#### INTRODUCTION: Regardless of political loyalty, immigration is a key issue to Americans.

Until the COVID-19 pandemic, immigration was one of the most important political topics to both the general public and to politicians. A 2018 Gallup report found that immigration was the second most important issue to American voters.¹ Almost 12 million people have been displaced from their homes and more than half of these victims are children.²

This was not a novel occurrence; immigration has consistently been a key issue to Americans for the past twenty years.¹ Obviously, as a result of the economic catastrophe of COVID-19, immigration has become much less of a priority to Americans. Nevertheless, once the dust settles and life returns to something approximating normal, immigration will once again be a staple of international and domestic political discussion.

Before the present pandemic nightmare, crises like the Syrian civil war, which is now in its 10th year, have spurred waves of migration across the world.² This caused a tension to develop between humanitarian and domestic concerns.

Immigration policy is based on a myriad of factors. Every country must determine how to balance the interest of its citizens with the provision of aid to people who are battling tragic circumstances. This challenge represents a difficult balancing act. Irrespective of political ideology, sound immigration policy requires accurate predictions of migration levels, especially during times of crisis when surges are likely to occur; resources must be appropriately allocated to care for those in need. Knowledge of these factors is also an asset to the public, and humanitarian organizations that need to plan logistics to effectively administer aid.

Public opinion has been influenced more by sensational anecdotes than statistical facts. Both sides of the political spectrum are guilty of simplifying this analysis. A functioning democracy is predicated on an informed electorate. Accurate predictions of migration levels allow the state to make prudent policy decisions and empower citizens to better exercise their civic duties. The most frequently hypothesized reason for why immigrants migrate to a new country is the relatively greater economic opportunity of that new country. *This analysis will test how income affects immigration.*

#### DATA: Income (Dependent Variable) is measured by GDP per Capita.

The data set used in this analysis was generated from the __World Bank’s World Development Indicators__ database³.

Click the following link to download the data set: **World Bank Indicators Data Set.**

Income is measured by *GDP per Capita*, which is a better measure of income than raw GDP. For example, a country might have a high GDP but also might have a high level of income inequality where wealth is concentrated in a small proportion of the country’s inhabitants. Thus, it’s very possible for a country to have a high GDP but have little economic opportunity.

Immigration levels are measured by *Net Migration,* which is the number of individuals entering a country minus the number of individuals exiting the country. Negative values indicate that more people exit a country than enter it during the time period in question and vice versa. Each observation of *Net Migration* measures the level over a 5-year period.

2002 is always the base year in the regression output. The dataset has four time periods:

- 1997-2002
- 2002-2007
- 2007-20012
- 2012-2017

So, the 2002 *Net Migration *value represents the 1997-2002 period. All regressors (independent variables) are lagged so that, for each observation, the regressors’ values come from the first year of the *Net Migration *5-year time period. These observations are combined in a pooled cross-sectional dataset.

A limitation of the dataset is the lack of observations for control variables for countries that need to be included to accurately measure income’s effect on immigration. Often, the countries with negative values of *Net Migration,* such as Syria, do not make economic or humanitarian information readily available for obvious reasons.

As a result, selection bias potentially leads to the oversampling of stable countries. To combat this, 191 different variables were tested to ensure the most robust analysis possible. The included regressors, shown in Figure 1, were chosen based on statistical significance, relevance to *Net Migration* and data availability. While more regressors (likely) exist in the true population model, the threat of high variance outweighed the concern of variable omission.

To account for the differences in populations across the world, each country’s *Net Migration* level is divided by its population, which yields *Scaled Net Migration*. Next, the natural logarithm of the main regressor, *GDP per Capita*, is taken. The logarithmic transformation is done to allow for a percentage point interpretation of *GDP per Capita’s *ceteris paribus effect on *Scaled Net Migration* (as opposed to how one extra dollar of *GDP per Capita *correlates with the independent variable).

###### NOTE: Year and country dummy variables not shown in summary statistics.

Here are the definitions of each variable, which are derived or copied from the World Bank’s indicator definitions³:

= natural log of (sum of gross value added by resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products/mid-year population).ln(GDP per capita)

= % of the labor force that is without work but available for and seeking employment.Unemployment Rate

% of parliamentary seats in a single or lower chamber held by women.Women in Parliament =

= # of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with age-specific fertility rates of the specified year.Fertility Rate

% of total employment that accounts for workers that are self-employed.Self-Employed:

= % of total employment that accounts for people working in the services sector.Employment in Services

Military expenditures (% of GDP) derived from the NATO definition, includes all current and capital expenditures on the armed forces.Military Expenditure=

= supply of military weapons through sales, aid, gifts, and manufacturing licenses. Data cover major conventional weapons such as aircraft, armored vehicles, artillery, radar systems, missiles, and ships designed for military use. Excluded are transfers of other military equipment such as small arms and light weapons, trucks, small artillery, ammunition, support equipment, technology transfers, and other services. Figures are expressed in US$ m. at constant (1990) prices. A ‘0’ indicates that the value of deliveries is less than US$0.5m.Arms Imports

A quadratic transformation, named *Fer2*, is conducted on *Fertility Rate *to show its returns to *Scaled **Net Migration, *i.e., to show whether fertility has increasing or decreasing returns to the independent variable. If *Fertility Rate *has increasing returns to *Scaled **Net Migration *and is negatively correlated with it, then as *Fertility Rate *increases, *Scaled Net Migration *will decrease but the rate of the decrease will grow larger as the *Fertility Rate *increases.

Ideally, the log of *Scaled Net Migration *would be taken to allow for an elasticity (which allows for an intuitive interpretation – a percentage change in the independent variable leads to a percentage change in the dependent variable) but that’s not possible since the variable ** can **be negative and a negative value is outside the domain of a logarithmic function.

## Methodology

The analysis contains an initial simple linear regression (shown in Figure 2), an initial control multiple linear regression (shown in Figure 3), and a control multiple linear regression (shown in Figure 4) to account for potential omitted variable bias related to Geopolitical Instability.

The SLR shows the raw correlation between the dependent variable and the main regressor of interest without the inclusion of any control variables. MLR 1 adds six control variables to obtain a more accurate estimate of *GDP per Capita’s* effect on *Scaled Net Migration. *While the purpose of including *Unemployment Rate *is self-evident, the other variables warrant some brief explanation regarding their inclusion in the model. The *Women in Parliament *variable is intended to serve as a proxy for a country’s level of gender equality. *Fertility Rate *is related to a number of important factors, including the economic opportunity of women and education levels, which are other potential drivers of immigration. Due to the change in composition of developed countries from manufacturing-dominant economies to services-dominant economies, *Employment in Services* is included.

The most likely source of estimation bias (*besides the bias described in the data section*) is omitted variable bias due to, __first__, the scarcity of data for unstable countries, and __second,__ the difficulty in measuring a country’s geopolitical instability. The first source of bias is not mitigatable, but the latter one is. MLR 2 is intended to address this omitted variable bias.

The true population model likely includes a for geopolitical instability because of its profound effect on migration levels (wars and disasters create refugees). While there is not a variable that measures this, there are several that can serve as proxies.

*Arms Imports *was selected because volatile countries with large negative values of *Net Migration*, such as Syria, Myanmar and Afghanistan, import large numbers of arms (see data set for figures).

*Military Expenditure (% of GDP)* was also used as a proxy since totalitarian nations, such as Eritrea, N. Korea and Yemen, spend disproportionately more than freer countries (the U.S. is a notable exception) on defense. It is almost certain that the inclusion of the proxies does not eliminate all omitted variable bias, but due to data limitations and proxy feasibility, it’s the best mitigation possible.

The feasibility of *Arms Imports *and *Military Expenditure *was based on the ability to estimate country fixed effects and on the hypothetical regression of the two variables on the true population parameter of *Geopolitical Instability.* It is unlikely that the error terms of these two regressions are correlated with ln(*GDPperCapita)* because both variables are related to levels of military technology, geographic region and infrastructure, not income per se (take Switzerland for example).

Fixed time and country effects are controlled for with dummy variables, which also mitigate omitted variable bias that stems from an inability to measure an immigrant’s proximity to their country of origin. This is an important consideration because people often prefer to immigrate to countries closer to their native country due to a variety of factors.

Due to the variation across countries, heteroskedasticity was suspected. A Breusch-Pagan test yielded a P-Value <.0001, which provided strong evidence against the null hypothesis of homoskedasticity.

To mitigate this, robust standard errors are utilized. A VIF Test was conducted but didn’t signal any concerns related to multicollinearity; the Mean VIF was 8.42. No independent variable had a VIF over 10, except for *fer2* and *Fertility Rate*, which were caused by the quadratic transformation.

## Results

**The results for SLR and MLR 1 are both shown in Table 1. The results for MLR 2 are shown in Table 2. All columns include fixed time effects. **

*NOTE: The F-Test for Fer2 and Fertility Rate indicated joint statistical significance for columns (2) and (3): P-values were both less than .0001.*

**SLR**** (1)**

The SLR, shown in column (1) of Table 1, shows a large and statistically significant relationship between *Scaled Net Migration* and *GDP per Capita*. This bivariate result justifies further inquiry.

**MLR 1** **(2 & 3)**

MLR 1 is divided into three columns. Column (2) shows estimates calculated with standard errors. Column (3) shows estimates with robust errors. Column (4) shows estimates with robust standard errors and fixed country effects.

*ln*(*GDPperCapita) *remains significant at the .1% level, even when the presence of heteroskedasticity is dealt with in column (3) through robust standard errors and time fixed-effects.

Columns (2) & (3) show that a 1% increase in *GDPperCapita* leads to an approximate .015 percentage point increase in *S**caled* *Net Migration, *ceteris paribus. The scaling of the dependent variable allows us to use the percentage point interpretation since each country’s *Net Migration *value is divided by its population.

Another potentially more useful interpretation is that when *GDP per Capita *doubles for a country, on average, we would expect to see a 1.53 percentage point increase in *Scaled Net Migration*. So, when a country’s *GDP per Capita *doubles, we would expect to see a spike in immigration equal to roughly 1.53 percent of that country’s population.

The estimate of *GDP per Capita’*s effect on *Scaled Net Migration* is not lowered until fixed country effects are added. This reduces the significance of the coefficient to the 10% level and eliminates the significance of all other control regressors as well. This indicates that the fixed effects of nations (such as geography, climate, proximity to other nations, etc.) are critical for accurate immigration estimates. The coefficient in column (4) indicates that a 1 percent rise in *GDP per Capita *entails a .0082 percentage point rise in *Scaled Net Migration. *Put another way, when a country’s *GDP per Capita *increases by 100 percent, immigration levels rise by almost 1 percent of that country’s population.

**Based on the importance of fixed nation factors, the estimate in column (4) is likely the most accurate estimate of GDP per Capita’s effect on immigration levels. **

**MLR** **2** **(4)**

The results of MLR 2 are shown in Table 2.

In column (1), the two proxies for Geopolitical Instability are added to all control regressors featured in MLR 1. Robust standard errors are utilized and fixed time effects are employed. The coefficient estimate for *ln(GDPperCapita) *increases to 0.024 and stays significant at the 1% level while the coefficient estimate for *Military Expenditure* is significant at the 5% level and the coefficient estimate for *Arms Imports * isn’t significant (even at the 10% level). As a result, the coefficient estimate for *ln(GDPperCapita) *decreases and becomes statistically insignificant.

Even though both proxies weren’t shown to be significant in column (2), the larger estimate for *ln(GDPperCapita) *(relative to MLR 1’s column (3)) in column (2) was significant, which indicates that when Geopolitical Instability is unaccounted for, the *ln(GDPperCapita)* coefficient estimate will be biased. The direction of the bias is likely negative, as shown by the different signs of the proxies and their covariances with *ln(GDPperCapita).*

If only *Arms Imports* is used as a proxy variable, the bias is negative due to a positive 6.3e+07 covariance with *ln*(*GDPperCapita*) and negative coefficient estimates in columns (1) and (2). The same is likely true if only *Military Expenditure* is used, but this prediction is less certain due to its sign change from column (1) to column (2): a -.164102 covariance with *ln*(*GDPperCapita)* is paired with a positive coefficient estimate in column (1) but a negative estimate in column (2).

Some might look at the estimates for *ln(GDPperCapita)* and conclude that they’re not economically significant due to the small coefficient values. The U.S. had a *Net Migration* value of 4,961,716 between ’07 and ‘12. A 1% increase in *GDPperCapita *with a coefficient shift from .00821 to .0243 entails a *Net Migration *increase of ~41k to 120k. **The scaling of Net Migration means that relatively small changes in GDP per Capita can entail large changes in Net Migration.**

##### Findings Regarding Marginal Effects

**The***most notable finding of the analysis is the increasing marginal effect of GDPperCapita on*** Scaled Net Migration **(Fig. 5)

*.*

The increasing marginal returns to average income persist even when fixed country effects are taken into account. In other words, the more economic opportunity a country has (approximated by *GDP per Capita)*, the more attractive it will be to immigrants, regardless of their home country.

## Conclusion: THere's (A LOT) More to this story

This analysis provides limited evidence that a country’s economic opportunity is a contributing factor to immigration. This relationship remained significant (at the 10% level) even when fixed time and country effects were controlled for in MLR 1’s column (4).

Geopolitical Instability undoubtedly plays a role too, as shown by MLR 2. If Geopolitical Instability is not controlled for, the estimated effect of average income on immigration will be biased. However, if fixed effects of countries aren’t accounted for, the estimated effect of a country’s average income on immigration will be overstated.

Because the return to *GDP per Capita* on migration increases as *GDP per Capita* rises, high-income countries need to adopt policies that optimize the supply of immigrant capital for their domestic benefit. The ability to tap into the intellectual capital of immigrants is essential for countries to remain competitive in the global marketplace. Immigrants represent critical sources of talent, but they also require significant resources to be set up for success in their new homes.

Nevertheless, this analysis has shown that the totality of fixed attributes of countries, such as geography, location and culture, collectively, play a greater role in predicting migration than income alone.

### While far from trivial, income is only one piece of this complex puzzle.

Sources Referenced

- Newport, Frank. (2018). “Immigration Jumps as Top Problem, Still Trails Government.” Gallup, Inc. https://news.gallup.com/poll/227021/immigration-jumps-top-problem-trails-government.aspx
- World Vision. (2020). “Syrian refugee crisis: Facts, FAQs, and how to help.” https://www.worldvision.org/refugees-news-stories/syrian-refugee-crisis-facts#:~:text=Now%20in%20its%2010th%20year,in%20Syria%20need%20humanitarian%20assistance.
- World Development Indicators. (Accessed 2019). “World Bank Indicators Data Set.” The World Bank. https://databank.worldbank.org/reports.aspx?source=world-development-indicatorsdicators.