Voice After a Long Silence: Measuring Surplus Labour in the India’s Unorganised Sector

Abstract

There appears to be long silence in this field ever since the eighties. It is acknowledged perhaps that the yardstick of measuring surplus labour is highly subjective. This created serious doubts as to how to build up major theoretical and empirical conundrums on a subjective ground. The advent of efficiency analysis provided a rigid norm for defining what is “optimal” and hence “sub-optimal”. However, the only problem of efficiency is that it is a radial measure. Ray (in: Hosh, Neogi (eds) Theory and application of productivity and efficiency: econometric and DEA approach, Macmillan India Limited Chennai, 2005) introduced sub-vector efficiency to tackle this problem. Basically, the sub-vector defines the input requirement set when some of the inputs are fixed. Sub- vector efficiency is conditional to the choice of the prefixed inputs. This can then be used for assessing the extent of surplus labour. This method has been used by Sengupta et al. (Sarvekshana 29(95), 20–39, 2009, 2011) on a limited sphere. Our aim is to extend this methodology to the NSSO 73rd round data, covering all the states of India and with entire informal sector. We found significant instances of surplus labour. Among the factors that explain the surplus labour are the constraints that the firm have to deal with. Smallness can curb the desire to fly with open wings.

Appendix

(https://www.stata.com/support/faqs/statistics/pseudo-r2/)

In the STATA programme for estimating the pseudo-R², we use the formula

$${\text{pseudo}} - R^{2} = 1 - L1/L0$$

where L0 and L1 are the constant-only and full model log-likelihoods, respectively.

So far as discrete distributions are concerned, the log likelihood is the log of a probability, making it is always non-positive. Thus for such distributions, 0 ≥ L1 ≥ L0, implying 0 ≤ L1/L0 ≤ 1, hence 0 ≤ pseudo-R² ≤ 1.

For continuous distributions the issue is different. Here the log likelihood is the log of a density. It is easily seen that density functions can be greater than 1 (cf. the normal density at 0) Thus the log likelihood can be positive or negative. Similarly, mixed continuous/discrete likelihoods like tobit can also have a positive log likelihood.

If L1 > 0 and L0 < 0, then L1/L0 < 0, and 1 − L1/L0 > 1.

If L1 > L0 > 0 and then L1/L0 > 1, and 1 − L1/L0 < 0.

So, if the above formula is used for pseudo-R², it is possible to get it > 1 or < 0 for continuous or mixed continuous/discrete likelihoods like tobit.