Immigration and global output

A recently published IZA working paper by Clemens and Pritchett has provided an interesting development regarding the assessment of “optimal” rates of migration. Previous studies tended to focus on the impact of migration on income distribution in the countries that were being migrated to. The Clemens and Pritchett paper is part of a developing literature that, instead, examines the impact of migration on (global) efficiency).

Previous studies looking at the impact of migration on income distribution essentially assessed the extent to which migration affected wages in the countries/areas in which migrants were settling. These often produced mixed results – for example, Borjas found that increases in migration to a country were associated with decreases in wages in that country, whereas Ottaviano & Peri find that immigration actually increases wages in migrants’ destination countries. Just to confuse matters, Card finds that wages are completely uncorrelated with migration.

Hence, there is a need for an alternative way of looking at the impact of migration, which is where these recent developments in terms of the “global efficiency of migration” come in.

The basic idea is that the productivity of labour is low in the countries from which people migrate, but high in the countries to which migrates move. This means that moving people (i.e. labour) from a low productivity country to a high productivity country increases the mean global productivity of labour, such that global output increases.

Consider the stylised example set out in the table below, in which 50 people move from the low productivity country to the low productivity country – the rows indicate whether the situation is before or after this migration occurs. The second and third column of the table indicate the productivity of one unit of labour in, respectively, the migrants’ origin country (the low productivity country) and their destination country (the high productivity country). Columns four and five indicate the number of people in each country, while the fifth and sixth column indicate output in each country (simply each country’s labour productivity multiplied by the number of people in the relevant country).

The final column sums the output in each country to obtain total global output. Comparing this column before and after migration indicates that people moving from the low productivity country to the high productivity country can increase global efficiency. Empirical studies have found that, via this mechanism, global output could be increased by 50% – 150% if restrictions on migration were lifted.

Good case

However, a modification of this mechanism could mean that migration actually reduces global output. Specifically, it could be the case that people moving from low productivity (origin) countries to high productivity (destination) countries actually “bring” some of their low productivity with them, such that the productivity of all workers in the destination country is reduced. If the productivity of labour in the destination country is reduced by a sufficient amount, this could mean that migration reduces global output. In the previous example, it was assumed that the productivity of labour in each country (the second and third columns of the table above) remained unchanged after migration.Such “transference” of low productivity could occur via migrants bringing their cultural or institutional norms with them and potentially being slow to “assimilate” in their destination country.

The table below presents a revision of the previous example in which the only change is that labour productivity in the destination country is reduced by migration (note, however, that productivity in the destination country is still higher than that in the origin country). Even though everything else from the previous example is unchanged, if migration reduces productivity in the destination country, this could mean that migration actually reduces global output. This theory, called the “Epidemiological Model”, has been espoused by the likes of Borjas.

Bad case

Clemens and Pritchett’s working paper tries to bridge the gap between these two opposing mechanisms by modelling the impact of “transmission”, “assimilation” and “congestion” on the rate of migration that maximises global output while eqaulising labour productivity. In this context:

  • transmission refers to the extent to which migrants’ low productivity travels with (i.e. to what degree do migrants actually “bring” any cultural and institutional low productivity with them when they migrate);
  • assimilation is defined as the proportion of migrants that “convert” to being high productivity (i.e. of those that migrate, how many obtain the same high productivity as workers in the destination country); and
  • congestion refers to the impact of un-assimilated migrants on the overall productivity in the destination country.

As such, the model constructed by Clemens and Pritchett trades off the gains of moving labour from a low-productivity country to a higher-productivity country against the reduction in the productivity in the high-productivity country resulting from un-assimilated migrants. Hence, the model embodies the two opposing potential mechanisms by which migration can imapct global output as described above.

The model’s results indicate that optimal migration is higher when:

  • transmission is lower – i.e. if cultural and institutional low-productivity does not “travel” well;
  • assimilation is higher – i.e. if migrants easily and predominantly obtain the same high productivity as workers in the destination country; and
  • congestion is lower – i.e. un-assimilated migrants do not substantially reduce the productivity level in the destination country.

Although these results might seem relatively obvious given the description above, the paper then goes on to use estimates of  the rates of transmission, assimilation, and congestion to obtain an estimate of the “optimal” rate of migration from the perspective of maximising global output. The paper finds that this optimal rate is substantially higher than the actual rate of migration, with the implication that global output could be raised by reducing the current restrictions on migration.

However, there are some flaws with the paper. First, the model of global output that is used to determine the optimal rate of migration only includes labour as an input – i.e. it does not include capital (machinery, infrastructure etc.) as a determinant of output. This is despite the fact that most basic models of output do include capital. The absence of capital from this model is not a problem if migration does not affect incentives to invest in capital, but if migration does affect those incentives, then the results of the model are unlikely to hold in reality.

In particular, if migration increases investment (by reducing labour productivity, thereby making investment more attractive relative to labour), then increased migration increases output such that optimal migration would be higher. Alternatively, if migration reduces incentives to invest, then increases in migration could lead to reductions in capital, potentially decreasing global output. Although the paper tries to cover this off in a single paragraph towards the end of its results, this is far from sufficient (the paper only mentions the first potential impact of capital and sues that to claim that its results are conservative).

Second, the paper notes that the rates of assimilation, transmission, and congestion are relatively unknown yet it does not include a rigorous assessment/estimation of the true value of these parameters. Instead, in order to obtain empirical estimates of these rates, the paper relies on very simple regressions that appear far too basic to capture the various determinants of these rates. For example, the estimates of the rates of assimilation and transmission are based on regressions where the dependent variable is a person’s wage yet the paper only includes controls for age, education, and gender as well as the immigrant status of a person (the variable of interest), despite the fact that estimating the determinants of wages is a highly complex exercise.

Finally, the paper assumes that changes to productivity only flow in one way (i.e. that low productivity workers reduce the productivity in the destination countries but productivity in the origin country is unchanged despite the potential for technology transfers or stimulation of foreign direct investment) and claims that is conservative. In other words, the paper claims that ignoring this possible transfer means that their estimate of the optimal rate of migration is actually lower than the truly optimal rate.

However, this fails to take into account the fact that if such productivity changes flowed both ways, then the productivity in the low-productivity origin country would increase in future, thereby reducing the productivity difference between the high and low productivity countries (i.e. reducing the positive impact of labour moving from the origin to the destination country). This could have the effect of reducing the future optimal rate of migration, but is further complicated by the fact that raising productivity in the origin country might also mean that any reduction in productivity in the destination country through migration is ameliorated somewhat. However, the paper just glosses over this complex dynamic aspect.

Nonetheless, despite these flaws the paper does provide a useful framework and some novel insights regarding how the assessment of restrictions on migration can be developed in future.

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