Changing the Discount Rate by Adjusting the Pure Rate of Time Preference
Bibliographic record
Abstract
The Ramsey (1928) equation decomposes the real discount rate into the pure rate of time preference plus a term that accounts for the changing marginal utility of consumption. Discussions about the appropriate discount rate to apply in Cost Benefit Analysis sometimes refer to variations induced by alternative values of the pure rate of time preference as if the two vary on a one-to-one basis. But the optimal consumption path, which determines the marginal product of capital and hence the discount rate, depends on the rate of time preference. Hence the discount rate depends on time preference through the marginal utility term. We derive an analytical expression of this relationship and show that the derivative of the discount rate with respect to time preference only equals unity in the steady state and converges from below. We estimate the derivative using US data from 1930 to 2015. Based on a semi-parametric regression model with time-varying coefficients we find it is about 0.9, but we cannot rule out 1.0 being included in the 95% confidence interval. The implied pure rate of time preference after 1980 is about 1.6 percent.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.028 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".