Index: Girosi King 2007 - Understanding the Lee-Carter Mortality Forecasting Method

Girosi King 2007 - Understanding the Lee-Carter Mortality Forecasting Method

Routing Summary

This folder captures Girosi and King (2007), Understanding the Lee-Carter mortality forecasting method (working paper, 35 pages). 6 notes.

• Whole paper map and key result? → Girosi King 2007 - Understanding the Lee-Carter Method - Overview
• Need the model, SVD estimation and RWD forecast of the index? → Girosi King 2007 - Lee-Carter Model Estimation and Forecasting
• Need percent of variance explained and Table 1 across 24 countries x 10 causes? → Girosi King 2007 - Information Loss with One Principal Component
• Need the RWD equivalence and bias theorem? → Girosi King 2007 - Lee-Carter as a Random Walk with Drift
• Need universal increasing nonsmoothness? → Girosi King 2007 - Universal Increasing Nonsmoothness of Age Profiles
• Need second-stage reestimation and Wilmoth WLS vs Poisson MLE? → Girosi King 2007 - Second-Stage Reestimation and Wilmoth Estimators

Concept Map

Concept	Note	Type	Depends On	Key Result
Lee-Carter model	Girosi King 2007 - Lee-Carter Model Estimation and Forecasting	definition	-	$m=\alpha +\beta \gamma +ϵ$
Variance explained	Girosi King 2007 - Information Loss with One Principal Component	example	SVD	one PC > 90% for 14/24 countries (all-cause)
RWD equivalence	Girosi King 2007 - Lee-Carter as a Random Walk with Drift	theorem	LC model	${\Sigma }_{LC}={\sigma }^2\psi {\psi }^{\prime }/\Vert \psi {\Vert }^2+2{\sigma }^{2}I$
Bias asymmetry	Girosi King 2007 - Lee-Carter as a Random Walk with Drift	theorem	RWD equivalence	LC biased under general $\Sigma$
Nonsmoothness	Girosi King 2007 - Universal Increasing Nonsmoothness of Age Profiles	theorem	linear forecast	$\propto {\gamma }_t^2$, grows without bound
Second stage / WLS / MLE	Girosi King 2007 - Second-Stage Reestimation and Wilmoth Estimators	definition	LC model	0, 1 or 2 roots; WLS invalid; Poisson MLE valid

Notes

• Girosi King 2007 - Understanding the Lee-Carter Method - Overview — CONTAINS: question, contributions, Source Map, E111 link.
• Girosi King 2007 - Lee-Carter Model Estimation and Forecasting — CONTAINS: Eqs. 1-9, identification, SVD, forecasting, code.
• Girosi King 2007 - Information Loss with One Principal Component — CONTAINS: Eq. 10, Figure 1, full Table 1 reproduced.
• Girosi King 2007 - Lee-Carter as a Random Walk with Drift — CONTAINS: Eqs. 11-19, equivalence, bias theorem, example.
• Girosi King 2007 - Universal Increasing Nonsmoothness of Age Profiles — CONTAINS: Eqs. 20-24, nonsmoothness theorem, empirical patterns, U-shape example.
• Girosi King 2007 - Second-Stage Reestimation and Wilmoth Estimators — CONTAINS: Eqs. 25-27, root counting, WLS critique, Poisson MLE, concluding remarks.

Sources

• Girosi King 2007 - Understanding the Lee-Carter Mortality Forecasting Method - Girosi F, King G (2007), working paper, 35 pages (author copy from gking.harvard.edu).

See Also

• Factor Analysis and PPCA, Forecast Evaluation and Backtesting
• Concept notes - life tables and counterfactual mortality path