Simulation

in migration frictions causes sufficiently large migration flows. This is the case when the countries whose labor markets integrate are different enough in initial fundamental characteristics. If these negative welfare effects occur in countries in which many of country i’s workers live and are strong enough to dominate the positive welfare effects of the decrease in κ_ni, this leads to a fall in mean utility of those workers.

Two qualifications are in order. First, it is important to stress that this argument about the possibly negative welfare effects of a migration shock is only valid in an equilibrium with (costly) trade. Starting from complete autarky with fixed populations and no trade any decrease in either trade costs or migration frictions will have unambiguously positive welfare effects. The negative effects only occur relative to the level of welfare in an equilibrium with trade.

Second, while the negative welfare effects may occur for countries that receive a suf-ficiently large inflow of migrants, the sending countries naturally experience a welfare increase. Abstracting from congestion and productivity spillovers, labor mobility there-fore redistributes the welfare gains from goods trade from high real income countries to those with low real income. In particular, countries with high real income tend to be at-tractive migration destinations. Citizens ofsending countries gain for two reasons. Those who emigrate enjoy a higher real income in their destination than what they would have earned at home. Those who stay benefit from cheaper access to foreign high-technology goods because the cost of production there is lowered by the increase in labor supply.

This improves their terms of trade.

The aggregate welfare effect of a migration shock can be measured using the population-weighted change in mean utility around the world,

ˆ¯

U =X

i

N_i N

ˆ¯

Ui, (II.24)

where N = P

iN_i is the total number of workers around the world.¹⁵ In Sections II.3 and II.4 I show that ˆU¯ is positive in response to a migration shock, while some countries’

workers may experience an increase or a decrease in their mean utility.

I can disentangle the different channels outlined above and show that even in the absence of technology spillovers and congestion effects, the terms of trade channel can produce the negative welfare effect.

II.3.1 Setup

I construct a grid of 100 points representing countries. For each country I draw values for the number of citizens N_i, technology µ_i and amenities B_i from a log-normal distri-bution. All countries are assigned the same value for the endowment of residential land H_i. Distances between the countries are measured as the Euclidean distance between the points on the grid and determine trade and migration costs in the model. For simplic-ity, I abstract from tariffs here. I also need to calibrate the four structural parameters, the trade elasticity θ, the migration elasticity , the share of goods consumption in the households’ budget α as well as the strength of the technology spillover controled by β.

Following Head and Mayer (2014) and Simonovska and Waugh (2014), I set θ = 4, and = 3 following Bryan and Morten (2017). The goods consumption α= 0.75 is taken from Davis and Ortalo-Magn´e (2011) and I set β = 1 to be consistent with Eaton and Kortum (2001).

Figure II.1: Country Grid and the Migration Barrier

Note: Grid of simulated countries in latitude-longitude space and the migration barrier.

The policy change I consider in this simulation is the removal of a migration barrier between the two halves of the grid, called “West” and “East”. Figure II.1 depicts the migration barrier as a black line. In the initial situation all points on the grid trade with each other, but migration is only possible on either side of the grid. The removal of the barrier then allows workers to migrate to the other region. The welfare effects of

this change are used to demonstrate the mechanisms and channels active in the proposed model.

II.3.2 Results

To show that the terms of trade effect inducing utility losses for citizens of some countries does not occur mechanically, I consider the opening of the migration barrier under two scenarios. In the first, countries on either side of the grid draw all their fundamental values from distributions with identical means, implying that countries on both sides of the divide are on average equally attractive, equally productive, and have the same number of citizens on average. In the second scenario, I let countries west of the divide draw their productivity levels µ_i from a distribution with a larger mean, making them more productive on average than the eastern countries. Table II.1 shows the mean values of fundamentals on both sides of the migration barrier for each scenario.

Table II.1: Fundamental Values in the Simulation avg. prod. avg. amen. avg. nat. pop.

West East West East West East equal distr. 1.64 1.71 1.63 1.71 1532 1498 high µ 7.37 0.38 1.63 1.71 1532 1498

Note: Means of random draws of location fundamentals for 100 simulated countries.

Essentially, this is an application of the idea from Davis and Weinstein (2002) in a quantitative multi-country setting. Figure II.2 plots each country’s value of µ_i relative to the most productive country on a log-scale on the horizontal axis and the change in average utility of the country’s citizens ˆU¯_i on the vertical axis. It is important to note that each point represents the change in average utility for the citizens of a country, wherever they may live. This means that the value also accounts for the utility increases of workers who left their home country, for example.

The top left panel of Figure II.2 shows the results when the two regions draw their fundamentals from identical distributions. Accordingly, both triangles (East) and circles (West) are homogeneously spread over the horizontal axis. The vast majority of points lie slightly above the zero-change line indicating that there are utility gains from reduced migration frictions for the citizens of most countries. In the top right panel the exercise is repeated but with countries in West drawing the productivities from a distribution with a higher mean. Accordingly, the circles are clustered at the higher end of the relative pro-ductivity line. A clear pattern emerges in which the citizens of most countries in West lose slightly from labor market integration, some outliers in both directions notwithstanding.

Figure II.2: Removal of the Migration Barrier - Welfare Effects

0.01 0.1 0.5 1

productivity, rel to max -5

0 5 10 15 20 25

change in average utility, percent

Similar Regions: All Channels

West East

0.01 0.1 0.5 1

productivity, rel to max -5

0 5 10 15 20 25

change in average utility, percent

High Productivity West: All Channels

West East

0.01 0.1 0.5 1

productivity, rel to max -5

0 5 10 15 20 25

change in average utility, percent

High Productivity West: No Congestion

West East

0.01 0.1 0.5 1

productivity, rel to max -5

0 5 10 15 20 25

change in average utility, percent

High Productivity West: No Congestion, No Spillovers

West East

Note: Results of a simulation of the removal of the migration barrier with 100 countries.

The utility gains for the citizens from East are disproportionately larger. This underscores that the aggregate change in welfare is positive. In fact, weighting the changes in average utility with the citizen shares accounted for by each country, the migration liberalization scenario increases global utility by 3.43% when the geometric mean is considered. The global change in real income is calculated as the geometric mean of the changes in real income in each country, with the new equilibrium labor forces as weights. Global average real income increases by 0.09%.¹⁶

The bottom left panel keeps productivity high in West but removes the congestion effect by setting α = 1. This exercise shows that in the presence of technology spillovers alone, the redistributive mechanism is not strong enough to generate systematic welfare losses in the more productive region. Finally, the bottom right panel additionally removes the technology spillover, leaving only the terms of trade effect through changes in the nominal wage as the only channel through which trade and migration interact. The familiar pattern reemerges, with small but systematic losses in West and larger gains in East.

In the next section, I confront these theoretical results with the data.

16The numbers only change mildly, when the arithmetic mean is considered. Global average utility then increases by 3.68% and global average real income increases by 0.13%.