D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties

Carl Schmertmann
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Carl Schmertmann: Florida State University

Demographic Research, 2021, vol. 44, issue 45, 1085-1114

Abstract: Background: High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these purposes, but it in small samples it can often produce implausible age schedule estimates. Objective: I propose and evaluate a new type of P-spline model for estimating demographic rate schedules. These estimators, which I call D-splines, regularize and smooth high-dimensional splines by using demographic patterns rather than generic mathematical rules. Methods: I compare P-spline estimates of age-specific mortality rates to three alternative D-spline estimators, over a large number of simulated small populations with known rates. The penalties for the D-spline estimators are derived from patterns in the Human Mortality Database. Results: For mortality estimates in small populations, D-spline estimators generally have lower errors than standard P-splines. Conclusions: Using penalties based on demographic information about patterns and variability in rate schedules improves P-spline estimators for small populations. Contribution: This paper expands demographers' toolkit by developing a new category of P-spline estimators that are more reliable for estimating mortality in small populations.

Keywords: mortality estimates; splines; penalized likelihood (search for similar items in EconPapers)
JEL-codes: J1 Z0 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:dem:demres:v:44:y:2021:i:45

DOI: 10.4054/DemRes.2021.44.45

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