- The problem: We’ll describe the environment and the phenomenon often referred to as “illegal immigration” or “undocumented entry” along the US Southwest Border (SWB). Spoiler alert: it’s difficult.
- The data: We will describe the public data as reported by the Office of the Border Patrol (OBP) currently, and how we augmented it with additional relevant information. All of our data comes from publically available sources.
- The model: Recent strides in computational power and algorithm design have enabled the analysis of high-dimensional, analytically intractable probability models by means of Monte Carlo sampling. We’ll show how we used such tools to analyze a Hierarchical Bayesian Generalized Linear Model (HB GLM) formulation to treat these immigration data by using Andrew Gelman’s Stan software.
- The results: The output of these models is a density estimate of expected apprehensions by Border Patrol sector and month. We’ll show some of the more interesting estimates plotted against observed apprehensions as well as variable importance over time.
Challenges of Apprehension on the Border and Past ResearchBefore describing the environment, it’s useful to provide the interested reader with some references that underpin some of our theory about the quantitative treatment of the illegal immigration phenomenon. There has been intermittent interest in statistical analysis of immigration patterns at the SWB . Our particular approach and thinking owe a great deal to Hanson and Spilimbergo’s article “Illegal Immigration, Border Enforcement, and Relative Wages: Evidence from Apprehensions at the US-Mexico Border.” Complexity #1: Varying geography The first factor contributing to the complexity of immigration apprehensions is the varying geography (topography, weather, demography… you get the picture) along the Southwest Border of the United States. To tailor its posture to these diverse tactical environments, the Office of the Border Patrol (OBP) breaks the border into nine sectors. As an example, consider the San Diego Sector (SDS), which is a densely populated urban environment bordered by the Pacific Ocean. By contrast, the Rio Grande Valley Sector (RGV) is thinly populated, and is bordered by the Gulf, rather than the Pacific. These and other factors affect the type of immigrant, their techniques, and the methods available to law enforcement. Complexity #2: Border crossing techniques It’s worth it to spend some time explaining the techniques employed by border crossers. The uninitiated reader may assume that most people who try to cross illegally do so by picking a spot on the border and running north. In fact, considerable planning underlies many attempts. Most of these individuals enter into a contractual relationship with a smuggler who handles the logistics of the crossing attempt. These smugglers, colloquially called “coyotes,” offer experience and knowledge of the geography and avoiding detection by Border Patrol Agents to their clients. The business nature of this relationship gives us hope that measurable forces affect the phenomenon in a predictable way. That is, coyotes will be more careful in their observation of conditions around the border, and will make choices accordingly. Those choices could, we hypothesize, lead to signal in the available data. Complexity #3: Variation in border crossers Adding to the problem’s complexity is the variation in the border crossers themselves. One such way in which they vary is their motivation for entry. For some, their main motivation for a crossing attempt is access to employment or higher wages. We’ll call these people economic migrants. A second category of crossers could, informally (as Refugee/Asylee status is a determination made through a legal process initiated most often by presenting oneself at a POE), be considered refugees, seeking a more secure existence from political unrest, criminal gangs and other hardships in their home country. Complexity #4: Population origins of border crossers Origin is yet another source of heterogeneity in the population of people attempting to cross the border between legal POEs. The convention in the law enforcement community is to separate these people into those originating in Mexico or countries Other-than-Mexico (OTM). OTMs are more likely to fall into the social migrant category than a person from Mexico. Further, the incentives (or disincentives) differ for each category depending on the current policy structure. We will examine the effect of the removal of the so-called “catch and release” policy later in the blog. Complexity #5: Exogenous factors or non-law enforcement policies The second to last complexity that we’ll discuss here are what we call exogenous factors. These are things that are outside of the control of law enforcement in general, and OBP specifically. These include weather, economic indicators, policy decisions, and many others. In the next post we’ll describe the most prominent example of an exogenous factor, the public policy disposition of the government toward different classes of immigrants. Complexity #6: Law enforcement policy, strategy and doctrine Finally, there are law enforcement policy, strategy, and doctrine factors, which drive the nature, frequency, and quality of border encounter data. As an example, one major historical policy, informally referred to as “catch-and-release”, changed the way OTMs that were apprehended crossing the border were processed. These individuals were furnished with a “notice to appear” in immigration court and were permitted to remain in the US until an immigration court could hear their case. Because so few immigrants adhered to the terms of the “notice to appear,” refused to present themselves to authorities, and instead opted to remain in the United States illegally, some commentators derisively referred to the documents as “notices to disappear.” Without judging the value or wisdom of such a policy, it is clear that it reduced the efficacy of border enforcement efforts. “Catch and release” was ended in 2006, replaced by a policy of detaining border crossers from countries OTM until their repatriation could be arranged. An article on this change quotes Homeland Security Secretary Michael Chertoff touting the deterrent effect of this new policy, noting that during the summer of 2006, the Department of Homeland Security (DHS) apprehended 20,000 fewer immigrants compared to the previous year. The same article, however, also points out that the decline may be due to a shift in immigrants’ tactics, which now favor more remote and dangerous routes. Building on this overview, our future posts will discuss the publically available data to inform our modelling efforts, the model we developed, and the results it achieved.
 Owen McCarthy and Connor Hartnett performed most of the data collection and curation tasks. Our fearless leader Rob Lantz provided inspiration, deadlines and ideas. David Elkind devised the model, wrote the simulation programs, and performed all related model assessment tasks. Technical errors are his alone.  For the purposes of this study we limit ourselves to modeling the apprehensions of attempting illegal immigrants between ports of entry, which falls under the jurisdiction of the Office of the Border Patrol.  Dr. Gelman’s decision to name his software after an Eminem song has puzzled the authors for some time.  Lara Jakes Jordan. “U.S. Ends ‘Catch-And-Release’ at Border.” The Associated Press. 23 August 2006. Online.