Who loses and who wins with the PEC 287/2016? An analysis of the pension wealth variation for the urban beneficiary of Brazilian Social Security System.

Martins, Fábio Garrido Leal; Campani, Carlos Heitor

doi:10.1590/0034-761220180062

Fábio Garrido Leal Martins

Universidade Federal do Rio de Janeiro / Coppead Graduate School of Business, Rio de Janeiro / RJ — Brazil

http://orcid.org/0000-0001-8845-2404

Carlos Heitor Campani

Universidade Federal do Rio de Janeiro / Coppead Graduate School of Business, Rio de Janeiro / RJ — Brazil

http://orcid.org/0000-0003-1896-7837

Fábio Garrido Leal Martins - PhD Student and Master in Administration focused on finance from Coppead (UFRJ); Master in Actuary from PUC-Rio. E-mail: fabio.garrido@coppead.ufrj.br

Carlos Heitor Campani - Post-doctorate from Princeton University (USA); PhD in finance from Edhec Business School (France); Professor at Coppead (UFRJ). E-mail: carlos.heitor@coppead.ufrj.br

AGE AND CONTRIBUTION PERIOD (YEARS)		TIME REMAINING TO RETIRE CURRENT RULE (YEARS)	TIME REMAINING TO RETIRE TRANSITIONAL RULE (YEARS)	WELFARE FACTOR CURRENT RULE	REPLACEMENT FACTOR NEW RULE	ACTUARIAL WEALTH BEFORE REFORM (R$ THOUSAND)	ACTUARIAL WEALTH AFTER REFORM (R$ THOUSAND)	GAIN OF ACTUARIAL WEALTH (%)
45	29	6.0	13.0	0.595	1.000	398	418	5.0
46	29	6.0	12.0	0.616	1.000	04	425	5.1
46	30	5.0	12.0	0.595	1.000	400	421	5.2
47	29	6.0	11.0	0.639	1.000	410	431	5.3
47	30	5.0	11.0	0.616	1.000	406	428	5.4
47	31	4.0	10.0	0.595	1.000	403	443	10.0
48	29	6.0	10.0	0.662	0.975	416	428	3.0
48	30	5.0	10.0	0.639	1.000	412	435	5.6
48	31	4.0	9.0	0.616	1.000	409	451	10.3
48	32	3.0	8.0	0.595	1.000	405	467	15.1
49	30	5.0	9.0	0.662	0.975	418	432	3.4
49	31	4.0	8.0	0.639	0.975	415	448	8.0
49	32	3.0	7.0	0.616	0.975	411	464	12.8
49	33	2.0	7.0	0.595	1.000	408	471	15.6
50	30	5.0	8.0	0.687	0.950	424	429	1.2
50	31	4.0	7.0	0.662	0.950	421	445	5.8
50	32	3.0	6.0	0.639	0.950	417	461	10.5
50	33	2.0	6.0	0.616	0.975	414	469	13.3
50	34	1.0	5.0	0.595	0.975	410	485	18.3
51	31	4.0	6.0	0.687	0.925	427	442	3.5
51	32	3.0	5.0	0.662	0.925	423	458	8.2
51	33	2.0	5.0	0.639	0.950	420	466	11.0
51	34	1.0	4.0	0.616	0.950	416	482	15.9
52	32	3.0	4.0	0.687	0.900	429	454	5.8
52	33	2.0	4.0	0.662	0.925	426	463	8.7
52	34	1.0	3.0	0.639	0.925	422	479	13.6
53	33	2.0	3.0	0.687	0.900	432	459	6.4
53	34	1.0	2.0	0.662	0.900	428	476	11.2
54	34	1.0	1.3	0.687	0.875	435	467	7.5
55	34	1.0	1.3	0.713	0.875	441	456	3.4

AGE AND CONTRIBUTION PERIOD (YEARS)		TIME REMAINING TO RETIRE CURRENT RULE (YEARS)	TIME REMAINING TO RETIRE TRANSITIONAL RULE (YEARS)	WELFARE FACTOR CURRENT RULE	REPLACEMENT FACTOR NEW RULE	ACTUARIAL WEALTHBEFORE REFORM (R$ THOUSAND)	ACTUARIAL WEALTH AFTER REFORM (R$ THOUSAND)	GAIN OF ACTUARIAL WEALTH (%)
40	21	9.0	18.0	0.556	0.975	345	362	4.8
40	22	8.0	18.0	0.538	1.000	345	368	6.8
40	23	7.0	17.0	0.520	1.000	344	384	11.4
40	24	6.0	16.0	0.504	1.000	346	400	15.4
41	21	9.0	17.0	0.575	0.950	350	360	2.8
41	22	8.0	17.0	0.556	0.975	349	366	4.8
41	23	7.0	16.0	0.538	0.975	349	381	9.4
41	24	6.0	15.0	0.520	0.975	348	397	14.0
41	25	5.0	15.0	0.504	1.000	348	404	16.1
42	22	8.0	16.0	0.575	0.950	354	364	2.8
42	23	7.0	15.0	0.556	0.950	353	379	7.3
42	24	6.0	14.0	0.538	0.950	353	395	11.9
42	25	5.0	14.0	0.520	0.975	352	402	14.0
42	26	4.0	13.0	0.504	0.975	352	418	18.7
43	23	7.0	14.0	0.575	0.925	358	377	5.3
43	24	6.0	13.0	0.556	0.925	357	392	9.8
43	25	5.0	13.0	0.538	0.950	357	400	11.9
43	26	4.0	12.0	0.520	0.950	357	416	16.6
43	27	3.0	11.0	0.504	0.950	356	432	21.3
44	23	7.0	13.0	0.595	0.900	362	374	3.3
44	24	6.0	12.0	0.575	0.900	362	390	7.7
44	25	5.0	12.0	0.556	0.925	362	397	9.9
44	26	4.0	11.0	0.538	0.925	361	414	14.5
44	27	3.0	10.0	0.520	0.925	361	430	19.1
44	28	2.0	10.0	0.504	0.950	361	438	21.4
45	23	7.0	12.0	0.616	0.875	367	372	1.3
45	24	6.0	11.0	0.595	0.875	367	387	5.6
45	25	5.0	11.0	0.575	0.900	366	395	7.8
45	26	4.0	10.0	0.556	0.900	366	411	12.3
45	27	3.0	9.0	0.538	0.900	366	427	16.9
45	28	2.0	9.0	0.520	0.925	365	436	19.2
45	29	1.0	8.0	0.504	0.925	365	453	24.0
46	24	6.0	10.0	0.616	0.855	371	387	4.2
46	25	5.0	10.0	0.595	0.875	371	392	5.8
46	26	4.0	9.0	0.575	0.875	371	408	10.2
46	27	3.0	8.0	0.556	0.875	370	425	14.7
46	28	2.0	8.0	0.538	0.900	370	433	17.1
46	29	1.0	7.0	0.520	0.900	370	450	21.8
47	24	6.0	9.0	0.639	0.835	376	386	2.7
47	25	5.0	9.0	0.616	0.855	375	392	4.4
47	26	4.0	8.0	0.595	0.855	375	408	8.7
47	27	3.0	7.0	0.575	0.855	375	424	13.2
47	28	2.0	7.0	0.556	0.875	375	430	14.9
47	29	1.0	6.0	0.538	0.875	374	447	19.5
48	24	6.0	8.0	0.662	0.815	380	385	1.3
48	25	5.0	8.0	0.639	0.835	380	391	2.9
48	26	4.0	7.0	0.616	0.835	380	407	7.2
48	27	3.0	6.0	0.595	0.835	379	424	11.6
48	28	2.0	6.0	0.575	0.855	379	430	13.4
48	29	1.0	5.0	0.556	0.855	379	447	17.9
49	25	5.0	7.0	0.662	0.815	385	390	1.5
49	26	4.0	6.0	0.639	0.815	384	406	5.8
49	27	3.0	5.0	0.616	0.815	371	423	13.9
49	28	2.0	5.0	0.595	0.835	384	429	11.8
49	29	1.0	4.0	0.575	0.835	383	446	16.3
50	26	4.0	5.3	0.662	0.795	389	401	3.0
50	27	3.0	4.0	0.639	0.795	389	422	8.5
50	28	2.0	4.0	0.616	0.815	388	428	10.3
50	29	1.0	3.0	0.595	0.815	388	445	14.7
51	27	3.0	3.9	0.662	0.775	393	402	2.2
51	28	2.0	3.0	0.639	0.795	393	428	8.7
51	29	1.0	2.0	0.616	0.795	393	444	13.1
52	28	2.0	2.7	0.662	0.775	398	413	3.7
52	29	1.0	1.3	0.639	0.775	398	437	10.0
53	29	1.0	1.3	0.662	0.775	402	427	6.1
54	29	1.0	1.3	0.687	0.775	407	416	2.2

H_{x + t} = 13 ∙ [{{}_{z_{1} - z_{0} - t /}a}_{x + t}^{(13)} + (1 - ρ) . a_{x + t : \bar{z_{1} - z_{0} - t}|}^{(13)} + ρ . (a_{\bar{z_{1} - z_{0} - t}|}^{(13)} + {{}_{z_{1} - z_{0} - t /}a}_{y + t}^{(13)} - {{}_{z_{1} - z_{0} - t /}a}_{x + t y + t}^{(13)})]

β = \sum_{k = 1}^{t} {{}_{k - 1}p}_{x}^{a a} . p_{x + k - 1}^{a i} . v^{k - \frac{1}{2}} . B_{x + k - \frac{1}{2}} . H_{x + k - \frac{1}{2}}^{i (13)}

H_{x + k - \frac{1}{2}}^{i (13)} = 13 ∙ [{{}_{z_{1} - z_{0} - k + \frac{1}{2} /}a}_{x + k - \frac{1}{2}}^{i (13)} + (1 - ρ) . a_{x + k - \frac{1}{2} : \bar{z_{1} - z_{0} - k + \frac{1}{2}}|}^{i (13)} + \dots + ρ . (a_{\bar{z_{1} - z_{0} - k + \frac{1}{2}}|}^{(13)} + {{}_{z_{1} - z_{0} - k + \frac{1}{2} /}a}_{y + k - \frac{1}{2}}^{(13)} - {{}_{z_{1} - z_{0} - k + \frac{1}{2} /}a}_{x + k - \frac{1}{2} y + k - \frac{1}{2}}^{{(13)}_{i}})]

γ = \sum_{k = 1}^{t} {{}_{k - 1}p}_{x}^{a a} . q_{x + k - 1}^{a a} . v^{k - \frac{1}{2}} . B_{x + k - \frac{1}{2}} . H_{y + k - \frac{1}{2}}^{(13)}

H_{y + k - \frac{1}{2}} = ρ ∙ (a_{\bar{z_{1} - z_{0} - k + \frac{1}{2}}|}^{(13)} + {{}_{z_{1} - z_{0} - k + \frac{1}{2} /}a}_{y + k - \frac{1}{2}}^{(13)})

[1] Fábio Garrido Leal Martins - PhD Student and Master in Administration focused on finance from Coppead (UFRJ); Master in Actuary from PUC-Rio. E-mail: fabio.garrido@coppead.ufrj.br

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Who loses and who wins with the PEC 287/2016? An analysis of the pension wealth variation for the urban beneficiary of Brazilian Social Security System.

Abstract