I don’t think it makes sense to compound the model distributions (e.g. from 1 year to 10 years). Doing so leads to non-intuitive results that are difficult to justify.
1) Compounded model results (e.g. 10x impact in 10 years) are highly sensitive to the arbitrarily assumed shape, range, and skewness parameters of the variable distributions. Also, these results will vary wildly from simulation to simulation depending on the sequence of random draws. This points to the model’s fragility and leads to unnecessary confusion.
2) The parameter estimates may use annualized growth rates, but they need not correspond to an annual time frame. Indeed, it is more realistic to make estimates for longer horizons because short-term noise averages out (i.e. Law of Large Numbers). In other words, it is far easier to estimate a variable’s expected mean than its underlying distribution. Estimates for the expected mean will already be highly uncertain. I don’t think it’s possible to reasonably defend distribution assumptions of the variables themselves.
The exercise is to compare giving-today vs. investing-to-give-later. The post usefully identifies key variables in this consideration. I think the most it can do is propose useful estimates of these variables’ expectations over the long run (i.e. their averages over time) and their key uncertainties (i.e. Knighting uncertainty and not quantifiable distribution parameters). If the expectations’ net sum is above 1, it makes sense to give later. If it falls below 1, it makes sense to give now. Reasonable areas of uncertainty can be further discussed and debated. Already, there will be much irreconcilable (rational) disagreement. Compounding returns using arbitrary distribution parameters won’t (and shouldn’t) reconcile any differences and likely confuses the matter.
I don’t think it makes sense to compound the model distributions (e.g. from 1 year to 10 years). Doing so leads to non-intuitive results that are difficult to justify.
1) Compounded model results (e.g. 10x impact in 10 years) are highly sensitive to the arbitrarily assumed shape, range, and skewness parameters of the variable distributions. Also, these results will vary wildly from simulation to simulation depending on the sequence of random draws. This points to the model’s fragility and leads to unnecessary confusion.
2) The parameter estimates may use annualized growth rates, but they need not correspond to an annual time frame. Indeed, it is more realistic to make estimates for longer horizons because short-term noise averages out (i.e. Law of Large Numbers). In other words, it is far easier to estimate a variable’s expected mean than its underlying distribution. Estimates for the expected mean will already be highly uncertain. I don’t think it’s possible to reasonably defend distribution assumptions of the variables themselves.
The exercise is to compare giving-today vs. investing-to-give-later. The post usefully identifies key variables in this consideration. I think the most it can do is propose useful estimates of these variables’ expectations over the long run (i.e. their averages over time) and their key uncertainties (i.e. Knighting uncertainty and not quantifiable distribution parameters). If the expectations’ net sum is above 1, it makes sense to give later. If it falls below 1, it makes sense to give now. Reasonable areas of uncertainty can be further discussed and debated. Already, there will be much irreconcilable (rational) disagreement. Compounding returns using arbitrary distribution parameters won’t (and shouldn’t) reconcile any differences and likely confuses the matter.