Lots of progress on poverty

But inequality much more stubborn

Gini coefficient across countries

Where does this data come from?

• How do we calculate poverty and inequality?
  • In developing countries, usually household surveys

Where does this data come from?

Where does this data come from?

Where does this data come from?

Where does this data come from?

• In developed countries, this is often administrative data
  • Usually for the entire year
  • Example: ATO/IRS tax data tax data
• But we nonetheless tend to compare across developed and developing countries
  • “Poverty rate is the proportion of people living on less than X dollars per person per day”
    • This value is X lower in country Y than country Z
  • “The gini coefficient is higher in country A than country B”

But…

• Merfeld and Morduch (2024): But poverty in the two contexts measures something inherently different
  • In developing countries, the poverty rate is the mean proportion of the year that people live in poverty

Something similar with inequality

• How do we interpret inequality?
  • Differences in income/expenditures across households

Inequality, mathematically

• We start with a Theil index into both of these components. What we think we are measuring:

\[\begin{equation} T_{L} = \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{\overline{x}_i} \right) \end{equation}\]

• \(\overline{x}_i\) is each household’s mean expenditure
• \(\mu = \frac{1}{N} \sum^{N}_{i=1} \overline{x}_i\) is overall mean

Household expenditures

Household expenditures

We only observe one random month

Another possible sample

Inequality, mathematically

• What we are actually measuring (where \(x_{it}\) is observed expenditures, which is a random draw for each household):

\[\begin{align} T_{L-HF} = \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{x_{it}} \right) \color{#D7D1CC}{\neq \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{\overline{x}_i} \right)} \end{align}\]

Inequality, mathematically

• What we are actually measuring (where \(x_{it}\) is observed expenditures, which is a random draw for each household):

\[\begin{align} T_{L-HF} = \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{x_{it}} \right) \neq \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{\overline{x}_i} \right) \end{align}\]

Inequality, mathematically

• What we are actually measuring (where \(x_{it}\) is observed expenditures, which is a random draw for each household): \[\begin{align} T_{L-HF} =& \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{x_{it}} \right) \\ =& \frac{1}{N} \sum^{N}_{i=1} \ln \left( \frac{\mu}{x_{i}}\frac{x_{i}}{x_{it}} \right) \\ =& \frac{1}{N} \sum^{N}_{i=i} \ln \left( \frac{\mu}{x_{i}} \right) + \frac{1}{N} \sum^{N}_{i=i} \frac{1}{T} \sum^{T}_{t=i} \ln \left( \frac{x_i}{x_{it}} \right) \\ =& T_{L} + V_{L}. \end{align}\]

• We call these between inequality and within inequality, respectively

• Note that \(V_{L}\) is arguably of interest in its own right! It is within-household expenditure variability

Recovering traditional inequality

• We want to try and recover traditional inequality, \(T_{L}\)
  • This isn’t what we’re measuring!

Basic idea

1. Estimate XGBoost model to predict monthly expenditures in each month, \(x_{it}\)

Data

• Two sources of data in this paper:

Decision trees and XGBoost

Decision trees and XGBoost

1. Decision tree: makes prediction
2. Residual: difference between actual and predicted
3. New decision tree: makes prediction on residuals
4. Repeat steps 2 and 3 many times
5. Final prediction: sum of all predictions

Validation with ICRISAT

NSS: Even better! Out-of-sample, monthly exp p.c.

Summary so far

• Starting point is estimating monthly expenditures
  • But we then want to aggregate to annual mean
  • We only use the annual values in the rest of our estimation

How much are we overestimating inequality?¹

Within-household expenditure variability

An application to PMGSY

• Pradhan Mantri Gram Sadak Yojana (PMGSY)
  • Rural road construction program in India
  • We use NSS data to estimate the impact of PMGSY on inequality
  • Shapefiles from https://geosadak-pmgsy.nic.in/opendata/

Rollout of PMGSY roads

Effects of PMGSY on inequality

Wrapping up

• Inequality as measured in LDCs is actually a combination of two things:
  • Traditional inequality (differences across households)
  • Within-household expenditure variability

Wrapping up

• We apply our method to PMGSY
  • We find that PMGSY has a small but significant impact on inequality as measured (what we normally see)

Next steps

• MGNREGS? Other programs?