The effect of migrant children on native-born childrens' academic performance

Back in July, I wrote a post about how the exposure to foreign-born students affected the academic performance of students in Florida. Unsurprisingly, there is a lot of related research on the impact of immigrant students on native-born students. The effect will depend on the characteristics of the immigrant students (e.g. whether they speak the language of instruction; or the education level of their parents) and how teachers respond (e.g. do they change the way that they present material) and how schools respond (e.g. are immigrant students clustered into particular classes).

Identifying the effect of school peers (including immigrant students) on academic performance is quite difficult, mainly because there is a problem of selection bias. Parents often get to choose what school to send their children to. Schools usually get to choose how to allocate students across classrooms, sometimes on the basis of academic merit (often referred to as 'streaming'). These selection effects mean that the observed relationship between academic performance and the number (or proportion) of immigrant peers is going to be biased. Researchers must find some way to deal with the selection bias.

In this 2020 article (open access) by Kelvin Seah (National University of Singapore), published in the journal Australian Economic Review, selection bias is reduced by comparing student performance between two consecutive cohorts of students at the same school. That deals with any selection bias in relation to schools (because the comparison is within schools). Using data from entire school cohorts might deal with class selection issues (although I am not convinced - it simply means that the bias might be positive for some students, and negative for others, but there is no guarantee that it averages out to zero).

Seah uses data from the 1995 TIMSS study, for Australia, Canada, and the United States. This study collected data on maths and science performance for students in seventh and eighth grades. The data set includes over 40,000 students from over 700 schools across the three countries. Measuring exposure to immigrant students as the proportion of non-native-born students in each school cohort, Seah finds that:

There are marked differences in the share of immigrant students to which native students are exposed in the three countries. On average, natives in the Australian sample have the highest share of immigrant peers in their grade level in school while natives in the Canadian sample have the lowest.

Looking at the effects on maths achievement in the TIMSS test, Seah finds that:

For Australia... the maths achievement of native students is positively associated with the share of immigrant peers in the grade... a 10‐percentage point rise in the grade share of immigrants increases native maths achievement by about 0.093 standard deviations (significant at the 5 per cent level)...

For Canada... the share of immigrant students in the grade is negatively associated with natives’ maths achievement (this relationship is statistically significant at the 5 per cent level)... A 10‐percentage point increase in the share of immigrant grade peers is estimated to reduce native maths achievement by 0.048 standard deviations...

For the United States... Once non-random sorting of immigrant and native students across schools is taken into account, the relationship between these variables disappears and the coefficient falls to essentially zero. The result is unaltered when controls for individual, family, and school‐grade characteristics are added...

The results for Australia might seem a little surprising at first, but Seah shows that immigrant children in Australia perform better in maths than native-born children. The results are similar (but the size of the effects are much smaller) for performance in science. Digging a bit deeper into the maths results, Seah finds that:

...the peer effects of immigrant students are more adverse when immigrant students are non‐native speakers of the test language and when they have less‐educated parents. Further, the estimated peer effects of immigrant students attenuate when subject achievement of immigrant students is controlled for, suggesting that peer effects are at least partially working through immigrant students’ achievement.

There's nothing too surprising there. Seah then tries to tie the disparate results for Canada and Australia to the degree of autonomy that teachers have in setting the curriculum, and finds that:

...the results for maths achievement indicate that the peer effects of immigrants are more positive in schools where teachers have a high degree of influence in determining curriculum.

That suggests that, if we want to limit any negative effect of immigrant students on native-born students' achievement, we should allow teachers to better tailor their course offerings for their class. Unfortunately, that is almost the opposite what we might conclude from this 2018 article by Hu Feng (University of Science and Technology Beijing), published in the Journal of Comparative Economics (sorry, I don't see an ungated version online). Feng uses data from the China Education Panel Survey (CEPS), and instead of international migrants, the focus here is on internal migrants. So, at the least, there is unlikely to be much of a language effect in Feng's sample. Interestingly, Chinese middle school students (who are the focus of Feng's study) are mostly allocated to classes either randomly, or using a "balanced assignment rule" (which means that the best and worst students go in one class, the second-best and second-worst in another class, and so on). This random allocation allows Feng to deal with the class selection issue (but I'm not entirely convinced about the absence of school selection, because wealthy parents could opt their children out of public schools).

Feng looks at the effect of migrant peers on performance in maths, Chinese, and English, and finds that:

...the presence of migrant peers in the classroom has negative and statistically significant effects on math scores of local students... a ten-percentage-point increase in the proportion of migrant students in the classroom reduces local students' math test scores by 1.06 points, which is equivalent to 0.11 standard deviations...

...migrant peers have large and negative effects on local students’ Chinese test scores... a ten-percentage-point increase in the proportion of migrant students in the classroom reduces local students’ Chinese test scores by 1.06 points, which is equivalent to 0.11 standard deviations... Finally... migrant peers have negative but relatively small effects on local students’ English test scores.

Feng also finds that the results are larger for male than for female students. They then go on to look at how teachers respond to migrant students. They find that:

...in the classes with higher proportions of migrant students teachers are less likely to use the methods of group discussion and interaction with students, which are usually assumed to better improve students’ cognitive abilities... On the other hand... the presence of migrant students in the classroom has negative effects on the use of relatively advanced teaching media like multi-media projector, Internet, and pictures, models, or posters, which are important for teaching effectiveness.

So, it appears that when teachers have the ability to change the mode of instruction, they do so in ways that make local students worse off, when there are more migrant children in the classroom. This is probably exacerbated by teachers' attitudes, because Feng reports that teachers "prefer to teach classes with fewer migrant students". Unfortunately, Feng's study is silent on whether teachers modify the curriculum in response to the presence of more migrant students.

It is worth noting that the negative effects in these two studies are contrary to the findings of Figlio et al., which I referred to in my earlier post. They found no effect of immigrant exposure on native-born students. This literature is crying out for a meta-analysis at some point. We also need some further studies to unpack the mechanisms, since it is important to better understand whether changing curriculum or teaching modes, or both, to suit immigrant students has a net negative or positive effect overall.

Read more:

• Exposure to foreign-born students and the academic performance of U.S.-born students

Teaching the minimum wage and economic justice

The conventional approach to teaching the minimum wage is to focus on the market-level impacts of the policy. This might involve the traditional model of supply and demand, or less commonly, a monopsony model or a search model of the labour market. These approaches share in common the focus on the labour market itself. Through teaching using the market as a lens, we lose focus on the workers who are receiving the minimum wage.

I recently read this interesting 2013 article by Aaron Pacitti and Scott Trees (both Siena College), published in the journal Forum for Social Economics (sorry, I don't see an ungated version online). Pacitti and Trees outline an in-class exercise for teaching the minimum wage from the perspective of workers, and in particular considering the associated social and ethical issues. The exercise is very simple, and involves groups of students working together to prepare a budget for a single 22-year-old with no spouse or dependent children, who works full-time for the minimum wage. It is not an easy task, and there are lots of trade-offs involved, and the money does not stretch very far (especially when you consider housing costs!). After the groups have completed their task, the lecturer can work through a class discussion of the various spending categories and how much each group allocated to them, which I think would further identify just how little the minimum wage can really buy. Pacitti and Trees note that:

Once students are challenged to prepare a detailed budget by spending category, they quickly realize that minimum wages do not generate enough income to support a sustainable standard of living, defined as the income necessary to maintain proper health, nutrition, and living arrangements without receiving any form of government, family, or charitable assistance. Results from using this exercise suggest that class discussion quickly moves beyond the blame-the-victim arguments that are commonly heard from students. The exercise shifts the analysis away from the market nexus and individual choice models, and toward the social, institutional, political, and ethical dimensions of minimum wages, giving students a broader and more holistic perspective on economics.

Pacitti and Trees also suggest a number of extensions, including more realistic scenarios (for people with debt repayments, those looking for a new job, or those with a family to support). They also suggest some further discussion points, including economic justice (that is, whether the outcome is ethical or fair), normative economic policy and distributional issues, and economic alternatives to the minimum wage.

All of this seems so obvious, but the problem may be trying to squeeze an exercise like this into an already crowded curriculum. However, it is likely that there are large gains to be made, not least in having students appreciate that market participants are not simply chess pieces to be moved around (which is one of the fallacies that Thomas Sowell cites in his book Economic Facts and Fallacies, which I reviewed here). And it can easily be extended into an interesting assignment for assessing students. I'll have to seriously consider whether this is something that I can fit into one of my papers.

The productivity effects of coronavirus infection among professional footballers

It's easy to see that coronavirus infection has negative productivity effects. People who are infected are unable to work at first, and even after they return, their work performance is likely to be negatively affected for a while. However, working out how much productivity is negatively affected is difficult, because individual productivity is often difficult to measure, and infection with coronavirus may or may not be symptomatic. Measuring only the productivity effects on symptomatic cases would tend to over-estimate the actual effect of a coronavirus infection.

In a new working paper, Kai Fischer (Heinrich Heine University), James Reade (University of Reading), and Benedikt Schmal (Heinrich Heine University) look at the impacts on professional football (soccer) players in two top professional leagues in Europe (the Bundesliga in Germany, and Serie A in Italy). Their focus on footballers is important, because as they note:

...we are able to differentiate precisely between infected and non-infected individuals as the soccer leagues implemented rigid regimes of frequent and systematic testing for all players.

So, that gets around any problems of asymptomatic players resulting in over-estimated effect sizes. Productivity can also be precisely measured. Fischer et al. use the number of passes in a game. They justify this measure as: 

Productivity can rather be considered as a function of various health aspects; mainly physical measures, for example acceleration, condition, and endurance, but also the cognitive capability to position oneself optimally on the pitch. The number of passes is related to all of these measures, which is why we base our analysis on this parameter. We consider COVID-19 as a shock to the underlying health aspects, that consequently causes a deterioration in performance.

Fischer et al. use a difference-in-differences format, essentially comparing infected players before and after their coronavirus infection, with the performance for uninfected control players. They use a variety of public sources to identify infected players, and over the period they consider (up to the middle of July 2021):

There have been 81 true-positive tests among players in Germany and 176 in Italy until mid of July 2021. We can clearly identify 76 players in Germany and 157 in Italy...

257 infections among 1,406 players imply that 18% of all players got infected until mid of July 2021. 

That appears to be a similar infection rate than among the general population of the same age. Importantly, vaccination of players only started after the conclusion of the 2020/21 football season. Their dataset then includes 72,807 game observations on 1406 players over the 2019/20 and 2020/21 seasons (including 40,607 observations of players who played at least some game time). Looking at the effects on productivity, Fischer et al. find on the extensive margin that:

...players have a 5.7 percentage points lower probability to play. However, effects appear to be mechanical, mainly driven by the first weeks after an infection, when quarantine breaks do not allow a player to participate in a match. The observed drop in playing frequency becomes insignificant quickly, but does not fully return to its former level. These results indicate that players marginally experience persistent effects on their likelihood to play...

So, infected players are less likely to play, both immediately during their infection period, and somewhat afterwards (although the latter is not statistically significant). Similarly:

Immediately after the infection and his return on the pitch, a player spends on average 6 minutes less on the field than before – this corresponds to a decrease by almost ten percent... The effect is visible right after an infection but quite long-lasting. Only after approximately 150 days or five months minutes played return to a level which does not significantly differ from pre-infection match times.

So, infected players play less time, even when they are playing. In terms of in-game productivity (measured by the number of passes), Fischer et al. find:

...a highly significant static difference-in-differences effect of -5.1 percent. Hence, we can precisely identify a deterioration in work performance following a cured COVID-19 infection. This effect is not transient but actually remains notably negative in course of time.

So in addition to playing less, when they are playing, infected players are less productive. Note that these results control for the number of minutes played, so the reduction in the number of passes isn't a result of playing less time. Digging a bit further, they find that:

...especially players of an age above 30 face the strongest performance drops of above ten percent. In comparison, younger players up to 25 years are only affected marginally.

That result would seem to make sense, if older players' fitness is affected more severely, or older players take longer to recover from their infection. Also, in relation to fitness:

...performance declines over the course of a match. While the effect seems to be stable at around -3% in the first thirty minutes, post-infected players face a deterioration of some additional three percentage points in later phases. Such a downward trend would be in line with COVID-19 affecting player’s endurance.

Fischer et al. also demonstrate that the effect of coronavirus is larger than for other respiratory illnesses (such as colds or flu), as well as other minor injuries. They also show some suggestive evidence that there are negative spillover effects on other members of the team, from an infected player's poorer performance.

Overall, this suggests that there are significant and long-lasting negative productivity effects of coronavirus infection. That in turn suggests that the estimated negative economic impacts of the coronavirus pandemic may have been underestimated, if they fail to consider longer-term productivity impacts.

[HT: Marginal Revolution] 

How and when we develop our strategic reasoning

Some years ago, my son introduced me to the "Game of 21". The first player chooses a number (1 or 2), and then players take turns incrementing the count by 1 or 2. So, for example, if the first player chooses 1, then the second player could choose either 2 or 3, but if the first player chooses 2, then the second player could choose either 3 or 4. The winner is the player that chooses 21. My son beat me handily, but he knew the winning strategy, which is to always choose a multiple of 3, if one is available. To see why that's a winning strategy, we can work backwards from 21. If you choose 18, then your opponent must choose either 19 or 20, in which case you can choose 21. If you choose 15, then your opponent must choose either 16 or 17, in which case you can choose 18, and then 21 after their next choice. And so on (15, 12, 9, 6, and 3). It turns out that there is a clear second-mover advantage in the Game of 21, since the second player can always choose 3, regardless of what the first player chooses, and the first player can never choose a multiple of 3 if the second player does so.

The winning strategy seems obvious when it is explained to you, but it is far from obvious to most people before the game begins. How long does it take for people to figure it out, and would a shorter game (say, a "Game of 6") help? Those are the research questions that this 2010 article by Martin Dufwenberg (University of Arizona), Ramya Sundaram (George Washington University), David Butler (University of Western Australia), published in the Journal of Economic Behavior and Organization (ungated version here), tackle. Using a sample of 72 research participants, they had 42 of them pair up (in a round-robin format) for five rounds of the Game of 21 (G21) followed by five rounds of the Game of 6 (G6), and 30 of them did the reverse (five rounds of G6, then five rounds of G21). Essentially, they test whether playing the simpler G6, where recognising the multiple-of-3 winning strategy is much easier, helps players to recognise the winning strategy for G21. Indeed, that's what they find. Looking only at players who play second (the 'Green' player in their wording), since only those players have a dominant strategy, they look at the proportion of players playing a 'perfect' game.

First, Dufwenberg et al. note that:

...most subjects playing five rounds of G6 realize that G6 may be solvable by rational calculation...

...most subjects playing the Green position in G21 for the first time do not immediately figure out that choosing multiples-of-three is the best they can do... Across treatments, in G21, only 49 of 179 games (27%) are played perfectly... The rates of perfect play are especially low in the early rounds of the G21-then-G6 treatment (e.g. 2 out of 20, or 10%, in round 1).

Then, turning to their main research question, Dufwenberg et al. find that:

Green players play G21 perfectly in the G6-then-G21 treatment 37% of the time, compared to 21 percent in the G21-then-G6 treatment. This difference is significant at the 5% level (Z statistic = 2.20).

They also show that, among players who appear to have figured out the winning strategy in G21, players who played G6 before G21 choose the winning strategy earlier, on average, than those who played G21 before G6. That suggests that we can learn how to optimise in difficult strategic situations if we are first presented with similar but simpler situations.

An interesting side-point of the Dufwenberg et al. paper was the reference to level-k reasoning. Level-k reasoning refers to the number of steps of reasoning a decision-maker is capable of undertaking. As they note:

...level-0 players may choose randomly across all strategies. Level-1 players assume everyone else is level-0, and best respond; level-2 players assume everyone else is a level-1 player, and best respond; etc...

G6 and G21 don't really require much in the way of steps of reasoning, because once you realise what the winning strategy is, it doesn't matter much what the other player does (unless they don't know the winning strategy).

However, one game that does test level-k reasoning is the 'beauty contest'. Each player must choose a number between 0 and 100, and the winner is the player who chooses the number that is closest to two-thirds (or some other fraction) of the average of all guesses. I played this game many times with students when I was teaching a third-year Managerial Economics and Strategy paper. Level-0 reasoning would lead to a player choosing randomly. If all players did that, then the rational choice for a Level-1 reasoning player would be to choose 33 (two-thirds of the average of 50). However, if you believed that everyone else was a Level-1 reasoning player, making you a Level-2 reasoning player, then you should choose 22 (two-thirds of 33). And, if you believed that everyone else was a Level-2 reasoning player, making you a Level-3 reasoning player, they you should choose 14 (two-thirds of 22). And so on. The Nash equilibrium here is for everyone to choose 1 (or 0, depending on how the game is scored). However, the outcome is never that the winning score is 0. From memory, the winning score in my class was always around 10-20.

How many steps of reasoning do people engage in? That question has drawn a lot of research attention. One interesting aspect is how we early in life we develop level-k reasoning. That's the topic of this new article by Isabelle Brocas and Juan Carrillo (both University of Southern California), published in the Journal of Political Economy (ungated earlier version here). Brocas and Carillo created a very simple three-player game that could be easily solved by backward induction (for those who understand some game theory). As they describe it:

...subjects were matched in groups of three and assigned a role as player 1, player 2, or player 3, from now on referred to as role 1, role 2, and role 3. Each player in the group had three objects, and each object had three attributes: a shape (square, triangle, or circle), a color (red, blue, or yellow), and a letter (A, B, or C). Players had to simultaneously select one object. Role 1 would obtain points if the object he chose matched a given attribute of the object chosen by role 2. Similarly, role 2 would obtain points if the object he chose matched a given attribute of the object chosen by role 3. Finally, role 3 would obtain points if the object he chose matched a given attribute of an extra object.

The accompanying Figure 1 in the paper helps to understand the game (although the figure is in black-and-white, and the description refers to colours, which doesn't help as much as it could!):

Player 3 is asked to match the shape, so they should choose the dark square C. Player 2 is asked to match the colour that Player 3 will choose, so they should choose the dark triangle B. Notice that Player 2 needs to undertake two steps of reasoning, working out what Player 3 is doing in order to work out what they should do. Player 1 is asked to match the letter that Player 2 will choose, so they should choose the light circle B. Notice that Player 1 needs to undertake three steps of reasoning, because they must work out what Player 3 will do and then what player 2 will d, in order to work out what they should do.

Brocas and Carillo run their experiment with a number of samples of children and young adults, and each research participant played the game 18 times (six times in each of the three positions). They expect to find:

...four types of individuals: R (subjects who always play randomly), D0 (subjects who play at equilibrium only if they have a dominant strategy), D1 (subjects who play at equilibrium when they have a dominant strategy and can best respond to a D0 type), and D2 (subjects who can play as D0 and D1, as well as best respond to D1).

And in terms of behaviour:

The predicted behavior is simple. R plays the equilibrium strategy one-third of the time in all roles, D0 always plays the equilibrium strategy in role 3 and one-third of the time in roles 1 and 2, D1 always plays the equilibrium strategy in roles 2 and 3 and one-third of the time in role 1, and D2 always plays the equilibrium strategy.

Their first study involves students from third to eleventh grade from a private school in Los Angeles, along with undergraduate students from USC. Classifying the research participants into the four types outlined above, Brocas and Carillo find that:

Subjects either recognize only a dominant strategy or always play at equilibrium. Also, some very young players display an innate ability to play always at equilibrium while some young adults are unable to perform two steps of dominance.

In other words, there are no D1 players, as every player who can reason beyond one step can reason all the way through the steps. Then, looking only at the 234 grade school students in their sample, Brocas and Carillo find that:

Performance in roles 1 and 2 increases significantly up to a certain age (around 12 years old), and then stabilizes...

So, older students perform better, but only up to the age of 12 years. They then go on to replicate similar findings for a Los Angeles public school (where overall performance was lower) - there is no difference in performance from sixth to eighth grade (12-14 years old).

Finally, Brocas and Carillo study a sample of students from kindergarten to second grade. They simplify the game so that there are only two players (rather than three), and only two attributes (rather than three). With their sample of 117 children, they find that:

Equilibrium behavior is not significantly different between K and grade 1 in roles 2 and 3, and they are both lower than in grade 2 (p < .02, FDR adjusted).

The evolution of strategic behaviour as people age is interesting. That isn't quite what Brocas and Carillo are studying, since they don't follow the same children over time, but instead look across cohorts of different ages. However, it's hard to see how or why there would be a cohort effect here, so possibly they are observing an age effect. Interestingly, most of the improvement in strategic reasoning happens between the ages of 8 and 12 (second to sixth grade), and there is little improvement after that. That doesn't quite accord with the USC students performing better than the 11th-graders, so perhaps we need to know a little bit more about the evolution of strategic reasoning among older adolescents. However, in relation to younger children, Brocas and Carillo note that:

Existing research shows that by 7 years of age children may think ahead and form correct anticipations... Children have also been shown to develop inductive logic between the ages of 8 and 12...

Those are the sorts of skills that are used in developing level-k reasoning, so the mechanisms underlying the increase in strategic reasoning between ages 8 and 12 seem plausible. However, this clearly needs to be unpacked a bit more, and that would be a fruitful avenue for future research.

Overall, these two studies help us to understand a little bit more about how (and when) our reasoning in strategic games develops.

[HT: My colleague Steven Tucker for the Dufwenberg et al. study; Marginal Revolution for the Brocas and Carillo study]