Detailed Distributional Analysis (g10)

# results.md

## Distributional Analysis Questions

Q1: Pooled types

Looking at the results for income quintiles when the types are grouped together (the results with "all" for the type), is the tax progressive, proportional, or regressive? How can you tell? What is the difference in ETR between the lowest quintile and highest quintile? Note that it's fine to calculate that with a calculator: you don't need to build it into the script.

• Answer: When all types are pooled the results look very nearly proportional. The difference between the ETRs of quintiles 1 and 5 is 0.07, which is small: it's about one eighth of either ETR. Moreover, apart from the lowest quintile's ETR, the ETRs are very nearly the same: about six tenths of a percent plus or minus a couple of hundredths. For all practical purposes, they are the same.

Q2: Pooled incomes

Now look at the results for types when all incomes are grouped together (the results with "all" for quint). Do the ETRs differ? If so, say a little about what you see.

• Answer: The ETRs differ quite a bit across the types, ranging from 0.69 for type 1 to 0.53 for type 4. Differences between groups are normal in distributional analysis and result from differences in consumption behavior. For example, northern households in the US spend more on home heating than households in the south, and the reverse is true for air conditioning. Similarly, households with small children spend more on child care. Technically, this is known as between-group variation. In this case, the original data was set up so that the higher-numbered types tended to spend a smaller share of their income on the good, and thus the ETRs tend to fall.

Q3: Disaggregated results

Now look at the detailed results that are disaggregated by both type and quintile. Within any given type does the tax look progressive, proportional, or regressive? What is the difference between the ETRs of the highest and lowest quintiles for each group? As above, using a calculator is fine for this.

• Answer: Within each type the results are clearly progressive, with an increase of about 0.2 in the ETR going from the lowest to highest quintile. Notice that the swing is substantially larger than either the pooled change in question 1 or the difference in the ETRs across groups in question 2. Technically, this is known as within-group variation. The original data was set up such that within each group, the good had an income elasticity greater than 1: that is, as income rises, each group tends to spend a rising share of income on it.

Q4: Conclusion

If an analyst failed to calculate the detailed results and looked only at the ETRs by overall quintile (question 1), would they overstate or understate the policy's progressivity or regressivity? Briefly explain. If possible, also explain why happens using the insights above.

• Answer: Pooling the data causes the progressivity of the tax to be significantly understated. That is, the analyst would probably say the policy is approximately proportional when it's actually progressive. The problem is that the within-group progressivity is masked by the between-group differences in preferences.
URL: https://wilcoxen.maxwell.insightworks.com/pages/6209.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 03/17/2021