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Maybe these questions are silly for many of you but I’m trying to conduct a beta convergence analysis using data from the Penn World Table, and I have run into some uncertainties.

For the dependent variable (which is GDP per capita growth in time period 1970-1990), I keep seeing slightly different specifications between papers. In some cases, it appears as if they just take the natural logarithm of the end period minus the logarithm of start period. enter image description here

Where $y_{it}$ is GDP per capita (end, 1990) and $y_{it-T}$ is GDP per capita (initial period, 1970)

In other cases, they divide by the number of years. enter image description here

In the third case, they divided the ln variables above (but I suppose that is equivalent to subtracting from the logarithm rules?) (However, when I divided versus subtracted in Excel I ended up with slightly different numbers)

I tried regressing using the data I retrieved from the "three" methods, and the results are similar in terms of sign and significance, but the size of the coefficients vary.

Then I want to perform a conditional beta convergence analysis, where I include data on population growth rate. Can I once again just take the logarithm of the population variable, subtract the end and start period and divide by the number of years to get the average annual growth rate for the period?

To get a control variable for investment, I decided to use the variable “Share of gross capital formation at current PPPs”, and then I took the average for each country for the time period I’m interested in. Do you think that is a valid approach to account for investment, or would it better to look at the growth of the gross capital formation share? (or in fact a different variable)

And lastly, would you recommend using Expenditure-side real GDP or Output-side real GDP for a convergence analysis?

If you could help me out I would really appreciate it!

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