Erie Ins Exchange Grp — Workers' Compensation

Schedule P Part 3B/4B/D — net workers' compensation, 1988–1997 accident years. GRCODE 2135 (Erie Ins Exchange Grp). Values in $000s, net earned premium and net losses.

Actual outcome known

Source: CAS Loss Reserve Database (Meyers & Shi), NAIC Schedule P. Meyers, G.G. and Shi, P. (2011). The Retrospective Testing of Stochastic Loss Reserve Models. CAS E-Forum, using data pulled from NAIC Schedule P Parts 1-4, 1988-1997.

Run quarterly rate & reserve review Open in WC pricing model Open in Chain-Ladder (paid)Open in Chain-Ladder (incurred)Open in Bornhuetter–Ferguson Open in Bootstrap

Accident year	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997
Net earned premium ($000)	48,688	55,333	60,752	75,475	96,829	130,110	159,408	179,277	175,727	154,661

Paid loss triangle, cumulative ($000), as-of 1997

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	7,113	14,528	18,795	21,034	22,823	24,123	24,935	25,620	25,979	26,113
1989	9,163	18,770	23,895	28,168	31,097	32,646	33,858	34,794	34,988	—
1990	11,334	22,075	29,191	34,085	37,103	38,853	40,359	41,015	—	—
1991	13,131	27,922	36,280	41,515	45,938	48,637	50,439	—	—	—
1992	17,184	36,928	48,542	56,210	60,699	63,051	—	—	—	—
1993	21,222	42,519	54,972	62,654	67,202	—	—	—	—	—
1994	20,546	42,675	54,280	61,579	—	—	—	—	—	—
1995	21,313	42,668	55,908	—	—	—	—	—	—	—
1996	21,886	42,087	—	—	—	—	—	—	—	—
1997	22,408	—	—	—	—	—	—	—	—	—

Incurred loss triangle, cumulative ($000), as-of 1997

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	29,567	29,430	27,116	31,452	32,749	35,662	28,078	30,688	31,026	32,415
1989	39,056	38,216	42,956	45,723	43,927	41,192	39,066	39,091	40,712	—
1990	41,423	48,308	50,785	48,033	46,757	44,100	44,560	48,428	—	—
1991	50,923	64,216	62,055	60,247	53,956	54,483	59,471	—	—	—
1992	74,650	86,173	79,967	70,570	71,621	79,012	—	—	—	—
1993	99,545	99,832	92,548	81,131	89,257	—	—	—	—	—
1994	111,411	123,006	98,504	88,410	—	—	—	—	—	—
1995	123,044	111,440	92,364	—	—	—	—	—	—	—
1996	111,037	88,980	—	—	—	—	—	—	—	—
1997	90,097	—	—	—	—	—	—	—	—	—

Realized paid-loss square, all 10 development lags ($000)

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	7,113	14,528	18,795	21,034	22,823	24,123	24,935	25,620	25,979	26,113
1989	9,163	18,770	23,895	28,168	31,097	32,646	33,858	34,794	34,988	35,341
1990	11,334	22,075	29,191	34,085	37,103	38,853	40,359	41,015	41,746	42,292
1991	13,131	27,922	36,280	41,515	45,938	48,637	50,439	51,347	51,953	52,971
1992	17,184	36,928	48,542	56,210	60,699	63,051	64,866	65,883	66,571	67,213
1993	21,222	42,519	54,972	62,654	67,202	70,056	71,845	73,186	74,375	75,610
1994	20,546	42,675	54,280	61,579	66,108	69,448	71,215	72,806	74,130	75,470
1995	21,313	42,668	55,908	63,797	68,508	71,877	73,940	75,017	75,911	76,870
1996	21,886	42,087	54,041	61,492	65,364	67,909	69,771	71,068	72,352	73,705
1997	22,408	43,692	56,734	63,775	67,365	69,614	71,527	72,424	73,872	74,731

Realized incurred-loss square, all 10 development lags ($000)

AY \ Age	1	2	3	4	5	6	7	8	9	10
1988	29,567	29,430	27,116	31,452	32,749	35,662	28,078	30,688	31,026	32,415
1989	39,056	38,216	42,956	45,723	43,927	41,192	39,066	39,091	40,712	41,269
1990	41,423	48,308	50,785	48,033	46,757	44,100	44,560	48,428	47,619	47,041
1991	50,923	64,216	62,055	60,247	53,956	54,483	59,471	59,194	58,641	58,456
1992	74,650	86,173	79,967	70,570	71,621	79,012	77,831	75,548	74,579	75,968
1993	99,545	99,832	92,548	81,131	89,257	87,511	84,896	83,715	86,394	84,819
1994	111,411	123,006	98,504	88,410	87,655	84,279	83,527	84,959	85,917	88,185
1995	123,044	111,440	92,364	91,687	87,268	86,340	87,679	87,452	89,746	91,487
1996	111,037	88,980	87,611	84,405	83,459	84,785	84,067	84,726	86,844	86,225
1997	90,097	90,275	88,142	87,182	87,853	91,260	91,050	92,422	92,341	92,353

Hindsight test: chain-ladder vs. realized outcome

A volume-weighted chain-ladder projection from the 1997 upper triangle, compared against the actual realized ultimate now that the full square is known.

Accident year	Age at 1997	Projected ultimate	Realized ultimate	Error %
1988	10	26,113	26,113	0.0%
1989	9	35,168	35,341	-0.5%
1990	8	41,604	42,292	-1.6%
1991	7	52,338	52,971	-1.2%
1992	6	67,843	67,213	0.9%
1993	5	75,840	75,610	0.3%
1994	4	75,539	75,470	0.1%
1995	3	78,715	76,870	2.4%
1996	2	76,878	73,705	4.3%
1997	1	83,119	74,731	11.2%

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