There are various different opinions on whether or not begging is considered an economic activity.
It depends largely on whether you consider economics to be predicated on capitalism. If such is the case, capitalism usually denotes a circular motion whereby capital is constantly taken out and put back in by consumers.
In laymen's terms, we earn money and we spend it, thus contributing to the economy. In this way, begging might not be considered an economic activity since money is not being earned, but simply 'passed on.'
On the other hand, since the beggar is in effect using the money, to by food, clothes or whatever necessary, in a sense it can be considered an economic activity since money is ultimately being restored into the system. Whether the money is passed on or earned, the result is that it is being spent, so in that sense it can indeed be considered an economic activity.
I hope this helps.
