Here’s a quick explanation of the multiplier effect. So if you invest £1m into the economy, £(1+x)m circulates because of, say, increases in business confidence.
There’s a tendency to treat this x as fixed over time, which I am arguing might not necessarily be the case.
I’m suggesting something of the form:
X_[t] = C + aX_[t-1] + bX_[t-2] + …
Where X_[p] is the Keynesian multiplier at time period ‘p’
This formula implies that the Keynesian multiplier is a variable that takes into account effectiveness of the policy in the past (which would be the past multiplier)
In terms of what values the constants C, a, b etc. are for each type of policy, it’ll be worth diving into some statistical data and backing out the variables, so I’m not too sure about what they’ll be!