Is Amazon’s takeover of Whole Foods anti-competitive? Probably not.

This originally appeared as a guest post on the Adam Smith Institute’s blog last week.

A few days ago, Amazon announced its plans to purchase the predominantly USA-based grocery retail chain Whole Foods for almost $14bn. Although both companies operate in many countries, the main competition issues (if any) are likely to arise in the US, were both companies have a non-negligible presence.

Indeed, this announcement has resulted in a number of people claiming that the proposed merger will be anti-competitive. Specifically, there are some claims that the merger would result in 1) bundling and foreclosure of rivals; and/or 2) predatory pricing. In short, the first theory of harm posits that Amazon would force customers that wanted to purchase its distribution (or other) services to also purchase from Whole Foods (or vice versa), while the second theory of harm suggests that the merged entity would price below cost in order to drive out rival grocery firms before increasing prices once those rivals exited.

Importantly, both of these theories of harm require that the merged entity have some form of “market power” (i.e. the ability to charge a price above the competitive level and to act independently of its rivals). Typically, this is most likely to occur when a firm has a share of sales in a particular market of over 40%. However, as a general point, these theories of harm gloss over the fact that Amazon and Whole Foods’ shares in grocery sales are tiny – less than 5% combined in the US. As such, it is difficult to see how the combined entity can have any market power.  Clearly, the merged entity would not satisfy this for sales of groceries at the moment of the merger.

Bundling

However, others might argue that Amazon does have a sufficiently high share of sales of “online retail” to be classed as dominant. As such, they argue that Amazon could “leverage” its power in that area to grocery retail by bundling some of its services with those of its groceries. However, as the merged entity will be active at the retail level of groceries, it is not obvious exactly what other services offered by Amazon could be bundled with them – for the bundling strategy to work, consumers would still have to want at least one of the items in the bundle, and could continue to purchase them separately from Amazon or elsewhere anyway. Hence, there does not appear to be a viable mechanism through which this bundling theory of harm could occur.

Predatory Pricing

Moreover, for the predatory pricing theory of harm to be valid, there must be strong evidence that 1) the merged entity would price its groceries below some measure of cost that represents the extra cost that would be incurred by supplying one extra unit of output (usually measured as average variable cost of long-run average incremental cost); and 2) it would have an incentive to do so.

The first condition is notoriously difficult to prove – one first has to decide which costs should be included / excluded in the measure (which really isn’t as easy as one would think – e.g. should advertising spend that applies to brand-related marketing, but isn’t specifically related to groceries, be included), as well as deciding the relevant time-frame over which costs are assessed.

The second condition requires proving that the merged entity would become dominant (and therefore be able to recoup the losses it had made in pricing below cost) in the future. This is where the theory of harm becomes incredibly speculative – it assumes that sufficient sales would switch to the merged entity from rival grocery firms that the merged entity would be dominant. In other words, it assumes that pricing below cost would be sufficient in and of itself to persuade consumers to switch (regardless of e.g. quality of service provided) and that rival grocery firms would not respond in any way to the merged entity’s actions. Clearly both of these assumptions are likely to be violated in practice and, as such, the predatory pricing theory of harm seems unlikely.

Summary

Given that the merged entity is unlikely to have the incentive or ability either to bundle its products together or recoup any losses made from pricing below costs, both of the theories of harm currently being bandied about are unlikely to be valid. As such, it is difficult to see how the cries that the proposed merger is anti-competitive are anything more than “a big firm is buying someone so they have to be stopped”. That should not be a basis on which a merger can be prevented.

What a surprise! Taking in refugees isn’t detrimental to society

Back in 2015, Germany, recognising the humanitarian crisis in Syria agreed to allow any refugee that had made it to another EU country to file claim asylum in Germany. Inevitably, this resulted in a large influx of refugees – roughly one million were registered at German borders in 2015, with a further 400,000 or so registering in 2016.

Equally inevitably, this was met with howls of protests from those who wanted to “protect their borders”. For example, claims regarding the level of crimes committed by refugees and immigrants littered the likes of the Daily Mail and the Express, despite the fact that said crimes accounted for an infinitesimal proportion of all crimes in Germany during that period.

However, until now there hasn’t been a systematic study of the impact of Germany’s decision to accept large numbers of refugees – a paper by Gehrsitz and Ungerer fills this gap.This paper looks at the impact of the number of refugees on local crime rates; domestic and refugee success in the job market; and domestic attitudes to refugees and immigration.Although there have been some studies that find that immigration / refugees are detrimental, but those studies are either methodologically flawed (e.g. the one by Piopiunik & Ruhose) or written by biased fools such as Borjas.

Given the fact that large numbers of refugees were accepted into Germany, if accepting refugees was detrimental to any of these areas, then those effects would be almost certain to show up in this analysis. However, the study indicates that accepting large numbers of refugees is not detrimental to the local population.

In order to do so, the study makes use of the fact that refugees were allocated to different German states simply based on what accommodation spaces were available, creating a pseudo-random distribution of the number of refugees across the different German states.In essence, provided that these allocations were not correlated with factors such as the initial (and trend) income, unemployment etc across the different states, this provides a natural experiment by which the impact of the number of refugees on the domestic population can be estimated. Importantly, the paper finds that there is no correlation between a state’s initial labour market conditions, demographics, crime rates etc. such that the inferences resulting from the analysis are highly likely to be valid.

The paper then looks at the impact of the number of refugees that entered a particular state during the 2015-2016 period on a state’s 1) change in crime between 2013 and 2015; 2) change in unemployment rate between 2013Q1 and 2016Q1; and 3) change in share of the vote obtained by the anti-immigration “Alternative fur Deutschland” party between the federal election in 2013 and the state elections in 2016, while also controlling for other factors (such as state GDP per capita, demographics etc.) that vary across the German states.

Perhaps unsurprisingly, the paper finds that refugee inflows have:

  • no negative impact on the rate of domestic unemployment in a state (in fact, the results suggest that an increase in refugees actually decreases domestic unemployment, but slightly increases unemployment among non-German workers likely because the refugees themselves start to show up in the unemployment figures);
  • a tiny impact on crime rates – a large increase in refugees does not lead to an “explosion” in crime, but merely increases reported crimes by only 1.5%, with the majority of this appearing to come from an increase in fare dodging on public transport;
  • no impact on support for the anti-immigration political party – in other words, having more refugees in an area does not seem to lead to people in those areas voting in favour of decreasing immigration.

Now, one potential issue with some studies that find “no effect” of a variable is that this finding of no effect is driven by the coefficients being estimated imprecisely – this is usually indicated by standard errors that are improbably large. However, in the case of this study, the standard errors do not appear to be overly large, such that there is no reason to believe that the findings of no effect are due to imprecise estimates of the coefficient.

Hence, there is strong reason to believe that accepting even a large number of refugees is not detrimental to the local population in terms of crime or unemployment (or other factors that might drive local people to vote for an anti-immigration political party). Although these results do only refer to short-term effects (i.e. those occurring within 6-12 months of a large influx of refugees), there is no reason to believe that the long-term effect would be any different. Indeed, many studies (e.g. Foged & Peri, the IMF) find that the domestic population actually benefits from taking in refugees and immigrants in the long-run.

In other words, arguments that taking in refugees will harm (or be at the expense of) the domestic population are highly likely to be false.

George Osborne: A solid, but not spectacular Chancellor

As announced last night, George Osborne is no longer Chancellor of the Exchequer. Plenty of articles have already been written regarding how he’ll be remembered and whatnot (see, for example, here), but what really matters in an evaluation of his performance as Chancellor is focusing on the long-term impact of his main policies.

Of course, the main focus of Osborne’s term as Chancellor was “austerity” (or, as it is described in technical terms, a “fiscal consolidation”). There is lots of debate as to whether austerity is harmful or is beneficial to growth in the short-run – for example, Alesina & Ardagna, and some parts of the IMF, find that fiscal consolidations actually increase short-term growth, whereas the likes of Guajardo et al. and other parts of the IMF believe that fiscal consolidations harm short-term growth.

However, what really matters in evaluating the impact of austerity is its likely affect on long-term growth. Here, none of the aforementioned studies have anything to say, but there are good reasons to believe that austerity is beneficial for long-term growth. For example, it seems plausible that the amount of time required for a country to re-establish any lost credibility (either with taxpayers or the central bank) that arises from running continually large fiscal deficits could be relatively high – convincing people that a country is now fiscally responsible is unlikely to be the matter of a few years’ work.

In other words, it is plausible that it could take longer than just a few years for people to change their opinion regarding a country’s fiscal responsibility, such that the full impact of fiscal consolidations are only likely to be felt far into the future. Moreover, even though a recent working paper (by Fata & Summers) suggest that fiscal consolidations hamper long-run growth, those papers are based on a methodology that is fundamentally flawed.) Hence, austerity per se could have been a good policy of Osborne’s.

However, Osborne erred when he cut government spending on investments and infrastructure. At a time of incredibly low interest rates, it would have made sense to borrow to invest in projects that would have reaped a return in the future – the costs of borrowing are low, while the expected future benefits of such investments are likely to be high (in terms of their impact on future growth and on future tax revenues). Therefore, Osborne’s focus on cutting all, rather than just day-to-day, spending was misguided. Just as misguided (for the same reasons, since it prevented Osborne from borrowing to invest in infrastructure) was his Fiscal Charter.

Similarly, protecting spending on the NHS and on international development meant that there was little incentive for those departments to find savings despite the fact that they, and the NHS in particular, is bloated and full of inefficiencies (witness the large NHS deficits). If those departments had not had their budgets protected, a more efficient and equitable distribution of the cuts to day-to-day spending could have been achieved (since if the NHS or development budgets had been cut slightly, then other departments’ budgets would not need decreasing as much). Likewise, the triple lock on pensions. So, another negative point for Osborne there.

On the other hand, Osborne did set up the Office of Budget Responsibility (OBR), which was undoubtedly a very good thing. Although not quite as dramatic as Labour granting the Bank of England (instrument) independence in 1997, this step was important since it enabled and promoted independent oversight of government forecasts and spending plans. Moreover, it added much-needed rigour to Treasury analysis, evaluation of government performance against fiscal targets etc. since those working in the Treasury know that people at the OBR will review and evaluate any plans and forecasts.

Getting on to some of the smaller issues, the pasty-tax debacle was also a negative point. Specifically, the introduction of the tax was actually a decent idea – it removed some of the myriad of exemptions that apply to VAT, thereby simplifying the tax system – but the subsequent reversal of the policy in the face of (relatively small) public backlash was weak and disappointing to see. Likewise, the introduction of the National Living Wage policy was a good idea, but restricting it to over 25s seems rather a cop-out, and instead the minimum wage should (and could easily) have been increased to the level of the NLW, thereby benefiting more people without substantially increasing businesses’ costs.

There are also things that Osborne couldn’t really do much about, but for which some might blame him anyway. The lack of productivity growth might be one, but that’s more the responsibility of other departments than it is the Treasury. Failing to meet, or continually adjusting, his fiscal targets could be another – but Osborne was hampered in meeting those because of sluggish growth in the global economy.

Overall, then, it seems as though there are plenty of things over which Osborne can be criticised (e.g. refusing to borrow to invest, protecting certain departments’ budgets), but equally there are plenty of policies he introduced that are worthy of praise (e.g. the OBR, consolidating day-to-day fiscal spending). As such, Osborne will most likely go down in history as fairly middle of the road – some good bits, some bad bits, but generally not outstanding in either category.

Pesky immigrants, coming over here, making our lives better

Further to a previous post about how immigration can benefit the global economy, it’s also important to examine how immigration can affect the people in areas to where people have migrated. One of the main arguments used by those that try to claim that immigration is harmful is that immigration hurts the wages / employment of the low-skilled because supposedly cheaper immigrants take those jobs away from domestic workers. The fact that this argument is based on the false “lump of labour” theory has been covered well elsewhere (see, for example, here), but it can also be tested empirically.

To that end, a recent paper by Foged & Peri investigates the impact of immigration on domestic workers of various different skill types. To do so, it makes use of a quirk in the system that Denmark used to re-locate successful asylum-seekers and the fact that in subsequent years, relatives of those asylum seekers came to join them. Specifically, between 1986 and 1998, Denmark distributed refugees across the country taking into account only the refugee’s family size, the nationality of the refugee (so as to try to achieve “clusters” of refugees that would help each other out), and the availability of housing in each area.

In this way, the location of refugees was almost entirely independent of local labour market conditions. (Note that it is not entirely independent because there is likely to be some relationship between an area’s labour market and the availability of housing.) Nonetheless, this distribution of refugees was followed by a period between 1995 and 2003 in which immigrants from various regions moved to Denmark (most of these were from the likes of the Former Yugoslavia, Somalia etc. and were trying to escape local conflicts).

The people in this “new wave” of immigrants tended to settle in areas where earlier refugees/immigrants with the same nationality had settled – in this way, the initial distribution of refugees (that was mostly independent of labour market conditions) also drove future immigrants’ decisions of where to settle. Hence, the increase in immigration to Denmark from 1995 on can be used to assess the impact of immigration on the labour market in Denmark since the locational decisions of those immigrants was mostly independent of the labour market conditions themselves. (This is important because otherwise the results of an analysis of the impact of immigration on the labour market would be biased if the amount of immigration to a particular area itself was affected by the labour market in that area).

Therefore, in order to assess the impact of immigration on Danish workers, the paper uses a “longitudinal cohort study” – i.e. a frequent survey of a large group of people over a prolonged period of time (in this case, the Danish Integrated Database for Labour Market Research). This survey contains information related to someone’s age, municipal location, whether or not they are employed, their occupation, the number of hours they work, their salary etc. Coupled with information on where immigrants settled as per the previous paragraph, this dataset thus enables the researchers to investigate the impact of immigration on domestic workers.

The results of the study are extremely interesting. Contrary to the fallacious argument that low-skilled workers are harmed by immigration, the results of this study indicate that immigration actually benefits low-skilled workers in multiple ways.

First, immigration motivates and enables low-skilled workers to progress into more complex occupations. Second, these more complex jobs are associated with higher wages, such that immigration actually increases the hourly wage of low-skilled workers. Third, immigration does not result in (some number) of low-skilled workers becoming unemployed. In other words, immigration doesn’t force low-skilled workers out of a job, but instead enables them to obtain better jobs.

In addition, the study also looks to see if the impact of immigration falls different across different sets of low-skilled workers. It finds that the positive impact of immigration is felt most strongly by those low-skilled workers that are either young (less than 46 years old) or have not been in their jobs very long (less than four years), but also that there are no statistically significant negative effects for older workers or those that have been in their jobs a long time.

Overall, therefore, this study is pretty conclusive that immigration is beneficial to low-skilled workers and that those that claim that immigration harms those on low wages really don’t know what they’re talking about.

Why the difference between correlation and causation matters

A blog post by a member of the Economic Policy Institute (a US think-tank) has claimed that the decline in Trade Union membership is the cause of the increase in (a single measure) of inequality in the USA.

The blog post looks at how membership of Trade Unions and the share of income that goes to the top 10% change during the period 1917-2012, notices that they appear to be negatively correlated, and therefore concludes that decline in trade union membership is responsible for the increase in inequality.

First, it is important to note that inequality has actually decreased over time, rather than increased as the article claims (see, for example, here and here). Moreover, the blog’s use of a very specific measure of inequality, focusing solely on the income share of the top 10%. It does not take into account any other factor that determines the level of inequality within a country – for example, whether the majority of income in the top 10% is distributed evenly across that 10%, or is concentrated in the top 1% or even the top 0.1%.

Indeed, a more comprehensive measure of inequality (such as the Gini coefficient) takes into account the distribution of income across the entire spectrum rather than merely focusing on a subset of that distribution. When looking at such measures over time, it becomes apparent that inequality across the entire distribution of incomes has barely increased since the 1960s, despite the measure used in the blog post having increased since that time.

(And that is not withstanding other ways in which inequality might arise, such as via the distribution of wealth, access to healthcare, and/or access to education.)

Second, the author’s evidence to support their argument that a decline in trade union membership is responsible for the increase in inequality  consists solely of the fact that the measure of US inequality they choose is negatively correlated with US Trade Union membership.

There are plenty of examples of two series being correlated over time, despite there not being any way in which a causal relationship can exist between them. For example, Tyler Vigen presents such examples as Arcade revenues being correlated with number of Computer Science PhDs being awarded, and there being a strong correlation between Maine’s divorce rate and per capita consumption of margarine.

Moreover, the article’s “analysis” fails to account for the countless other factors that could have affected inequality over the course of the almost 100 years covered. For example, demographic changes, changes in the industries, technological developments, new infrastructure, changing societal attitudes individually and together are likely to have contributed to the changes in inequality. Indeed, the correlation between the US Trade Union membership and the chosen measure of inequality appears to be the large increase in TU membership and the large decrease in inequality between 1936 and 1945. And it’s not as though there were other things going on during that period of time at all!  Despite this, the article attributes the changes in inequality solely to changes in Trade Union membership.

Finally, the article does not even try to come up with a mechanism by which Trade Union membership can affect inequality beyond a vague description of how trade unions increase bargaining power. There are no doubt plenty of other things that are negatively correlated with the measure of inequality used in the report and that the report’s author presumably also thinks is just as likely a reason for changes in inequality as is Trade Union membership (US military strength might well be one, as could the number of black and white television sets in use).

I look forward to the Economic Policy Institute writing about those in due course.

 

 

Glassdoor’s “contribution” to gender wage gap research

In a whirlwind of publicity and self-promotion, Glassdoor recently released the results of a “study” that claimed to prove the existence of a gender pay gap even when potential differences in areas such as “personal characteristics, job title, company, industry and other factors” are accounted for. As a result, Glassdoor boldly claims that men are paid about 5% more than women.

However, the approach used by Glassdoor is subject to a major problem. In particular, Glassdoor’s approach relies on them being able fully to control for all other factors (such as experience, qualifications etc) that might determine someone’s wage. Although Glassdoor notes this themselves (in a single paragraph relegated to the back of their report), they do not qualify any of their headline results with an acknowledgement of this.

Seeing as Glassdoor only includes controls for a few personal characteristics (such as age, qualifications, and experience) and some factors relating to a person’s occupation and industry (such as job title and company name). In other words, Glassdoor excludes a number of relevant factors that are likely to be relevant when it comes to explaining someone’s wage.

Indeed, other studies have found that factors such as ethnicity, whether or not someone is a member of a trade uniona person’s mental and physical health, and even language skills can be important determinants of a person’s wage. The Glassdoor study does not account for any of these, and thereby erroneously attributes differences in wages that could be due to these (or other factors) to the gender pay gap.

In addition, the Glassdoor study does not seem to account for whether or not someone is working part-time or full-time – as part-time workers are likely to be paid less than full-time workers, even on an hourly basis, Glassdoor’s apparent failure to include such a distinction in their analysis could bias their results substantially. Similarly, the Glassdoor study does not even try to account for potential unobservable differences (such as personal preferences regarding careers), and this failure further biases Glassdoor’s estimate of the gender pay gap.

Finally, the data used by Glassdoor are from self-reported salaries and characteristics that are recorded by members of the Glassdoor website. There are plenty of reasons to suspect that these data are unreliable – at the very least, it is widely recognised that figures that are self-reported are likely to be subject to considerable bias, such that relying on them for a study such as this is nonsensical.

Therefore, it is clear that Glassdoor’s “study” into the gender wage gap is merely an exercise in self-promotion rather than a useful contribution to the substantial amount of past research that has been conducted on this issue.

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.