用于解释组均值差异的方法咨询——以地区收入差距为例

Great question! Let's break this down clearly:

First off, you shouldn't use the mean income gap as your dependent variable (DV). That $25,000 gap is a single summary statistic—regression models require a dataset with multiple observations (like individual or household-level records, each tied to their income, state of residence, and your predictor variables). Using a single number as the DV would leave you with a model that has zero degrees of freedom, making it useless for meaningful inference.

Instead, here are the right approaches to unpack and explain that income gap:

1. Multiple Linear Regression with a State Dummy Variable #

Treat each individual's income as the DV, then build your model with:

• A dummy variable (e.g., NJ = 1, FL = 0) to flag which state someone lives in
• Your full set of predictor variables (age, education level, occupation, industry, etc.)

What this delivers:

• The unadjusted coefficient for the state dummy will match exactly that raw $25,000 gap
• Once you add control variables, the dummy's coefficient becomes the net income gap after accounting for those factors
• Comparing the raw vs. adjusted coefficients shows you how much of the gap is explained by differences in your predictors between the two states

2. Oaxaca-Blinder Decomposition #

This is the gold standard for decomposing group mean differences. It splits the total $25,000 gap into two distinct parts:

• Characteristics effect: The portion of the gap caused by differences in predictor variables (e.g., New Jersey has a higher share of college-educated workers than Florida)
• Coefficients effect: The portion caused by differing returns to those characteristics (e.g., a college degree gives a bigger income boost in New Jersey than it does in Florida)

Even better, it can quantify how much each individual predictor contributes to the total gap—perfect for your goal of pinpointing exactly where the difference comes from.

3. Hierarchical Models (If You Have Granular Data) #

If your dataset includes sub-state geographic details (like cities or counties), a hierarchical linear model can add more nuance:

• First control for individual-level variables
• Then layer in state/regional factors (cost of living, local industry mix, policy differences) to see how they shape income disparities

A Quick Critical Note #

Make sure you're working with individual-level data, not just state-level summary stats. If you only have state-level data, you'd need to expand to include more states (treating each state as an observation, with mean income as the DV) but this limits how deeply you can explain the specific NJ-FL gap.

Also, keep an eye out for endogeneity (e.g., high-earners choosing to move to NJ instead of FL)—but for a first pass at explaining the gap, regression and Oaxaca-Blinder are more than sufficient.

内容的提问来源于stack exchange，提问作者Zach Goldberg