microsimulation and the objective of our study.

Additionally, in particular with regard to the demographic structure of the databases (age, education, ...), the reader can refer to other available documentation.²⁷

Leaving aside those XB households which do not presently involve any active worker in Luxembourg may reduce the total public revenue due to Luxembourg, compared to what has been identified up to now, whatever in terms of social contributions or personal income taxes ignored.

We show now how, building on outcomes from the EUROMOD/HFCS-R and EUROMOD/HFCS-XB platforms, we choose to roughly complete the picture to add to social contributions and personal income taxes revenue from those XB households ignored up to now, what we call a “macro adjustment”. Table B1 (for social contributions), Table B2 (for the income tax) and Table B3 (for the global consolidation) are summarizing the point.

Table B1 is first consolidating outcomes in relation with social contributions (section [C]). The first column on left is mentioning references ([I], [II], ...) that may be used later on in the computations. Percentages are emphasized through specific markers: [%1], [%2], ... . An intermediate column is complementarily explaining the details of the computations undertaken.

We complete the information collected up to now in a structured way: [C.1] is consolidating past results, [C.2] is completing for uncovered XB households through macro adjustments and [C.3] is summing up outcomes for social contributions.

[C.1] is reminding past results (see Table 2): 3.71 billion € have been identified for social contributions from residents through the EUROMOD/HFCS microsimulation, on top of 2.03 billion € from active XB households, that is 5.75 billion € on total in 2017 (reference “[IV]”, also referred to as [SC/HFCS+], “+” for underlying the contents in terms of aggregation between resident and active XB outcomes).

[C.2] is hypothesizing that XB households not covered by the HFCS-XB survey, yet having a socio-fiscal link with Luxembourg, are mainly composed of pensioners (hypothesis H2 – for the notation, see Section 2 and H1 regarding bilateral fiscal agreements). If considering that pensions received by the retired members of the XB active households are coming from countries out of Luxembourg (a strong but maybe sole possible positioning and approximation in a first step, H3), the pensions going to otherwise uncovered pensioners correspond to what Luxembourg is offering as pensions to all XBs. Those are approximatively evaluated as 1.11 billion € in 2017 ([V], source: IGSS and author’s computation) and give rise to the payment of social contributions for health in-kind at the level of 2.8% (*2, taking into account personal contributions and credited ones H4), that is 62 million € additional ([VI]).

On the whole, [C.3] is concluding that total social contributions paid to Luxembourg amount to 5.81 billion €, based on EUROMOD/HFCS data and microsimulation platforms, our hypotheses Hx and a final macro adjustment ([SC/HFCS++], “++” for underlying the contents in terms of aggregation between resident and all XB households).

As a matter of validation, we might compare this amount to external statistics, like from OECD (tax revenue in 2017, “2000 Social security contributions”: 6.13 billion €), but it appears extremely difficult to find external sources fully comparable to what has been taken into account in the present data and microsimulation platforms.²⁸ Therefore, and for the time being, we refer to this reference as an indication that our simulation outcomes do not seem too far from the “real” world (5.81/6.13=95%) and might be a good basis for the analysis of changes in the of socio-fiscal system of policies. Other experiments to validate microsimulation models sometimes show much larger differences (see Islam et al., 2020, Annex 2, for EUROMOD/SILC).

The next step is dealing with adjustments of the total personal income taxes (section [T], Table B2). Still, the task is divided into 3 steps.

[T.1] is gathering previous outcomes (see Table 2) and conducting to a total of 4.26 billion € in 2017 ([TAX/HFCS+]).

The macro adjustment, in [T.2] is more demanding. [T.2.1] is first reminding several indicators, including the average global tax after tax credits (10.4%), which are consistent with Table 2. Then, [T.2.2] is starting from additional gross income attributed to the uncovered XBs (the same amount [V] as for social contributions, H5) and considering that income taxes for that sub-group might correspond, on average, to the ones derived for the covered XBs (another strong hypothesis, H6), that is here 10.4% * 1,109 million € = 115 million € additional ([XV]).

Finally, [T.3] is summing up those results, leading to a total amount of personal income taxes from (all) XBs equal to 4.38 billion € ([TAX/HFCS++]).

As a matter of validation, we might compare this amount to external statistics, like from OECD (tax revenue in 2017, “1100 Taxes on income, profits and capital gains of individuals”: 5.06 billion €), but it appears here again to be extremely difficult to find external sources fully comparable to what has been taken into account in the present data and microsimulation platforms.²⁹ For the time being, we refer to this reference as an indication that our simulation outcomes do not seem fully out of the scene (4.38/5.06 = 87%) compared to what can be commonly achieved through microsimulation. Anyway, this might also be a good basis for the analysis of changes in the of socio-fiscal system of policies, coming next.

All those considerations lead, in section [R] of Table B3, to total revenue from social contributions and personal income taxes amounting to 10.19 billion € ([TOT/HFCS++]), as derived from EUROMOD/HFCS-R, EUROMOD/HFCS-XB, macro adjustments and author’s working hypotheses H1 to H6. This amount corresponds to 10.19 / (6.13 + 5.06) = 91% of (supposed) comparable external sources.

We conclude this Appendix by mentioning that we could have opted for another strategy for the derivation of total public revenue: working basically with EUROMOD/SILC, computing from EUROMOD/HFCS platforms ratios between XB outcomes and the ones for residents, when relevant, and applying those ratios to EUROMOD/SILC results for deriving total amounts. This approach has been implemented in Tables B. It leads to a total amount of 10.31 billion € ([TOT/SILC++]), rather than 10.19 billion € mentioned earlier. Those outcomes are remarkably close each other (a 1.2%-gap).

This research was carried out as part of the project “Alternative Ways for Funding the Luxembourgish social security system, with distributional effects » (2022-2023) funded by the Chambre des Salariés du Luxembourg/CSL under agreement dated 18 July 2022.

The research presented in this paper is part of a study initiated and financed by the Chambre des Salariés du Luxembourg (CSL). Numerous exchanges with experts (social partners) enabled us to provide an approach more in line with the questions and final expectations of our usual public targets.Yet the present paper mentioning Philippe Liégeois as sole author, its outcomes result from a larger network.The developments presented here are initially based on the model EUROMOD/SILC version I4.62+ Beta release (3.4.10). Originally maintained, developed and managed by the Institute for Social and Economic Research (ISER), since 2021 EUROMOD is maintained (with regard to resident populations), developed and managed by the Joint Research Centre (JRC) of the European Commission in Seville, in collaboration with EUROSTAT and national teams from the EU countries (including LISER for Luxembourg).The EUROMOD/HFCS-R model is building on the same core version as EUROMOD/SILC, yet running on HFCS data rather, and was developed for its base versions (socio-fiscal policies up to 2017) by Jonas Boone, Johannes Derboven, Sarah Kuypers and Gerlinde Verbist, from the University of Antwerp, together with Francesco Figari, from the Università degli studi del Piemonte orientale. An extension to the new EUROMOD/HFCS-XB model, involving microdata related to cross-borders for Luxembourg, has been set up by Johannes Derboven, in collaboration with Philippe Liégeois. A specific documentation for extending EUROMOD/HFCS-XB to all cross-borders, through macro adjustments, was also gathered by Anasse El Maslohi, from LISER. Even if HFCS results from a European-wide effort, Michael Ziegelmeyer from the Banque Centrale du Luxembourg, and Carla Martins from LISER, more specifically but among many others, have indirectly supported the present study through their expertise in those data for Luxembourg.

We are also grateful to the editor of the International Journal of Microsimulation and two anonymous referees for many stimulating suggestions. Obviously and meanwhile, the results developed here and their interpretation are the author’s sole responsibility at this stage.

1. Version of Record published: August 20, 2025 (version 1)

© 2025, O’Donoghue et al.

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