Basically it is done by comparing new and hold hybrids in different fields. For details you may ask a reprint of https://dl.sciencesocieties.org/publications/books/abstracts/cssaspecialpubl/geneticcontribu/1 to the publisher
You can take your countries production statistics and calculate a change in yield from your starting time. Basically Time After Yield minus Start Time yield is equal to change in yield over time Delta Crop Yield.
The Delta Yield figure divided by by baseline at start time is the proportion of change and if multiplied by 100 gives a percentage change.
When we take the percentage change and divide by the number of years of statistics we get a rate of yield change which is a response to genetic improvements and the improvements of agronomic practices.
A lot of work suggest for field crops about one half the calculated gain is from genetics or crop breeding improvements and the other is from the improvement in agronomic practices.
The Yield as a Dependent factor can be related to crop years or time as the independent factor and the regression of the trend can be calculated and the slopes of the trend lines can give some comparative context. The regressions can be done with difference crops to look for areas of stagnation in the genetics and agronomic programs.
One of areas around the world where cropping has been most frustrating is Africa where results in improvements have been lagging. Most genetic improvement is found in maize where well funded programs take advantage of tried and true breeding strategies and innovation in agronomics and biotechnology are being implemented.
Guido suggestion of using planned experiments is also good but more expensive and involved.
Dear Rahul, You may be interested in this new publication. It has quantified the contribution from a third factor (in addition to genetic improvements and agronomic improvements) to historical yield improvements in corn in the US Midwest. Apparently, improvements in solar radiation reaching the ground due to improvements in air quality (solar brightening) has contributed about 27% of the historical yield improvement in corn during the last two decades. Interesting!
The contribution of solar brightening to the US maize yield trend (Nature -Climate Change)