Impact of the Demographic Transition on Tax Collection in Brazil: an analysis of the federative aspect

Tiné, Rafael Ferreira; Freitas, Carlos Eduardo de; Paes, Nelson Leitão

doi:10.1590/0101-41615012rcn

Rafael Ferreira Tiné

PhD, Analista − Banco Central do Brasil − Endereço: Setor Bancário Sul (SBS), Quadra 3 Bloco B - Ed. Sede - Brasília/DF − Brasil − CEP: 70074-900 − E-mail: rafaeltine@hotmail.com.

http://orcid.org/0000-0003-1362-5459

Carlos Eduardo de Freitas

Professor - Universidade Federal de Rondonópolis (UFR-FACAP) − Endereço: Av. dos Estudantes, 5055 − Cidade Universitária − Rondonópolis - Mato Grosso/MT − Brasil − CEP: 78735-901. E-mail: cefreitas@ufmt.br

http://orcid.org/0000-0002-6347-011X

Nelson Leitão Paes

Professor - Universidade Federal de Pernambuco (UFPE-PIMES) − Endereço: Av. Prof. Moraes Rego, 1235 - Cidade Universitária − Recife/PE - Brasil − CEP: 50670-420 − E-mail: nlpaes@gmail.com.

http://orcid.org/0000-0001-6246-4503

Editor Responsável: Rafael Terra de Menezes

Variable	Value	Variable	Value
Consumption (% of GDP)	60.18	Federal Revenues (% of GDP)	24.18
Government Consumption (% of GDP)	18.95	States Revenues (% of GDP)	8.45
Capital Stock (% of GDP)	760.33	Municipals Revenues (% of GDP)	1.86
Investment (% of GDP)	20.86	Social Security Revenues (% of GDP)	7.15
Real Interest Rate (%)	2.28	Social Security Expenditure (% of GDP)	10.92
Share of labor Income (% of GDP)	61.80	Depreciation (%)	2.70
Working Hours	0.3928

Variable	Description	Value
τ_kf	Tax rate on Capital Income - federal	τ_kf = 0,125
τ_ke	Tax rate on Capital Income - states	τ_ke = 0,016
τ_km	Tax rate on Capital Income - municipalities	τ_km = 0,019
τ_l	Tax rate on Labor Income - only federal	τ_l = 0,107
τ_sf	Social Security Tax Rate - federal	τ_sf = 0,1078
τ_se	Social Security Tax Rate - states	τ_se = 0,0053
τ_sm	Social Security Tax Rate - municipalities	τ_sm = 0,0026
τ_cf	Tax Rate on Consumption - federal	τ_cf = 0,1007
τ_ce	Tax Rate on Consumption - states	τ_ce = 0,19
τ_cm	Tax Rate on Consumption - municipalities	τ_cm = 0,04

Age Group	Share of Goods	Share of Services	Age Group	Share of Goods	Share of Services
21-25	69.6%	30.4%	51-55	62.6%	37.4%
26-30	69.4%	30.6%	56-60	64.1%	35.9%
31-35	68.4%	31.6%	61-65	61.2%	38.8%
36-40	64.6%	35.4%	66-70	62.7%	37.3%
41-45	64.1%	35.9%	71+	60.7%	39.3%
46-50	63.7%	36.3%	Average	64.5%	35.5%

Age Groups	21-25	26-30	31-35	36-40	41-45	46-50	51-55	56-60	61-65	66-70	+71
2013	13.5	13.9	13.2	11.6	10.5	9.7	8.5	6.9	5.4	3.9	2.8
2040	8.7	9.2	9.8	10.3	10.3	10.2	10.1	10.0	8.5	7.1	5.9
2060	7.6	7.9	8.3	8.7	9.1	9.6	10.1	10.4	10.1	9.5	8.7

Variable	2013	2040		2060
Variable	% GDP	% GDP	S.S^* * percentage change from steady state (2013).	% GDP	S.S
Macroeconomic Aggregates
- Output (Y)	100	100	-8.1	100	-10.9
- Private Consumption	60.2	59.0	-10.0	58.2	-13.8
- Public Consumption	18.9	18.9	-7.9	18.9	-10.6
- Investment	20.8	23.0	1.4	23.0	-1.4
Tax Revenues
- Total (including Social Security)	34.5	34.3	-9.0	33.9	-12.5
- Labor Income	6.6	6.5	-9.1	6.5	-12.1
- Consumption	15.3	14.9	-10.5	14.8	-13.7
- Capital Income	5.5	5.4	-9.1	5.4	-12.7
Social Security
- Revenues	7.1	7.1	-8.5	7.1	-11.3
- Benefits	10.9	24.0	102.8	27.2	122.0
Revenues by Government Units
- Federal Revenues	24.2	24.0	-8.7	23.9	-12.0
- State Revenues	8.4	8.2	-10.7	8.1	-14.3
- Local Revenues	1.9	1.9	-10.5	1.8	-15.8

Variable	2013	2040		2060
Variable	% GDP	% GDP	S.S^* * percentage change from steady state (2013).	% GDP	S.S
Macroeconomic Aggregates
- Output (Y)	100	100	-10,1%	100	-11,3%
- Private Consumption	60,2	54,2	-19,1%	53,0	-22,0%
- Public Consumption	18,9	21,0	0,0%	21,3	0,0%
- Investment	20,8	23,7	2,3%	24,8	5,6%
Tax Revenues
- Total (including Social Security)	34,5	50,2	30,8%	53,4	37,2%
- Labor Income	6,6	6,6	-10,3%	6,6	-11,5%
- Consumption	15,3	30,9	81,7%	34,2	98,0%
- Capital Income	5,5	5,5	-10,7%	5,5	-11,8%
Social Security
- Revenues	7,1	7,1	-9,6%	7,2	-10,7%
- Benefits	10,9	24,0	97,8%	26,8	118,1%
Revenues by Government Units
- Federal Revenues	24,2	27,4	1,6%	28,4	4,0%
- State Revenues	8,4	17,7	89,5%	19,4	105,2%
- Local Revenues	1,9	5,11	142,1%	5,55	159,5%
- tax rate on consumption	35,0	63,6	81,2%	72,7	107,8%

Variable	2013	2040		2060
Variable	% GDP	% GDP	S.S^* * percentage change from steady state (2013).	% GDP	S.S
Macroeconomic Aggregates
- Output (Y)	100	100	-6,7%	100	-12,9%
- Private Consumption	60,2	52,4	-18,8%	50,8	-26,4%
- Public Consumption	18,9	20,3	0,0%	21,7	0,0%
- Investment	20,8	27,1	21,4%	28,2	18,2%
Tax Revenues
- Total (including Social Security)	34,5	49,6	34,2%	55,0	38,8%
- Labor Income	6,6	6,6	-6,8%	6,6	-13,0%
- Consumption	15,3	13,3	-18,9%	12,9	-26,5%
- Capital Income	5,5	5,5	-7,3%	5,5	-13,5%
Social Security
- Revenues	7,1	24,3	218,7%	30,0	268,7%
- Benefits	10,9	24,4	108,6%	28,0	123,6%
Revenues by Government Units
- Federal Revenues	24,2	37,6	45,0%	42,9	54,4%
- State Revenues	8,4	8,9	-0,8%	9,0	-6,9%
- Local Revenues	1,9	3,08	51,1%	3,14	44,2%
- tax rate on social security	11,56	42,0	239,4%	55,8	320,5%

u_{j, t} (c_{j, t^{'}} l_{j, t}) = {(c_{j, t}^{(1 - \frac{1}{ρ})} + α l_{j, t}^{(1 - \frac{1}{ρ})})}^{\frac{1}{(1 - \frac{1}{ρ})}}

\max_{\{c_{j, t,^{, l} j, t}\}} U_{t} = \frac{1}{1 - \frac{1}{γ}} \sum_{j = 1}^{55} {(1 + β)}^{- (t - 1)} p_{j} u_{j, t}^{(1 - \frac{1}{γ})}

\begin{matrix} \sum_{j = 1}^{35} \{(W_{t} e_{j} (1 - l_{j, t}) (1 - τ_{lt} - τ)) \prod_{m = 1}^{t} {[1 + r_{m} (1 - τ_{kt})]}^{- 1}\} + \\ \sum_{j = 36}^{55} \begin{matrix} \{(b_{t} + {Tr}_{t}) \prod_{m = 36}^{t} {[1 + r_{m} (1 - τ_{kt})]}^{- 1}\} \geq \sum_{j = 1}^{55} \{((1 + τ_{ct}) c_{j, t}) \prod_{m = 1}^{t} {[1 + r_{m} (1 - τ_{kt})]}^{- 1}\} \\ l_{t} < 1, \forall t = 1,... 35 . \\ l_{t} = 1, \forall t = 36,... 55 . \end{matrix} \end{matrix}

\begin{matrix} c_{j, t} = c_{j - 1, t - 1} \cdot {(\frac{{(1 + β)}^{t - 2}}{{(1 + β)}^{t - 1}})}^{γ} \cdot {([1 + r_{t} \cdot (1 - τ_{kt})])}^{γ} \cdot {(\frac{P_{j}}{P_{j - 1}})}^{γ} \\ \cdot {(\frac{1 + τ_{ct - 1}}{1 + τ_{ct}})}^{γ} \cdot {(\frac{1 + α^{ρ} {(w_{j - 1, t - 1}^{*})}^{(1 - ρ)}}{1 + α^{ρ} {(w_{j, t}^{*})}^{(1 - ρ)}})}^{\frac{ρ - γ}{ρ - 1}} \end{matrix}

\begin{matrix} l_{j, t} = l_{j - 1, t - 1} \cdot {(\frac{{(1 + β)}^{t - 2}}{{(1 + β)}^{t - 1}})}^{γ} \cdot {([1 + r_{t} \cdot (1 - τ_{kt})])}^{γ} \cdot {(\frac{P_{j}}{P_{j - 1}})}^{γ} \\ \cdot {(\frac{1 + τ_{ct - 1}}{1 + τ_{ct}})}^{γ} \cdot {(\frac{1 + α^{1 + ρ} {(w_{j - 1, t - 1}^{*})}^{(1 - ρ)}}{1 + α^{1 + ρ} {(w_{j, t}^{*})}^{(1 - ρ)}})}^{\frac{ρ - γ}{ρ - 1}} \\ \cdot {(\frac{w_{j - 1, t - 1}^{*}}{w_{j, t}^{*}})}^{ρ} \end{matrix}

\begin{matrix} {(\frac{c_{j, t}}{c_{j - 1, t - 1}})}^{- (\frac{1}{ρ})} {(\frac{c_{j, t}^{(1 \frac{1}{ρ})} + α l_{j, t}^{(1 - \frac{1}{ρ})}}{c_{j - 1, t - 1}^{(1 - \frac{1}{ρ})} + α l_{j - 1, t - 1}})}^{(\frac{\frac{1}{ρ} - \frac{1}{γ}}{1 - \frac{1}{ρ}})} \\ = (\frac{{(1 + β)}^{- (t - 2)}}{[1 + r_{t} (1 - τ_{kt})] {(1 + β)}^{- (t - 1)}}) (\frac{P_{j - 1, t - 1}}{P_{j, t}}) (\frac{1 + τ_{ct}}{1 + τ_{ct - 1}}) \end{matrix}

\begin{matrix} T_{t} = \sum_{j = 1}^{35} N_{j, t} τ_{lj} W_{t} e_{j} (1 - l_{j, t}) \\ + \sum_{j = 1}^{55} (N_{j, t} c_{j, t} τ_{cft} + N_{j, t} ω_{j} c_{j, t} τ_{cet} + N_{j, t} (1 - ω_{j}) c_{j, t} τ_{cmt}) \\ + (τ_{kft} + τ_{ket} + τ_{kmt}) (r_{t} + δ) k_{t} + S_{t}^{A} \end{matrix}

POF Goods or Services	Correspondence Complementary Law nº 116
Habitation
Services and Fees	10 - Intermediation and similar services.
Housekeeping	7 - Services related to engineering, architecture, geology, urbanism, construction, maintenance, cleaning, environment, sanitation and the like.
Household Repairs	14 - Services relating to third party goods.
Transport
Urban	16 - Municipal transport services.
Maintenance and accessories	14 - Services relating to third party goods.
Health care
Health Plan / Insurance	4 - Health, medical and similar services.
Dental Consultation & Treatment
Medical consultation
Medical and outpatient treatment
Surgery services
Hospitalization
Miscellaneous exams
Others
Education
Regular Courses	8 - Education, teaching, pedagogical and educational guidance, instruction, training and personal assessment services of any degree or nature.
Higher Course
Other courses and activities
Others
Recreation and culture
Recreations and sports	6 - Personal care, aesthetics, physical activities and similar services.
Others	12 - Amusement, leisure, entertainment and similar services.
Personal services
Hair salon	6 - Personal care, aesthetics, physical activities and similar services.
Manicure and pedicure
Repair of personal items	14 - Services relating to third party goods.
Others	14 - Services relating to third party goods.
Miscellaneous expenses
Games and betting	19 - Ticket distribution and sale services and other lottery products, bingo cards, cards, bets or coupons, sweepstakes, prizes, including those arising from capitalization bonds and the like.
Ceremonies and parties	12 - Amusement, leisure, entertainment and similar services.
Professional Services	17 - Technical, administrative, legal, accounting, commercial and similar support services.
Occasional Real Estate	9 - Services relating to accommodation, tourism, travel and the like.
Others

[1] Editor Responsável: Rafael Terra de Menezes

Brasil

Brasil

Impact of the Demographic Transition on Tax Collection in Brazil: an analysis of the federative aspect

Abstract