Philip Pilkington writes: Does mathematics, due to its formal nature, provided economists with clarity? This was then typically followed up with appeals to how economics might become a science by increasingly mathematising.
A good example of mathematics providing clarity is the case of the Keynesian multiplier. Even without inputting any numbers into the equation we can immediately discern the factors that will generate equilibrium income. It will be a component of autonomous consumption, investment, I, government spending, and exports, minus autonomous imports. It will also be positively multiplied by the consumption multiplier, and negatively multiplied by the import multiplier.
We know this because the components of income are in the numerator of the equation, while the multipliers are in the denominator. The multipliers are also being subtracted from/added to 1. The larger the denominator, the smaller the numerator and vice versa. So, anything that “subtracts” from the denominator — e.g. the consumption multiplier — will increase the ratio (same directional effect as adding to the numerator), while anything that “adds” to the denominator — e.g. the import multiplier — will decrease the ratio (same directional effect as subtracting from the numerator.
Compare this presentation, however, with your typical econometric study. Such studies contain innumerable “black boxes” in that the reasoning behind the assumptions made is often entirely unclear.
One thus spends hours attempting to interpret and reconstruct such a study and, all too often, one comes away realising that the assumptions lead one inevitably to interpret the results as being almost entirely arbitrary.
One recognises the labour that goes into such studies but at the same time untangling it becomes “a nightmare to live with”. Why? Because such studies do not promote clarity at all. Instead they promote complete and total obscurantism.
This is not to say that econometrics is entirely useless. As Keynes says in the Tinbergen critique: This does not mean that economic material may not supply more elementary cases where the method will be fruitful. Take, for instance, Prof. Tinbergen’s third example-namely, the influence on net investment in railway rolling-stock of the rate of increase in traffic, the rate of profit earned by the railways, the price of pig iron and the rate of interest. Here there seems a reasonable prima facie case for expecting that some of the necessary conditions are satisfied.
Alas, however, these mathematical techniques have a tendency, not to clarity at all, but to obscurantism and the moment one gives people a ticket allowing them to engage in obscurantist practices one runs the risk of spiking the proverbial punch.
It is far, far more difficult to engage in obfuscation and magical nonsense when using plain English than it is when using mathematics; not to mention the fact that it is far easier to catch people out. And as a general rule-of-thumb it is probably not unfair to say that as the number of equations grows, the lack of clarity tends to increase and so too do the difficulties in sorting the wheat from the chaff. It is thus the multiplication and proliferation of equations that tends to give rise to nightmares.
