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

Abstract

The models presented in this paper are intended to contribute to a debate on the impact of hypothetical changes in social security contributions and personal income tax on the distribution of household disposable income and on total public financial revenue from these sources for Luxembourg. Our aim is to take account as far as possible of the non-linearity of socio-fiscal systems and the precise structure of populations, hence the need for microsimulation modelling of both resident and cross-border commuter households. This latter population is involving an essential innovative extension compared with previous assessments. Cross-border commuters are very important in Luxembourg, accounting for over 40% of total employment: 41% in 2017, 43% in 2022. Static microsimulation tools and data are already available for residents (mainly via EUROMOD and EU-SILC), but not for cross-border commuter households. Therefore, there is need for a secondary simulation framework, for example based on EUROMOD and HFCS data (offering some information for cross-border commuters in addition), separately for resident and cross-border commuter households. Such publicly available distributional views on residents and cross-border commuters in countries with high openness where the latter may play an important role in public accounts are not numerous, or even unique in Luxembourg, if we except (expected) imputation-based approaches. The aim of this methodological article is to present the EUROMOD-type models implemented for the resident and cross-border commuter populations in Luxembourg and to highlight the particularities of their construction. Using these tools, we are then able to provide a complementary overview of the two populations “as they are today”. Another objective is to provide a toolbox for an immediate overview of tracks for − and impact of − changes in socio-economic policies. Given the important structural differences between resident and cross-border commuter populations in terms of socio-economic status and gross labor and taxable incomes, we show and explain to what extent total revenues from residents are higher than those from cross-border commuters, even considering the relative sizes of the two populations. For the same reason, a change in the socio-fiscal system of policies in Luxembourg could have remarkably different effects between cross-border commuter households and residents. More specifically, these results could also partially serve as a basis for the debate on a pension reform recently launched in Luxembourg. This research was initiated by the Chambre des Salariés du Luxembourg (CSL). Consequently, the contents reported here result from exchanges with social partners (not all of whom are familiar with the technicalities of the context). Such a context allowed us to propose an approach more in line with the questions and final expectations of our usual public targets. The present paper also aims to “open the black box”, which can lead to contents that are sometimes technical, but accessible to “practitioners” who would like to better understand the underlying forces and rely on these models for subsequent counterfactual analyses.

This article contains 4 figures and 12 tables.

Figures

**Figure 1.** Share of the whole population (in % of the total population in 2017), based on its employment (social-economic) status*

**Figure 2.** **[A]** Share of employees, based on their earnings compared to the MSW, in % of employees with positive (>0) labor earnings [*] (MSW = 1998.59 EUR / month in 2017). **[B]** Share of resident self-employed and pensioners, based on their earnings compared to the MSW, in % of self-employed and pensioners with positive (>0) earnings [*] (MSW = 1998.59 EUR / month in 2017)

**Figure 3.** Share of households across the types of households, as resulting from EUROMOD/HFCS-R and EUROMOD/HFCS–XB (Outcome from *imputation 1* only – see *Section 2.1*)

**Figure 4.** Share of Fiscal Households across the fiscal brackets, based on their yearly tax base [*], if >0 and class-1 (single without dependents) or class-2 households (couples), resulting from EUROMOD /HFCS-R and EUROMOD /HFCS-XB Note to the reader: it should be understood from the “27%” seen for bracket [26,457-45,897] for resident couples (class-2 fiscal households) that 27% of those households are experiencing a tax base situated between 52,914 €/year (twice 26,457) and 91,794 €/year, given that this tax base is divided by 2 in Luxembourg before applying the tax schedule for computing the tax on income (finally multiplied by 2 for an effective value). [*] Mean over all 5 imputations (see *Section 2.1*).

Tables

Table 1. Populations covered by the EUROMOD input databases (Income year 2017 for all).

Database	Number of Residence Households*		Number of Persons
Database	Unweighted	Weighted	Unweighted	Weighted
EUROMOD/SILC input (LU-Resident population)	3,833	252,336	10,493	574,184
EUROMOD/HFCS-R input (LU-Resident population)	1,616	226,378	4,333	535,897
EUROMOD/HFCS-XB input (“Active” Cross-border households)	2,362	147,380	7,341	418,997

All persons living in the same dwelling, not to be confused with the “residents” who involve inhabitants of Luxembourg.

Table 2. An overall view of the benchmark “STD” (income year 2017) for resident and XB households.

Data and EUROMOD platforms			SILC	HFCS-R	HFCS-XB (Active households & LU-incomes only)
Population covered by the survey (see Table 1), in persons			574,184	535,897	418,997
Taxable Income, before Tax allowances, in millions € / year (from tinty_s in HFCS-R, or tinty_lu_s for Active XB households)			20,808	20,041	7,947
… out of additional amount from XBs not covered by the survey (for subsequent macro adjustment, see Section 2.4)					1,109
Public Revenue (in millions € / year)
	Social contributions		[I]*	[II]	[III]
	Social contributions		3,914	3,714	2,030
	whose	Employee	1,820	1,693	945
		Self-employed	178	221	27
		Others (Long term care from Social assistance)	3	3	0
		Employers	1,710	1,667	1,059
		Credited (Replacement income, Social assistance, Pensions)	202	130	0
	… out of additional amount from XBs not covered by the survey (for macro adjustment)				62
	Personal Income Tax		[VII]	[VIII]
	Personal Income Tax		3,289	3,439	824
		Implicit Tax Rate on Tax Base (tinty_s – tinta_s, or LU versions if XBs), before Tax Credits		20.9%	14.4%
		Global Tax Rate (after Tax Allowances & Credits) = Income Tax / Taxable Income, on average		17.2%	10.4%
	… out of additional amount from XBs not covered by the survey (for macro adjustment)				115
	⇒ Total Public Revenue (before macro adjustment)		7,203	7,153	2,855
Inequalities					If All Incomes
	Gini
		Relative = Abs / (2*Avg)	0.2524	0.2993	0.1940
		Absolute (in € / month)	1,701	2,103	1,088
		Average (in € / month)	3,371	3,513	2,804
	Poverty
		Line (in € / month)	1,790	1,770	1,564
		Rate	11%	13%	2%
		by Type of Residence Household:
		Single (<65)	14%	16%	1%
		Single (65+)	8%	9%	2%
		Single with dependent(s)	31%	18%	0%
		Couple - 0 dep	6%	5%	2%
		Couple - 1-2 dep	11%	18%	2%
		Couple - 3+ dep	14%	21%	2%
"Well-being", as equivalized income (all in € / month), on average					If All Incomes
	All		3,371	3,513	2,804
	1st Decile		1,574	1,472	1,635
	by Type of Residence Household:
		Single (<65)	3,308	3,249	2,828
		Single (65+)	3,215	3,440	2,878
		Single with dependent(s)	2,473	2,661	2,530
		Couple - 0 dep	3,922	4,150	3,194
		Couple - 1-2 dep	3,117	3,292	2,768
		Couple - 3+ dep	2,673	2,826	2,353

The references [I], [II], ... refer to Table B1 and Table B2 (Appendix B)

Table 3. The components of the taxable income, in €/month [*].

Component (EUROMOD variable)	Meaning	HFCS-R		HFCS-XB^†
		HFCS-R		All incomes		LU-income
		Avg ^‡	% of total	Avg ^‡	% of total	Avg ^‡	% of total
tinty_IT_s	Taxable income, by fiscal household ^§	5,392		4,537		3,492
tinta_IT_s	Tax allowances, by fiscal household ^§
tinty_s	Taxable income, by person	3,116	100%	2,054	100%	1,581	100%
bsacm_s	Social assistance	58	1.9%	22	1.1%	0	0.0%
il_repl	Replacement income	10	0.3%	0	0.0%	0	0.0%
il_taxpen	Taxable pensions	626	20.1%	19	0.9%	0	0.0%
yem	Employee gross income	2,047	65.7%	1,894	92.3%	1,544	97.7%
yiy	Interest, dividends, profit from capital investments in unincorporated business	16	0.5%	18	0.9%	14	0.9%
ypp	Pension from private pension plans	43	1.4%	0	0.0%	0	0.0%
ypr	Income from property	128	4.1%	79	3.8%	0	0.0%
ypt	Regular inter-household cash transfers received	16	0.5%	0	0.0%	0	0.0%
yse	Gross income from self-employment	172	5.5%	22	1.1%	22	1.4%

Mean over all 5 imputations (see Section 2.1)

Averages for “All incomes” and “LU-Income” are considering the whole surveyed population

Mean = (weighted) total / number of persons or fiscal households in 2017

A fiscal household is gathering persons considered as to be taxed jointly on income, taking into account the relevant fiscal rules

Table 4. Share of fiscal households across the classes of tax (in % of Fiscal Households) as resulting from EUROMOD/HFCS-R and EUROMOD/HFCS–XB (mean over all 5 imputations – Section 2.1)

	Proportions, in % of Fiscal Households
Class of Tax	HFCS-R	HFCS-XB (Active Households)
0	17%	9%
1	47%	38%
2	37%	54%

Mean over all 5 imputations (Section 2.1)

Table 5. [A - Upper Part] The impact of fiscal brackets (whatever the households’ tax base behind) in the overall implicit tax rate on personal income for class-2 resident fiscal households (couples) – An approximation based on EUROMOD/HFCS-R ♦ [B - Lower Part] The impact of fiscal brackets (whatever the households’ tax base behind) in the overall implicit tax rate on personal income for class-2 active XB fiscal households – An approximation based on EUROMOD/HFCS-XB.

Part [A] – RESIDENTS) Fiscal Bracket (in €)	Share of Fiscal Households within the bracket, in p.p. (see Figure 4) [a]	Percent of Fiscal Households impacted by that bracket * [b] = [b>] + [a]	Mean Tax Base for that bracket [c]	Lower limit for that fiscal bracket (€, yearly) [d]	Income from tax payers belonging to that bracket, above the Minimum level of Fiscal Bracket [e] = [c] - [d]	Σ of Tax Bases impacted by that Bracket, for 100 fiscal households (€, yearly) [f] = [a] * [e] + [b>] * ([d>] - [d])	Approximate Marginal Tax Rate (+/- mean tax rate over the bracket ^†) (2017 STD system) [g]	Income Tax from that Tax Bracket, for 100 fiscal households (€, yearly) [h] = [f] * [g]	% of income Tax from that Tax Bracket [i] = [h] / [k] and Avg % tax below =[k] / [j]
> 0 and < 26,457	37.1	100	17,976	0	17,976	2,330,900	6.2%	144,944	17%
[26,457-45,897[	27	62.9	35,848	26,457	9,391	950,689	28.6%	271,611	31%
[45,897-100,002[	30.1	35.8	63,520	45,897	17,623	840,398	39.0%	327,755	38%
[100,002-150,000[	4.2	5.7	119,684	100,002	19,682	157,891	40.0%	63,156	7%
[150,000-200,004[	1	1.5	167,270	150,000	17,270	43,312	41.0%	17,758	2%
≥ 200,004	0.5	0.5	4,05,658	200,004	205,654	110,230	42.0%	46,297	5%
		Total Tax Bases [j], for 100 fiscal households ⇓						Total Tax [k]	(Avg % Tax: 19.7%)^‡ ^‡
			4,433,421					871,521	(Avg % Tax: 19.7%)^‡ ^‡

[b>]” refers to the value of [b] for the fiscal bracket above the present one (e.g. [150,000-200,004[, as for bracket [100,002-150,000[)

Approximate weighted mean tax rate over the Fiscal Bracket: for example in Part [A], “28.6%” = ( ([a]/100*28%) + ([b]-[a])/100*((20%+38%)/2) ) / ( [b]/100 ), where 28% is the tax rate at [c]-income and 20%/38% are the tax rates at the extremes of this fiscal bracket

20.9% on average, all fiscal classes considered for HFCS-R in 2017, including a 7% (mainly) or 9% Tax for Unemployment fund ⇒ about 19.5% without it

13.8% on average, all fiscal classes considered for HFCS-XB in 2017, including a 7% (mainly) or 9% Tax for Unemployment fund ⇒ about 12.9% without it

Table 6. [A - Upper part] The impact of the fiscal households, given their tax base bracket, in the overall implicit tax rate on personal income for class-2 resident fiscal households (couples) – An approximation based on EUROMOD/HFCS-R ♦ [B - Lower Part] The impact of the fiscal households, given their tax base bracket, in the overall implicit tax rate personal income for class-2 active XB fiscal households (couples) – An approximation based on EUROMOD/HFCS-XB.

Part [A] – RESIDENTS) Fiscal Bracket (in €)	Share of Fiscal Households within the bracket, in p.p. [a]	Mean Tax Base for that Bracket [b]	Lower limit Fiscal bracket (€, yearly) [c]	Approximate Marginal Tax Rate if Income reaching the Upper limit of the Tax Bracket * (2017 STD system) [d]	Tax receipt per Fiscal Household if Tax Base = lower limit of this Tax Bracket (€/year) ^† [e] = [e<] + [d<] * ([c] - [c<])	Tax receipt per Fiscal Household whose Tax Base lays within this Tax Bracket (€/year) [f] = [e] + [d] * ([b] - [c])	Tax receipt for ALL Fiscal Households whose Tax Base lays within this Tax Bracket, if considering 100 fiscal households on the whole (€/year) *[g] = [a] [f]**	% of Income Taxes from Fiscal Households belonging to this Tax Bracket [i] = [g] / [h]	Intensity of Contribution to Personal Income Taxes *[j] = [g] / ([a] [b])**
> 0 and < 26,457	37.1	17,976	0	7.5%	0	738	27,400	3%	0.04
[26,457-45,897[	27	35,848	26,457	29.0%	1,975	4,605	124,534	14%	0.13
[45,897-100,002[	30.1	63,520	45,897	39.0%	7,613	14,486	436,218	50%	0.23
[100,002-150,000[	4.2	119,684	100,002	40.0%	28,714	36,586	154,833	18%	0.31
[150,000-200,004[	1	167,270	150,000	41.0%	48,713	55,793	53,338	6%	0.33
≥ 200,004	0.5	405,658	200,004	42.0%	69,214	155,589	83,396	9%	0.38
	Total Tax Bases [k], for 100 fiscal households ⇓						Total Tax [h]		*(Avg % Tax: 19.8%)* ^‡
		4,433,421					879,719		*(Avg % Tax: 19.8%)* ^‡
Part [B] – XBs	[a]	[b]	[c]	[d]	[e] = [e<] + [d<] * ([c] - [c<])	[f] = [e] + [d] * ([b] - [c])	[g] = [a] * [f]	[i] = [g] / [h]	[j] = [g] / ([a] * [b])
> 0 and < 26,457	47.2	19,199	0	7.5%	0	952	44,964	11%	0.05
[26,457-45,897[	37.1	34,668	26,457	29.0%	1,975	4,274	158,632	38%	0.12
[45,897-100,002[	15.3	60,455	45,897	39.0%	7,613	13,290	202,832	48%	0.22
[100,002-150,000[	0.4	111,375	100,002	40.0%	28,714	33,263	13,305	3%	0.3
[150,000-200,004[	0		150,000	41.0%	48,713
≥ 200,004	0		200,004	42.0%	69,214
	Total Tax Bases [k], for 100 fiscal households ⇓						Total Tax [h]		*(Avg % Tax: 13.3%)* ^§
		3,160,620					419,733		*(Avg % Tax: 13.3%)* ^§

Approximate weighted mean tax rate over the Fiscal Bracket: for example, “29.0%” = (20% + 38%) / 2

“[c<]” refers to the value of [c] for the Fiscal Bracket below the present one (e.g. [100,002-150,000[, as for bracket [150,000-200,004[)

20.9% on average, all Fiscal Classes considered for HFCS-R in 2017, including a 7% (mainly) or 9% Tax for Unemployment fund ⇒ about 19.5% without it

13.8% on average all Fiscal Classes included for HFCS-R in 2017, including a 7% (mainly) or 9% Tax for Unemployment fund ⇒ about 12.9% without it

Table 7. Amending the personal income taxes - The impact of the fiscal households, given their tax base bracket, in the overall implicit tax rate on personal income for class-2 resident fiscal households (couples) – An approximation based on EUROMOD/HFCS-R.

Fiscal Bracket (in €)	Share of Fiscal Households within the bracket, in p.p. [a]	Mean Tax Base for that Bracket [b]	Lower limit Fiscal bracket (€, yearly) [c]	Approximate Marginal Tax Rate if Income reaching the Upper limit of the Tax Bracket * (2017 STD system) [d]	Tax receipt per Fiscal Household if Tax Base = lower limit of this Tax Bracket (€/year) ^† [e] = [e<] + [d] * ([c] - [c<])	Tax receipt per Fiscal Household whose Tax Base lays within this Tax Bracket (€/year) [f] = [e] + [d] * ([b] - [c])	Tax receipt for ALL Fiscal Households whose Tax Base lays within this Tax Bracket, if considering 100 fiscal households on total (€/year) [g] = [a] * [f]	% of Income Taxes from Fiscal Households belonging to this Tax Bracket [i] = [g] / [h]	Intensity of Contribution to Personal Income Taxes [j] = [g] / ([a] * [b])
> 0 and < 26,457	37.1	17,976	0.00	7.5%	0	738	27,400	3%	0.04
[26,457-45,897[	27.0	35,848	26,457	29.0%	1,975	4,605	124,534	14%	0.13
[45,897-100,002[	30.1	63,520	45,897	40.0%	7,613	14,662	441,525	49%	0.23
[100,002-150,000[	4.2	119,684	100,002	42.0%	29,255	37,521	158,789	18%	0.31
[150,000-200,004[	1.0	167,270	150,000	44.0%	50,254	57,852	55,307	6%	0.35
≥ 200,004	0.5	405,658	200,004	46.0%	72,255	166,856	89,435	10%	0.41
		Total Tax Bases [j], for 100 fiscal households ⇓						Total Tax [k]	*(Avg % Tax: 20.2%)* ^‡
			4,433,421					896,990	*(Avg % Tax: 20.2%)* ^‡

Approximate weighted mean tax rate over the Fiscal Bracket: for example, “29.0%” = (20% + 38%) / 2

“[e<]” refers to the value of [c] for the Fiscal Bracket below the present one (e.g. [100,002-150,000[, as for bracket [150,000-200,004[)

21.4% on average, all Fiscal Classes considered for HFCS-R in 2017, including a 7% (mainly) or 9% Tax for Unemployment fund ⇒ about 20.0% without it

Table 8. An overall view of the benchmark “STD” and an alternative fiscal policy for Residents and XBs (income year 2017).

		EUROMOD models (out of MACRO adjustment)
		EUROMOD /HFCS-R		EUROMOD/ HFCS-XB (Active households)
		STD	Alternative policy	STD	Alternative policy (LU-Incomes only)
Population covered by the surveys		535,897		418,997
Taxable Income, before Tax allowances (for XBs, LU-incomes only) in millions € / year [a + b]		20,041		9,056
a] Covered by the surveys (for XBs, LU-incomes only)		20,041		7,947
b] Additional amount not covered by the XB survey				1,109
Total Public Revenue (in millions € / year)
Social contributions [c + d]		3,714	3,714	2,092	2,092
c] Resulting from the microsimulation (based on HFCS surveys)		3,714	3,714	2,030	2,030
d] Contribution for XBs not covered by the HFCS-XB survey (evaluated based on b] and while hypothesizing that those persons are all retired)				62	62
Personal Income Tax [e + f]		3,439	3,517	939	947
e] Resulting from the microsimulation (based on HFCS surveys)		3,439	3,517	824	832
f] Additional tax from XBs not covered by the HFCS-XB survey (evaluated based on b] while hypothesizing that the tax rate applicable is the one determined for the covered households after tax credits [*])				115
and Tax Rates
Global Tax Rate on Tax Base, before Tax Credits, on average and through the HFCS surveys		20.9%	21.4%	14.4%	14.5%
[*] Global Tax Rate, after Tax Credits, through the HFCS surveys [e/a]		17.2%	17.5%	10.4%	10.5%
⇒ Total Revenue	Through the surveys, LU-incomes only for XBs [c + e] (in millions € / year)	7,153	7,231	2,855	2,862
	With macro adj., for XBs [c + d + e + f]	7,153	7,231	3,032	3,039
	General (Residents + XBs, including macro adjustment) (in millions € / year)	STD: 10,185		Alternative: 10,270
Inequalities
Gini				All Incomes
	Relative = Absolute gap / (2*Average)	0.2993	0.2966	0.1940	0.1934
	Absolute gap, on average (in € / month)	2,103	2,074	1,088	1,084
	Average well-being (in € / month)	3,513	3,496	2,804	2,802
Poverty				All Incomes
	Line (in € / month)	1,770	1,768	1,564	1,564
	Rate	13%	13%	2%	2%
"Well-being", as equivalized income (all in € / month), on average				All Incomes
All		3,513	3,496	2,804	2,802
1st Decile		1,472	1,472	1,635	1,635
9th Decile		4,943	4,923	3,820	3,816

Table A1. Final imputations in HFCS-XB, ex ante EUROMOD.

EUROMOD Variable		Imputation		Origin (in % of total)		Remarks
Name	Content	in % of (yem + yse) at household level	if another base	From LU	From ABROAD	Remarks
poa	Old-age Pension	20.3% if 1 pensioner in the household, 42.5% for each pensioner if more than 1, and 0.2% if no pensioner		0	100%	0.2% if no pensioner preferred to “0”, in conformity to HFCS-R
psu	Survival Pension		0	0	0	Incorporated in the imputation of “poa”
xmp	Maintenance payment		0	0	0	Lower amounts
yiy	Investment income	1.9%		In conformity with proportions in HXG0100x (total gross household income, separated based on its origins, LU versus other countries altogether)		May come from LU or other capital investments
yot	Other income by children < 16	1.3%		0	100%	Mainly from children, hence from “home”
ypp	Private pension		0	0	0	Lower amounts (in LU !)
ypr	Property income	4.1%		0	100%	“Properties” supposed from ABROAD

Table B1. Macro adjusting outcomes for dealing with missing XB households, uncovered up to now through the EUROMOD/HFCS (and SILC) data and platforms – Social contributions.

C] SOCIAL CONTRIBUTIONS

Reference	Component			Computation information	Value (in Millions €/year or %)

[I]	From model platforms (cf. Table 2)	SILC (Social contributions)			3,914
[II]		HFCS-R (Social contributions)			3,714
		⇒ HFCS-R [II], in % of SILC [I]		= [II] / [I]	94.9%
[III]		HFCS-XB (Social contributions for Active households & LU-incomes only)			2,030
[%1]		⇒ HFCS-XB [III[, in % of HFCS-R [II]		= [III] / [II]	54.7%

[SC/HFCS+] == [IV]	⇒ C.1] Social contributions for populations covered through HFCS-R & XB surveys			= [II] + [III]	5,745
[SC/SILC+]	Alternatively, Residents/SILC + XBs in % of SILC			= [I] * (1 + [%1])	6,054
			⇒ [SC/HFCS+], in % of [SC/SILC+]		94.9%

	C.2] MACRO Correction for Social Contributions from gross income from XBs not covered by the HFCS/XB survey
[V]	Additional gross LU-income from XBs not covered by the HFCS/XB survey, based on Pensions paid to XBs from Luxembourg in 2017 (considered as the LU-taxable income for that sub-population), whereas Pensions received by XBs covered by the HFCS survey are considered as from foreign origin only				1,109
[VI]	⇒ Additional contribution for XBs not covered by HFCS surveys (considering 2.8% * 2 of contributions for Health In-Kind, as for pensioners)			= [V] * 5.6%	62
[%2]	⇒ Total Social Contributions from XBs, in % of SC from RESIDENTS			= ([III] + [VI]) / [II]	56.3%

[SC/HFCS++]	⇒ C.3] TOTAL SOCIAL CONTRIBUTIONS, if considering All XBs, including those not covered by the HFCS/XB survey on top (based on HFCS)			= [IV] + [VI] = [II] + [III] + [VI]	5,807
	Alternatively, if based on SILC, completed by HFCS data for XBs			= [I] * (1 + [%2])	6,120

Table B2. Macro adjusting outcomes – Personal income taxes.

T] PERSONAL INCOME TAX (as for LU-Incomes, unless otherwise mentioned)

Reference	Component		Computation information	Value (in Millions €/year or %)

[VII]	From model platforms (cf. Table 2)	SILC (Personal Income Tax)		3,289
[VIII]		HFCS-R (Personal Inc Tax)		3,439
		⇒ HFCS-R, in % of SILC	= [VIII] / [VII]	105%
[IX]		HFCS-XB (Personal Income Tax for Active households & LU-incomes only)		824
[%3]	⇒ HFCS-XB, in % of HFCS-R		= [IX] / [VIII]	24%

[TAX/HFCS+]	⇒ T.1] Personal Income Taxes for populations covered through HFCS-R & XB surveys		= [VIII] + [IX]	4,263
[TAX/SILC+]	Alternatively, Residents/SILC + XBs in % of SILC		= [VII] * (1 + [%3])	4,077
		⇒ [TAX/HFCS+] in % of [TAX/SILC+]		104.6%

	T.2] MACRO Correction for Personal Income Tax from gross income of XBs not covered by the HFCS/XB survey
[X]	T.2.1] Total Taxable Income of HFCS-XBs (covered by the survey, LU-Incomes only), before Tax Allowances		= EUROMOD variable "tinty_lu_s" (on average) * 12 * HFCS-XBs Population in 2017 / 1,000,000	7,947
[XI]	Total Tax Allowances for XBs/HFCS (LU-incomes)		= EUROMOD variable "tinta_lu_s" (on average) * 12 * HFCS-XBs Population in 2017 / 1,000,000	1,627
[XII]	Income Tax for HFCS-XBs before Tax credits (LU-Incomes)		= "tin_lu_s" (/ year & for whole covered population)	911
[XIII]	⇒ Implicit Tax Rate on Tax Base for HFCS-XBs, before Tax Credits		= [XII] / ([X] - [XI])	14.4%
[XIV]	Total Tax Credits for HFCS-XBs		= [XII] - [IX]	87
[%4]	⇒ HFCS-XBs' Global Tax on Taxable Income, after Tax Credits, LU-Incomes only		= [IX] / [X]	10.4%

	T.2.2] Additional gross income from XBs not covered by the HFCS/XB survey, based on Pensions paid to XBs from Luxembourg in 2017		[V]	1,109
[XV]	⇒ Total Tax on Income for XB households not covered by the HFCS/XB survey, if Residents' average rate [%4] applied		= [V] * [%4]	115
[XVI]	& Equivalent computation taking into account Tax Allowances and Tax Credits		= ([V] - [XI] * [V]/[X]) * [XIII] - ([XIV] * [V]/[X])	115
[%5]	⇒ Total Income Tax from ALL XBs, in % of Tax from RESIDENTS		= ([IX] + [XV]) / [VIII]	27.3%

[TAX/HFCS++]	⇒T.3] TOTAL TAXES, if considering All XBs, including those not covered by the HFCS/XB survey on top		= [TAX/HFCS+] + [XV]	4,378

Table B3. Macro adjusting outcomes for dealing with missing XB households, uncovered up to now through EUROMOD/HFCS – overall consolidation.

R] TOTAL PUBLIC REVENUE: SOCIAL CONTRIBTIONS and PERSONAL INCOME TAXES as for LU accounts (hence from LU Incomes) & including ALL Cross-border households (whatever active or not) & Residents

Reference	Component	Computational information	Value (in Millions €/year or %)

[TOT/ HFCS++]	Total Public Revenue from Residents/HFCS + ALL XBs, if through HFCS data and models	= [SC/HFCS++] + [TAX/HFCS++]	10,185
[TOT/ SILC++]	Alternatively, Residents/SILC + ALL Cross-Borders considered through an additional % (derived from HFCS)	= [I] * (1 + [%2]) + [VII] * (1+ [%5])	10,307
	⇒ [TOT/HFCS++] in % of [TOT/SILC++]		98.8%