Final answer:
To explore the relationship between education and log(GDP), one must create a scatter plot, calculate the least-squares line, and assess the significance using the correlation coefficient and adjusted standard errors considering clustering effects.
Step-by-step explanation:
To analyze the relationship between education and log(GDP) and produce the desired statistical model, the following steps are to be followed:
- Draw a scatter plot of the data with education as the dependent variable and log(GDP) as the independent variable, identifying each year by a different color.
- Calculate the least-squares line using Ordinary Least Squares (OLS) methodology. The equation should be in the form ý = a + bx, where ý is the predicted value of education (dependent variable), a is the y-intercept, and bx is the slope coefficient multiplied by log(GDP).
- Draw this line on the scatter plot to visualize the relationship.
- Find the correlation coefficient to determine the strength and direction of the relationship between education and log(GDP).
- To handle the possible effects of clustering within countries and over years, standard errors should be adjusted. This can be accomplished by using the coeftest command in statistical software, after downloading the multiwayvcov library. When running coeftest, specify the cluster option with clusters defined by the country and year, and keep the type as "HC1".
Based on these analyses, we can discuss the estimates and deduce if the relationship between education and log(GDP) is significant and positive, negative, or non-existent. If clustering is present, it indicates that observations are not independent within clusters, which can affect the standard errors and significance levels of the estimates.