Session 4: Growth Models
📊 Exercise: Testing the Solow Model’s Convergence Prediction
Overview
One of the most striking predictions of the Solow-Swan model is absolute convergence: poor countries should grow faster than rich countries due to diminishing returns to capital, eventually leading all economies to the same income level.
Your task is to test this prediction empirically using real-world data from the Penn World Tables.
What You Need
Required packages
haven(for reading Stata files)dplyr(data manipulation)ggplot2(visualization)tidyr(data reshaping)broom(regression results)
Data Source
- Penn World Tables 11.0: Download
pwt110.dtafrom https://www.rug.nl/ggdc/productivity/pwt/ - Save the file in your R working directory
The Convergence Test
You will estimate this regression equation:
\[\frac{1}{T} \ln\left(\frac{y_{i,t+T}}{y_{i,t}}\right) = \alpha + \beta \ln(y_{i,t}) + \epsilon_i\]
Interpretation:
The crucial parameter to test is the convergence parameter \(\beta\):
- If \(\beta < 0\): Countries with lower initial income grow faster \(\rightarrow\) Convergence
- If \(\beta > 0\): Rich countries grow faster \(\rightarrow\) Divergence
Thus, the prediction of the Solow-Swan model is that \(\beta\) is significantly smaller than zero.
Analysis Requirements
There are different ways to test for convergence. In particular, you may vary the time horizon and the countries considered.
We suggest you test convergence for:
- Time Periods:
- 1960-1990 (30 years)
- 1990-2022 (32 years)
- Country Samples:
- All countries with complete data (the Solow-Swan case)
- OECD countries only (the case of conditional convergence)
What you should produce for every case:
- Regression results (\(\beta\) coefficient, \(p\)-value, \(R^2\))
- Scatter plots with trend lines
- Economic interpretation of findings
This exercise demonstrates how theoretical predictions from growth models perform when confronted with empirical evidence - a crucial skill in development economics research.