In our first year of college, we were confronted with a statistics question we found puzzling.

There are two classrooms full of students and a student moves from one classroom to another. Consequently, the average heights of students in both classrooms increase.

We thought it impossible that both sets of average heights should increase.

But it can happen. For instance, it can happen if the average height is higher in the classroom the student is migrating from than the average height in the classroom the student is migrating to and the migrating student's height is less than the average height in the first classroom but more than the average height in the second classroom.

Let's link this more closely to migration. The per capita income in the United States is $37,000 or thereabouts, while that in India is $550.

What happens now if there is migration? There is indeed a theory of cross-border labour mobility.

Stated simply, such migration will lead to equalisation of wages. Under certain conditions, free trade in goods will also lead to equalisation, but those conditions are stiff and unlikely to materialise.

But cross-border migration, from India to the US, will lead to a drop in real wages in the US and an increase in India. However, that's only if migration is on a large enough scale and such free mobility is across the board.

Take the case of a single migrant, where there is no incremental impact on wages. The US Census data tell us the average income of Persons of Indian Origin in the US is $52,000. Much higher than the US average.

This is for PIOs, not necessarily Non-Resident Indians. And this is the kind of people you see represented in annual jamborees like the Pravasi Bharatiya Divas. At the third PBD in Mumbai, it has now finally been decided that NRIs/ PIOs will be granted dual citizenship.

Who can deny them this long-standing demand? But citizenship is a vague demand unless you pin down rights that come with citizenship. It transpires that most NRIs/PIOs want voting rights, because that's the only way governance in India will improve.

While governance certainly needs to improve, it is somewhat surprising that these NRIs/PIOs aren't aware of the histories of the two countries most of them come from, the United Kingdom and the US.

Whether one goes back to Magna Carta or the Boston Tea Party, there can't be taxation without representation. Ipso facto, there can't be representation without taxation.

But if you mention taxation to these NRIs/PIOs, hell will break loose. Which is all the more surprising because all NRIs, if not PIOs directly, have been beneficiaries of explicit and implicit subsidies and a country like India effectively cross-subsidises developed countries through such migration.

This isn't an argument for imposing quotas on emigration, but is certainly an argument for eliminating subsidies and this brings one to another question.

What sort of people emigrate? What are their per capita incomes, compared to India's per capita income of $550? How much these NRIs would have earned, had they remained in India, is an impossible question to answer.

Not $52,000. PPP (purchasing power parity) exchange rates may be more plausible, though those too are imperfect indications.

Which gives us a figure of around $5,200. This figure isn't quite the issue. And admittedly, $5,200 PPP represents the higher end of Indian out-migration.

But whatever the figure, the relevant question is, does out-migration takes place from people who are above $550, or below?

I am not aware of any figures that exist. However, because of transaction costs associated with migration, one suspects it is people above the threshold that migrate. Even if it is to the Persian Gulf region. In that case, such out-migration reduces Indian per capita incomes.

At the margin, the effect on US per capita incomes is less clear. When there is a larger scale wage effect, such as in IT or Mexico vis-�-vis the North American Free Trade Agreement, there will naturally be downward pressure on US wages.

And even an upward pressure on real wages in those segments of the Indian labour market that are effectively integrated with the global labour market.

But the point is that notwithstanding negotiations on cross-border labour movements at the World Trade Organisation, such Indian enclaves are limited.

And let's not forget that WTO negotiations involve migration of skilled personnel. In the broad macro sense, Indian emigration probably leads to divergence in per capita incomes in the two countries, rather than convergence.

A similar principle operates for inter-State migration within the country. Stated differently, if one ignores the fact that not everyone is in working age groups, per capita income is a measure of productivity and the relatively more productive people migrate.

How does one ensure that less productive people migrate more? With all this talk of taxing foreign institutional inflows, perhaps we will have a tax on all migration that doesn't involve old people or children.