Multiplier and probability
Keynes begun his scientifïc career with probability theory. But, he had not the idea, as far as we can know, to give a probabilistic interpretation of his famous multiplier. This article is aimed at showing that probability theory, and especially finite Markov chains theory, gives an easier and even more natural interpretation of the keynesian multiplier than the traditional methods.
Multiplier theory may be looked on as old-fashioned today, but it is still at the heart of most of macroeconometric models. So, we define first the relative position of the multiplier, which is linear and actually static, inside these models which are non-linear and dynamic.
Secondly, we give a markovian interpretation of the income multiplier in both cases of the simple multiplier and the matrix multiplier. We compare it with the traditional interpretation: in the probabilistic interpretation every kind of economic agents (banks and firms, and not only households) take a part in the process of incomes which leads to the multiplier.
Finally, we enlarge our method to the neighbouring analysis of the money multiplier and of the velocity of money.
Our conclusion is that the markovian method could also be used for a keynesian crisis analysis.