fulgurafrango [blog]
17 September 2013


I mean literally. The labour statistics regularly provided by government show separate figures for the rates of unemployment and underemployment. People looking for a measure of total labour underutilisation in the economy may be tempted into the common—though quite understandable—mistake of adding the two together.

Why a mistake? The unemployment rate u is a proportion of the labour force L, which is the total of the employed N and the unemployed U (i.e., L = U + N). On the other hand,  the underemployment rate d is the number of underemployed D taken as a proportion of the employed N. That is, u = U/L and d = D/N. As any grade-schooler knows, these two rates cannot be simply added, since the denominators are different: “u + d” is an illicit operation.

What is valid however is to take the number of unemployed and the underemployed as a proportion of the labour force. Call this measure of total labour underutilisation:

m = (U + D)/L.

It can be shown (see Annex at the bottom of the page) that this can be computed using only the rates of un- and underemployment u and d as follows:

m = u + d(1 – u).

The correct formula weights the underemployment rate with the employment rate (1 – u), to account for its smaller base, namely the employed.

Using this on the data for the July data of 2012 and 2013, we have:

       u        d      m
     July 2013     0.073     0.192     0.251
     July 2012     0.070     0.228     0.286

To illustrate, for 2013 we obtain m = 0.073+ 0.912(1 – 0.073) = 0.251, and for 2012 we have
m = 0.07 + 0.228(1 – 0.070) = 0.286, as shown in the last column. In terms of total underutilisation amongst the labour force, m, therefore, there was actually some improvement between the two periods: the higher open-unemployment rate was offset by the drop in the underemployment rate. (Put another way, the proportion of the labour force that was fully employed (1 – m) rose between the two periods from about 71 to about 75 percent.)

The difference between these results and (wrongly) adding up u and d  (“0.265” and “0.298” for 2013 and 2012 respectively) will be noted. The  illicit procedure always gives a higher figure.

But adding underemployment and unemployment is a mistake in a wider sense.

In a developing country, neither unemployment nor underemployment is likely to be a good welfare measure, so measures like u, d, and even m miss the mark. Both government and its critics frankly focus on the wrong variables when they use un- and underemployment as measures of failure and success — especially if poverty eradication is the goal.

The reason is that none of these categories captures the bulk of the country’s poor population. Indeed, the poor cannot afford either to be fully or partly unemployed. Being fully unemployed implies one has sufficient means to support oneself (savings, networks that provide family transfers) in the process of job-seeking. Being underemployed, on the other hand, implies one has extra time on one’s hands to devote to the desired additional work. The dire situation of the truly poor places them beyond either situation. The poor are are mostly already “fully employed”. Their problem is that even as their jobs already pre-empt all of their time, these still fail to pay them enough to eke out a human existence.

Eliminating poverty requires not just counting jobs but raising productivity.



Proof that  m = u + d(1u):

m = (U + D)/L = (uL + dN)/L

= [uL + d(LU)]/L

= u + ddU/L

= u + ddu

= u + d(1 – u)