Long term care insurance with state‐dependent preferences
Bibliographic record
Abstract
We study the demand for Long Term Care (LTC hereafter) insurance in a setting where agents have state-dependent preferences over both a daily life consumption good and LTC expenditures. We assume that dependency creates a demand for LTC expenditures while decreasing the marginal utility of daily life consumption, for any given consumption level. Agents optimize over their consumption of both goods as well as over the amount of LTC insurance (LTCI). We first show that some agents optimally choose not to insure themselves, while no agent wishes to buy complete insurance, in accordance with the so-called LTCI puzzle. At equilibrium, the transfer received from the insurer covers only a fraction of the LTC expenditures. The demand for LTCI need not increase with income when preferences are non state-dependent or insurance is actuarially unfair. Also, preferences have to be state-dependent with no insurance bought to rationalize the empirical observation of a higher marginal utility at equilibrium when autonomous. Finally, focusing on iso-elastic preferences, we recover the empirical observation that health/LTC expenditures are not very sensitive to income, and we show that LTCI as a fraction of income should decrease with income and then become nil above a threshold.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".