On parlera ici de panel ou de cross-section data (ce qui n'est pas la même chose...). C'est-à-dire qu'ils ont collecté les données sur différents pays et les ont croisées pour effectuer leurs estimations.

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Note added at 3 hrs (2017-07-26 13:54:49 GMT)
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Lire "mesurées"

mesurés à travers leurs observations recoupées

My understanding is the following: The same correlation between two variables was calculated across countries using data relating to the same period.

The concept of 'overlapping observations' means that not all countries' data relate to the same period. So it was necessary to determine a sub-period in which data are available for all countries and it is possible to run the same correlation between the two variables in question across countries.

English term (edited): correlations measured across overlapping observations

Contexte : les auteurs confrontent leurs données (série relative à la masse monétaire au sens large) à celles d'autres auteurs (série relative à des prêts bancaires).

IOW different authors doing each their own research, independently of each other => there is nothing to make you expect that all these temporal series will cover exactly the same time interval!
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BASIC common sense / the most elementary requirement:

you can ONLY look for correlation in data that are from the same time period, so if you have two temporal series of data established by two authors, you can use only data covering the same time interval i.e. the only parts of both sets of data that will be of any use are those where there is an overlap of the time period data relate to,

example:
data set A: from 2000 to 2013
data set B; from 2003 to 2016

the ONLY period for which you'll have any chance of looking for correlation between A and B will be 2003 to 2013 i.e. where there is an "overlap" between the period covered by the series.

IOW it's about the most simple and plain "chevauchement des périodes de temps / chevauchement d'intervalles de dates"]

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Note added at 16 hrs (2017-07-27 02:53:45 GMT)
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for each country only the data from both sets that's covering the same time period i.e. "overlapping [in time]" can be used; I can't see any idea of using data from country X to cross-check data from country Z - the only "interaction" between countries is to compare the correlations between loans and broad money established for each of them.

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Note added at 3 days20 hrs (2017-07-30 06:32:20 GMT)
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this "overlapping" of temporal series is necessary only on a "per country" basis - as there is no way you can calculate a correlation coefficient for the given country if both temporal series do not cover the same time period;

so for each country you will have a a correlation coefficient between "masse monétaire au sens large" and " prêts bancaires" covering a period as long as the available data for that country makes it possible

BUT no one in his right mind would shorten the period for which the correlation is calculated in one country to match a shorter interval of data available for some other country - that would be a waste of usable data. If for 10 countries your data is covering about 20 years, and for one country only 10 years, you are not going to throw away half of the data to fit the smaller period covered in one country.

When you have comparisons between countries, the time periods covered do not always match exactly often it's only roughly the same period - not ideal, but you can only use what's available, and use as much of it as you can.