Correlation in defence purchases

Nitin Pai has a nice piece on defence procurement in Business Standard today. He writes:

Even if the planning process works as intended, it still means that the defence ministry merely adds up the individual requirements and goes about buying them. This is sub-optimal: consider a particular emerging threat that everyone agrees India needs to be prepared for. The army, navy and air force then prepare their own strategies and operational plans, for which they draw up a list of requirements. At the back of their minds, they know that the defence budget is more-or-less divided in a fixed ratio among them.

What he is saying, in other words, is that the defence ministry simply takes the arithmetic sum of demands from various components of the military, rather than taking correlation into account.

Let me explain using a toy example.

Let’s say that the Western wing of the Indian army (I’m making this up), the one that guards the border with Pakistan, wants 100 widgets that will come useful in case of a war. Let’s say that the Eastern wing of the Indian army, which guards the China border, wants 150 such widgets for the same purpose. The question is how many you should purchase.

According to Nitin, the defence ministry now doesn’t think. It simply adds up and buys 250. The question is if we actually need 250.

Let’s assume that these widgets are easily transportable, and let’s assume that the probability of a simultaneous conventional conflict with Pakistan and China is zero (given all three are nuclear states, this is a fair assumption). Do we still need 250 widgets? The answer is no, we only need 150, since we can quickly swing them over to where they are most required, and at the maximum, we need 150!

This is a case of negative correlation. There could be a case of positive correlation also – perhaps the chance of an India-China conventional conflict actually goes up when an India-Pakistan conventional conflict is on, and this might lead to more prolonged battles, meaning we might need more than 250 widgets! Or we have positive correlation.

The most famous example of ignoring correlation was the 2008 financial crisis, when ignored positive correlation led to mortgage backed securities and their derivatives blowing up. The Indian defence ministry can’t afford such a mistake.