I have employment status data for discrete time-series, with discontinuity, i.e. 1983, 1988, 1994, 2005, 2010. I wish to calculate "employment elasticity" over time. I have 2 options, a) interpolate the series and find point elasticity, or b) keep the data as such and go for arc elasticity. Which could serve as a better measure in empirical analyses? Are there any reasons behind it?
Hi Bassam,
You have written the formula of arc elasticity and I think S. J. Balaji knows this mid point formula of arc elasticity. His question is whether he will estimate arc or point elasticity. Calculating arc elasticity in this case requires only employment and GDP data and the function for the relationship between these two variables is not necessary. However the gap between two years (e.g., 1983 and 1988) and you will calculate average elasticity between these two points. If your interest is in this average figure then this is straight forward to calculate arc elasticity. In case of point elasticity, the two points between which elasticity is being measured essentially collapse on each other. In order to measure this infinitesimal change you need well defined employment function where GDP will be an independent variable along with other variables. If you have cross-section in each year then you can proceed for panel data analysis, no need for interpolation. If you have data only for employment and GDP then calculate both arc elasticity and point elasticity with interpolated data and see what is more plausible and useful for your purpose.
Dear SJ, why choosing ?
With a math software it will be quick to set up a polynomial regression on discrete data, the degree depending on how high R² you desire. So, point elasticity should be easy enough to estimate. Once PE available, you can compare it with arc elasticity which, less sharp from a purely mathematical point of view, sticks nonetheless on "real" data.
kind regards
Yes William, it seems better to have arc elasticity rather than point estimates. Being not sure about exact pattern of trend, it can't be a good idea to go for interpolation, either linear or other kinds....... Thanks.......
Dear Claudio, Thanks for suggestion. Would it be reasonable to go for polynomial functions when the trend is not exactly following the same? My trend line (at discontinuous points) doesn't show for 2nd or 3rd degree terms? Or, can you explain more.....
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