10 January 2017

Joule's heating, demonetisation and measuring health of economy

I was reading with my daughter (not sure whether I was helping her or she was helping me) about heat (H) being dependent on the resistance (Rto the flow of current as that would create some friction, the flow of current (I), and the length of time of the flow of current (T). Or, as Joule's heating principle indicates,

(1)     H=RI2T.

My wondering thought took me to compare this with the health of the economy (h) being dependent on the resistance (rto the flow of transactions as that would create additional activities because producer consuming the produce will lead to zero or no transactions while the selling of the produce to a trader and then to an aggregator and then to a wholesaler and then to a retailer and then to a consumer will have five different economic activities, the items (ior the quantum of goods and services being transacted per unit time, and the length of time (t). The relationship is indicated in, 

(2)     h=rit.

For ease of analysis, we restrict ourselves to t=1 for each period. Further, we state that the volume of economic activities or transactions is v=ri. Besides, we would also like to introduce a correction factor, a, for v to address concerns that some of the transactions per unit time are not captured (a>1). For the sake of completeness one can also use a to address double counting (0<a<1), which we will discuss later. Having said that, we now have,

(3)     h=av.  

Now, let us use equations (2) and (3) to analyse the impact of demonetisation on the health of economy.  We will divide our discussion into multiple one-week time periods: prior to demonitisation (2-8 November 2016), immediately after demonitisation (9-15 November 2016), and then after the immediate impasse (16-22 November 2016 or perhaps with some time lapse say, 4-10 January 2017) and refer to them in our notations through subscripts of 1, 2, and 3, respectively.  

Resistance to the flow of transactions like the analogy from Joule's heating has a positive connotation on the economy by increasing the number of activities. In this sense, demonetisation, reduced the number of activities leading to a reduction in resistance in the second period. There was some increase in activities in the third, but not reached the level of the first period. The number of goods and services transacted per unit time also reduced on account of demonitisation and its subsequent revival in the third period has been tardy and it is reasonable to assume that it has still not reached the pre-demonitisation scenario.

(4)     r1>r3>r2,

(5)     i1>i3>i2and

(6)     v1>v3>v2,.

The possibility of some transaction not being captured (and perhaps one of the reasons for demonitisation) will be a larger problem in a pre-demonitised situation. Not being able to capture transactions is likely to be non-existent immediately after demonitisation. And, this might have continued in that state or it is possible that some transactions might get double counted in the third period. Thus, 

(7)     a1>a2a3. a21.

Even if one would disagree with taking an analogy from Joule's heating principle, it would be reasonable to state that r and i, as also v are positively related to h. It follows that

(8)     h1>h3>h2.

This implies that the health of the economy has reduced. The various estimates about the economy growing at a positive (but, at a lower) growth rate is in that sense optimistic. This can happen only slowly, as there is a shift towards cashless transactions and new ₹500 notes are being infused into the system. That is meant for future analysis.

Getting back to equation (8), it is possible to state from a measurement perspective that the health of the economy in the third or for that matter in the second period is better or equal to that in the first period. This is possible because we do not have a measure of aIn the absence of that it would be considered as unity, â=1. Such an assumption would be closer to reality for the second (or, under certain assumptions in the third) period, but not for the first period. Hence, an estimate for the health of the economy for the first period will be, 

(9)     ĥ1=(1/a1)h1=v1.

It follows that if h3>ĥ1 then one could get into an illusory impression that h3>h1. Let us assume that a1=1.25, that is, about one-fifth of the economy is not captured - it can also serve as a guestimate for the black economy before demonitisation. However, if calculations use â1=1 then if four-fifths (â1/a1=4/5) of the actual transaction of the first period would get recorded in the third period through cashless mode then that would give an impression that we have already attained the situation where the health of the economy is equivalent to that of the first period.

Now, if a small proportion of the economy that was earlier not being captured comes into the fold then the health of the economy would look better. That, in fact, has been the purpose behind demonitisation, that is, to get the reality into our books. In other words, the purpose is to get the one-fifth of the economy (or whatever that figure) to be part of the economic accounting. Well, as implied earlier, this can be possible if either the economy has transited into a cashless transaction or if  new ₹500 notes are back in circulation and with the assumption that the demonetisation exercise has not dented the production base.

There is also another way, that is, by increasing the number of transactions virtually and without increasing the actual exchange of goods and services. This is nothing new. The financialisation of the economy with transactions through the stock market or trading in commodity futures have been taking this mode. They have also been in existence in cashless transactions through credit and debit cards, mobile phone and other e-wallets. Let me elaborate on this.

In a cash transaction, goods or services are paid for at the point of sale. In a cashless transaction the money payment is done at the point of sale to a third-party service provider who in turn makes the payment to the seller pf the produce. This is done electronically through real time and may give the impression of a single transaction, but in practice there are two transactions. Besides, the third-party service provider may also charge for its services (the current discussion on levy of Merchant Discount Rates by banks on card transactions would imply a third transaction). Further, taxes levied on account of these transactions could lead to an additional transaction. Some of these could lead to double counting. Or, â3=1.  

It follows that ĥ1<h1 (a type I error because something that is healthy will be identified as unhealthy), ĥ2h1, and ĥ3>h(a type II error where something that is unhealthy will be identified as healthy).  Hence, even when the reality is closer to equation (8), one may still end up estimating that ĥ3>ĥ1. In fact, there are already statements being made that the tax revenue by the Government in December 2016 has been higher than the previous months to convey that the health of the economy has improved. All one can say is that one should be cautious and careful.

Some of my earlier blogs on demonitisation are:

Demonetisation: one paise view

Demon-et-ise: 2K view

1 comment:

  1. Did you know you can create short links with AdFly and earn dollars for every click on your shortened links.