基于收入十分位数数据构建回归模型估算99百分位数收入是否可行？

Great question—estimating extreme percentiles like the 99th from only decile data is a common challenge, especially with income, which has a highly right-skewed distribution. Let’s break down your approach and better alternatives:

First, to address your core question: your regression-based idea is a plausible starting point, but it has significant limitations that make it unreliable for the 99th percentile. Here’s why:

• Income’s upper tail behaves very differently from middle deciles: The relationship between percentile and income isn’t just non-linear—it’s exponentially skewed at the top. A regression model trained only on the 10th to 90th percentiles won’t capture the rapid growth seen in the top 10%, let alone the top 1%.
• Extrapolation risk: You’re predicting a point 9 percentage points beyond your maximum data point (90th to 99th). Even non-linear models struggle to extrapolate outside their training range, especially for fat-tailed distributions like income.

Better Alternatives for Estimating the 99th Percentile #

Given these limitations, here are more robust approaches tailored to income data:

1. Fit a Pareto Distribution to Upper Deciles #

The Pareto distribution is the gold standard for modeling upper-income tails (it’s the basis for the "80/20 rule"). Here’s how to apply it:

• Use your 80th and 90th percentile income values (or 70th and 90th for more data) to fit the distribution’s parameters.
• The Pareto formula for percentiles is: P(X > x) = (x_min / x)^α, where x_min is the minimum value in the tail (e.g., your 90th percentile income) and α is the shape parameter.
• Solve for α using your known upper deciles, then plug in the 99th percentile to calculate the corresponding income. This method explicitly accounts for the exponential growth of high incomes.

2. Log-Transformed Regression #

If you prefer a regression-based approach but want to fix its limitations:

• Apply a logarithmic transformation to your income values first (since income grows exponentially in the upper tail).
• Train a linear regression model on log(income) vs. percentile, then exponentiate the predicted value for the 99th percentile. This adjusts for the skewness far better than a raw non-linear regression on untransformed income.

3. Use Aggregate Upper-Tail Data (If Available) #

If you can access metrics like the top 10% income share or mean income, you can refine your estimate:

• The top 10% share tells you the total income earned by everyone above the 90th percentile. Combine this with your decile data to model the distribution within the top 10% (e.g., using Pareto) and pinpoint the 99th percentile.

Key Takeaway #

While regression on deciles can give you a rough guess, it’s not reliable for the 99th percentile. The Pareto distribution or log-transformed regression are far better choices because they account for income’s unique skewness. Any additional data about the upper tail will make your estimate significantly more accurate.

内容的提问来源于stack exchange，提问作者Bobipuegi