Deportation Discretion: Tiered Influence, Minority Threat, and “Secure Communities” Deportations

As deportations from the United States rose to unprecedented levels, a nationwide immigration enforcement program Secure Communities helped identify deportable noncitizens under arrest in county jails. Examining county-level variation in deportation activity between 2008 and 2013, this paper contributes to immigration policy research by examining how county officials in some locations facilitated exceptionally restrictive deportation outcomes while others exercised the discretion to turn noncitizens over for deportation sparingly. Consistent with a hypothesized “tiered influence” relationship, but contrary to a “racial threat” hypothesis, Hispanic concentration predicts the highest levels of exercised discretion where Hispanic concentration is neither too small nor too large. Noncitizens under arrest seem to have benefited from above-average Hispanic concentrations, except in counties where Hispanics exceed about 40 percent of the population


Introduction
What do we know about how Hispanic and immigrant populations in a political system can affect policy?Studies have argued that demographics act as a source of racial threat, thus catalyzing restrictive policies, or as a source of political power, creating a buffer against such policies.The literature has come to competing conclusions regarding whether minority shares provoke (Avery, Fine, & Márquez, 2017) or prevent restrictionism (Newman, Johnston, Strickland, & Citrin, 2012); whether minority growth dampens (Creek & Yoder, 2012) or bolsters restrictionism (Hopkins, 2010;Monogan, 2013); or whether demographics matter at all (Gulasekaram & Ramakrishnan, 2015).In order to reconcile these inconsistent findings, this paper asks: do policy actors in counties with a small concentration of minorities address immigration policy similarly to those in counties with above-average concentrations?Competing perspectives predict less restrictionism either where (i) minority group size is most concentrated or (ii) the minority group is visible but not too large.The results are consistent with the latter scenario (referred to below as a "tiered influence" account) but not the former, which contradicts the racial threat hypothesis.
This paper advances empirical and theoretical research on the demographic determinants of policy environments in three important ways.First, it helps resolve conflicting results in research employing linear measures of threat, which assumes the relationship between policy and demographic factors is constant.However, the magnitude and direction of the relationship may vary across different levels of minority concentration when examining the local administration of a deportation program (Secure Communities).The program afforded sheriff departments the authority to exercise discretion when deciding whether to turn noncitizen arrestees over to federal authorities.The level of exercised discretion (i.e., proportion of noncitizens who were not deported among all noncitizen arrestees) responds to demographics in a nonlinear manner.
Second, the analyses address competing accounts of how policymaking can differ depending on minority proportions.One account extends two-tiered pluralism, which posits the context of minority composition predicts where we observe restrictionist outcomes because minority groups' influence over policy is not expected to apply uniformly (Hero, 1993).In this account (hereafter, tiered influence), the highest level of discretion is expected in counties where Hispanic concentration is neither too small nor too large.In contrast, a second explanation stems from research on minority threat (Stults & Swagar, 2018), which predicts the highest levels of discretion in counties with the largest concentrations of Hispanics (Jackson & Carroll, 1981;Jacobs & Tope, 2008).
Third, the analyses match deportation outcomes to local decisions (see also, Rocha, in press) made by sheriff departments, thus improving on previous research on the link between state-level policy outcomes and demographics.The analyses examine the implementation of Secure Communities, an administrative, data-sharing program implemented by the federal government and designed to collect the biometric data of all arrestees booked into county jails.The program relied on local cooperation from county jail administrators in order to facilitate the deportation of hundreds of thousands of noncitizens.Local decisions to cooperate with federal authorities reveal whether and how much county officials helped the federal government carry out immigration policy.The discussion then explores possible reasons why some sheriffs routinely helped deport noncitizens while others did so cautiously.In this paper, local elected officials were directly in charge of deciding whether noncitizens in custody were transferred to federal agents, and they possessed the authority to exercise varying levels of discretion.The analyses focus on authority exercised by sheriffs in their jails rather than analyzing rates of deportation because the latter involve decisions made by multiple law enforcement entities from initial arrest through eventual deportation.
This paper finds weak evidence of a racial threat account of variation in the discretion to deport under Secure Communities.Rather than trigger resentment, the concentration of Hispanics was related to higher levels of exercised discretion.Among counties with a sizable Hispanic presence, the fraction of noncitizens entering deportation proceedings was smaller than the national average.Any protective relationship between Hispanic concentration and discretion appears to have been limited to counties where Hispanic concentration was between 20 and 40 percent of the population.Further, the relationship between population composition and deportation discretion applied most reliably to groups with possible influence over policy-such as Hispanic adults, workers, and U.S. citizens-compared to groups with limited influence (e.g., Hispanic youth), populations not associated with risk of deportation (e.g., non-Hispanic, black residents), and the broader immigrant population which includes foreign-born groups at much lower risk of deportation.Given these results, I conclude the evidence is most consistent with the predictions of tiered influence.Hispanic group size appears to benefit noncitizens but under certain conditions: I find sheriff discretion to deport is least restrictive where Hispanics were a sizable minority.More restrictive activity was observed, on average, when Hispanic residents approached or exceeded the majority of a county.

Literature on How Minority Populations Trigger Threat
Responses (And Its Limits) A focus on immigration policy provides opportunities to study why some places choose to enact policies to either create a restrictive political climate or integrate immigrants.Since the 2000s, legislators have increasingly attempted to address immigration issues while federal immigration reform stalled.To understand why different localities craft different responses, researchers often turn to the concept of minority threat to explain existing policy variation.Yet the collective evidence does not speak with one voice regarding whether rising immigrant populations trigger restrictionism.This paper reviews the recent literature on variation in immigration policymaking and then offers theoretical accounts that predict curvilinear relationships between minority population size and policy outcomes.The paper analyzes whether restrictionism is more common where (i) minority concentrations are highest or (ii) minorities are visible but their relative size is not too large.
Over the past decade, researchers have studied variation in immigration policymaking by employing linear measures of population size or composition.In order to test whether minority threat explains restrictive policies, researchers most commonly account for the minority percent of a population and/or the percentage point change in the minority share.Studies also vary in the types of policy outcomes they examine from the proposal of laws to their passage.This variation in both dependent and key independent variables, as discussed in detail below, make it difficult to reconcile findings across the literature on immigration policymaking.However, I propose that some of the confusion and conflicting results may also result from something all of these studies have in common: using a linear functional form for their measures of population size and growth.
State and local studies that employ linear measures find that while the concentration of immigrants has a protective effect, percentage point changes or growth can provoke restrictionist policies (Boushey & Luedtke, 2011;Hopkins, 2010;Monogan, 2013;Newman et al., 2012;O'Neil, 2011;Walker & Leitner, 2011).Ebert, Estrada, and Lore's (2014) findings add further complexity by showing that a state's immigrant share predicts the proposal of restrictive laws, while the growth of a state's immigrant population is related to the passage of such laws.However, parallel studies only partially echo these findings.Focusing on Hispanic rather than foreign-born populations, some studies confirm the above results (Marquez & Schraufnagel, 2013;Steil & Vasi, 2014;Ybarra, Sanchez, & Sanchez, 2015), but other studies either come to different conclusions (Avery et al., 2017;Creek & Yoder, 2012) or find a weak relationship between demographics and immigration policymaking (Gulasekaram & Ramakrishnan, 2015;Ramakrishnan & Wong, 2010;Wallace, 2014;Wong, 2012).To complicate matters further, few studies measure both the proportion as well as the growth of minority populations (but see Chavez and Provine [2009] and Wong [2012]).
The conflicting results might be due to a number of reasons.Differences in coding of the dependent variables are common in this area of research (Gelatt, Bernstein, & Koball, 2015) and can yield incongruent results (Goodman, 2018;Monogan, in press).In addition, outcomes rely on counts of laws without regard to variation in the scope of laws, and few analyze policy proposals versus enactment (Ebert et al., 2014;Filindra & Pearson-Merkowitz, 2013).Results may also vary because researchers rarely report multiple specifications when testing demographic hypotheses (Filindra, 2018).However, the functional form of explanatory variables has received limited attention (but see Ward, 2017).Thus, this study contributes to the literature by analyzing whether policy outcomes are related to demographic factors but not in a constant, linear manner.
Both the classic theory of racial threat (Blalock, 1967) and the more recent account of two-tiered pluralism (Hero, 2000;Tolbert & Hero, 1996) predict a curvilinear relationship between population composition and policymaking.Although both theories predict a nonlinear relationship, they offer competing hypotheses about the direction and meaning of the relationship.These competing hypotheses allow me to examine not only the more general proposition of whether minority group size is related to a threat response, but also to explore the possibility that minority group size can function as a proxy for influence over policy.
In the racial threat account, legislators view small minority groups as constituents without clout.Once minorities comprise a formidable enough presence, their influence over legislative priorities translates into less restrictionist or welcoming policies.Racial threat research stems from the work of Blalock (1967), who predicted that restrictive measures should rise as the proportion minorities rise (see also Key, 1949) because legislators respond to pressure from a white majority by passing restrictionist policies affecting minority populations.However, Blalock also anticipated that, as an out-group's relative size passed a threshold, policymakers should feel pressure to represent an ascendant minority group (cf.Keech, 1986).In this phase, the white share of the population could decline due to an absolute rise in a minority population or an overall decline in the white population.Either way, initial restrictionism would give way to less exclusionary measures (Blalock, 1967, pp. 147-150).Researchers have found support for threshold effects (see a related discussion in Canon, 2005, pp. 287-288).Although evidence in support of racial threat is not unanimous (Ousey & Lee, 2008), early research found capital policing expenditures rise alongside increasingly visible black populations, and the relationship reverses course in majority black locations (Jackson, 1986;Jackson & Carroll, 1981).A curvilinear threat response also predicts excessive force by police (Smith & Holmes, 2014) and support for conservative candidates (Charitopoulou & García-Manglano, 2018;Jacobs & Tope, 2008).Threat research examines not only legislative outcomes but also the implementation of punishment policy.U.S. and cross-national research finds a curvilinear threat curve predicts imprisonment rates (Jacobs & Kleban, 2003;Jacobs, Malone, & Iles, 2012;Keen & Jacobs, 2009). 1  The threshold effects described above predict resentment due to racial threat.Such a response should taper off in communities where Hispanics are numerous enough to amass influence over local enforcement priorities.The resulting U-shaped curve anticipates the highest level of exercised discretion (i.e., less restrictive) where a sufficiently large concentration of Hispanics pressure sheriffs to deport sparingly.By contrast, two-tiered pluralism (Hero, 1993) emphasizes how Hispanic populations can exert clout over political decision making, albeit unevenly compared to other groups such as white residents.According to this account, Hispanic influence over policies varies according to their population size (Hero, 2000).In fact, consistent with two-tiered pluralism, counties with substantial Hispanic populations support galvanizing restrictionist immigration policy (Hero, 2000;Tolbert & Hero, 1996, 2001).Prior research attributes support for restrictionism in minority-dense communities to white residential approval of restrictionism, especially in majority-minority contexts (Tolbert & Grummel, 2003).It is also possible places with large Hispanic populations are also home to Hispanics who either support or remain ambivalent about restrictionist immigration policies.In empirical studies of individual-level behavior, the relationship between advocacy for less restrictionist immigration policies has been found to vary within the Hispanic population.Indeed, Hispanics do not uniformly advocate against restrictive policies (Newton, 2000;Pantoja & Segura, 2003;Pantoja, Ramirez, & Segura, 2001;Stringer, 2016).Furthermore, locations with more Hispanic elected officials do not necessarily shield vulnerable Hispanic communities from negative policy outcomes (Liang, 2018).Related research also finds Hispanics may not necessarily view immigration issues as a priority in places where Hispanic proportions are high (Valenzuela & Stein, 2014).Based on this body of research, it appears that efforts to translate group size into advocacy for minority interests may dissipate where Hispanics are most concentrated, thus blunting efforts to advocate for the interests of marginalized Hispanic groups, such as noncitizens under arrest.In other words, minority group size should be related to lower levels of restrictionism if the minority group is sizable enough to exert influence on policymakers, but such influence may wane where competing interests within a large Hispanic population can splinter efforts to advocate for the interests of noncitizens.When predicting deportation outcomes, counties where Hispanic residents are most concentrated should not pressure sheriffs to exercise high levels of discretion because advocating against deportations is either generally unpopular or not a high priority among Hispanic residents.In sum, unlike the racial threat hypothesis, the tiered influence relationship should be nonlinear and follow an inverted, U-shaped curve.

The Secure Communities Program and Its
Relevance for Minority Threat Theory Deportations became more commonplace following changes to immigration law in 1996 (Hagan, Rodríguez, & Castro, 2011), hastening a need to account for both the rise of-and spatial variation in-deportations (Coutin, 2015;Obinna, 2015).A central element of the Department of Homeland Security's (DHS) deportation system rests on discretion when deciding whether to deport noncitizens (Macías-Rojas, 2016;Moinester, 2018).Most enforcement programs focus on high-priority cases, such as recent border crossers or immigrants in prison (Armenta, 2015(Armenta, , 2017;;Capps, Rosenblum, Rodriguez, & Chishti, 2011;Rosenblum & Kandel, 2012).Relying on technological advances in immigration enforcement (Inda, 2008), Secure Communities differed from previous programs by relying on biometric data collected during the booking stage of every arrest recorded in county jails.The program identified noncitizen arrestees, including those in custody for minor offenses.Initially implemented in select counties in 2008, most counties participated by 2011, and it became active in every county by January 2013.By 2015, Secure Communities was replaced by the Priority Enforcement Program to address concerns that the program facilitated deportations for minor offenses.Most recently, Secure Communities was reintroduced with the goal of eliminating discretion exercised by local law enforcement.
Local discretion was built into county jail administrators' implementation of the Secure Communities program.Elected sheriffs run these jails and had ample latitude when deciding whether to turn noncitizens over to federal agents for deportation proceedings.DHS requested that county officials hold arrestees for 48 hours.Had Secure Communities helped deport all arrestees, the program would have amassed two million deportations.In practice, the program deported a fraction of noncitizens under arrest (Rosenblum & Meissner, 2014) because DHS repeatedly issued guidances to county officials to exercise discretion and prioritize serious offenses (Pedroza, 2013;Stumpf, 2015).As a result, 18 percent of noncitizens identified by Secure Communities for lower-level offenses were deported as of May 2013.
Research on Secure Communities has documented an uneven enforcement landscape.Cox and Miles (2013) demonstrate the program mirrored federal rather than local priorities and rolled out according to where Hispanics resided rather than where crime was high.Jung (2015) categorized counties according to how restrictively they administered the program.Chand and Schreckhise (2014) found Republican-leaning counties reported more deportations, while Jaeger (2016) contends partisanship predicts deportations where counties have sufficiently large policing budgets.Pedroza (2013) found variation in how much states targeted noncitizens arrested for serious offenses versus other offenses.Secure Communities arrests and deportations also vary according to local law enforcement characteristics, including officer's ethnicity (Dinsmore, 2015;Pedraza & Calderon, 2017).In sum, deportation data reveal where localities ramped up deportations while others shielded portions of noncitizens from deportation.

Hypotheses
Secure Communities provides an opportunity to analyze whether demographic contexts account for variation in the level of exercised discretion to deport noncitizens.A series of models accounts for the relative size and growth of minority populations (Hispanics vs. immigrants), following research which recommends using multiple specifications in threat research (Filindra, 2018).This paper also tests whether minority shares are nonlinearly related to deportation outcomes.Two scenarios are possible.First, consistent with a resentment account of minority threat, sheriffs should exercise less discretion as the relative size of Hispanics rises because Hispanics trigger a threat response as they become visible, but only up to a point.Beyond a threshold, sheriffs should exercise high levels of discretion because only the most concentrated Hispanic communities motivate county officials to transfer relatively few noncitizens to immigration agents.According to a racial threat perspective, we would expect a U-shaped curve (Figure 1).Conversely, as an extension of two-tiered pluralism, sheriff departments should exercise more discretion to deport as the concentration of Hispanics increases because sheriffs in these places

Racial Threat
Level of Discretion to Deport Percent Hispanic heed expectations to protect noncitizens from expedited deportation proceedings.However, the protective relationship should then taper off in counties with the largest Hispanic concentrations, including majority-Hispanic counties, as opposition to deportations among Hispanics splinters or becomes a low priority.This tiered influence relationship should resemble an inverted, U-shaped curve (Figure 1).

Data
The primary source of data comes from Secure Communities indicators available through the Immigration and Customs Enforcement (ICE) Freedom of Information Act (FOIA) online library (DHS, 2013).The analyses supplement ICE data with county-level variables collected by federal agencies and secondary sources cited below.

Dependent Variable
In order to analyze the above hypotheses, I measure how strictly county officials administered the Secure Communities program; namely, to what extent they exercised discretion after arrests.DHS issued requests to county officials to hold noncitizens after their scheduled release, and county law enforcement either ignored or honored requests.The level of exercised discretion captures how often county jail administrators decided not to turn noncitizen arrestees over to federal authorities for deportation: where the denominator equals the total number of noncitizens in custody identified as a match (m) and the numerator is the proportion of noncitizen arrestees not deported (total matches minus total deportations, m -d). 2 The denominator (biometric matches) approximates the number of noncitizen arrestees eligible for deportation in each county. 3As a result, low scores (minimum of 0) indicate jurisdictions where administrators used less discretion in handling noncitizen arrestees while high scores indicate the use of more discretion (maximum of 1).For example, administrators of Secure Communities using low levels of discretion turned over as many noncitizens as possible to federal authorities for deportation.If county officials instead decided to comply with DHS requests only for select cases, then only a small number of arrestees would end up in deportation proceedings (signaled by a high exercised discretion score).The level of exercised discretion varies widely across the nation.The weighted level of exercised discretion has a mean value of 82, which means 18 out of 100 noncitizens identified were deported.
To examine whether exercised discretion is responsive to demographic factors, this study analyzes counties with at least one biometric match for noncitizens under arrest (N = 2,669). 4The analyses focus on low-priority offenses because local law enforcement actors have ample latitude when deciding whether to exercise social control over low-level offenses and misdemeanors (Olzak & Shanahan, 2014;Stumpf, 2015).The analyses exclude matches and deportations following arrest for top-priority offenses (e.g., murder and rape), which are often governed by mandatory detention policies that constrain discretionary authority.Finally, this study analyzes Secure Communities activity through May 2013, before a wave of localities limited their cooperation with the program (Immigrant Legal Resource Center, 2016). 5

Primary Independent Variables
Hispanic Concentration.In this paper, the racial/ethnic group representing a threat in local communities is a county's Hispanic population because the visibility of Hispanics is expected to predict how restrictively sheriff departments administered the Secure Communities program.Notably, more than 9 out of 10 Secure Communities deportees are from Latin American countries (Kohli, Markowitz, & Chavez, 2011).By contrast, using a measure of the county's immigrant population would exclude the broader Hispanic community associated with immigration-related demographic change.Moreover, the foreign-born share of a county's population also includes immigrant groups at much lower risk of experiencing deportation and which are also not perceived to be in danger of deportation.I use American Community Survey data to measure a county's Hispanic proportion (Census Bureau, 2013).Since the analyses predict discretion as a function of Hispanic composition between 2008 and 2012, it is important to note that the program did not lead to Mexican immigrant out-migration (Gutierrez, 2013).
Minority Population Growth.Following the literature on the rapid growth of a minority population as a trigger of restrictionist outcomes, I measure the percentage point change in the foreign-born population as well as the Hispanic population.In past research, the baseline for measuring percentage point changes is either 1990 (Chavez & Provine, 2009;Commins & Wills, 2017;Newman et al., 2012;Newton, 2000), or 10 years prior to the passage of immigration laws (Ebert et al., 2014); and one study models county-year demographic changes (Creek & Yoder, 2012).Growth rates predicting the level of exercised discretion are calculated using two baselines: 1990 and 2000 (Census Bureau, 2013).

Control Variables
Partisanship.This paper measures Republican vote share based on 2008 and 2012 presidential election results (Leip, 2012).Previous research finds immigration policymaking is highly partisan (see especially Chavez & Provine, 2009;Gulasekaram & Ramakrishnan, 2015;Monogan, 2013;Ramakrishnan & Wong, 2010;Zingher, 2014).Studies also find a relationship between Republican support and deportations (Chand & Schreckhise, 2014;Jaeger, 2016;Jung 2015).Ybarra et al., 2015).Finally, since state and regional contexts shape county officials' relationships with immigration authorities, the analyses include state fixed effects (reference: Washington, DC) and cluster robust standard errors across 24 enforcement regions designated by DHS.State fixed effects account for states where sheriffs are appointed: Connecticut, District of Columbia, Hawaii, and Rhode Island.

Analytic Approach
The level of exercised discretion varied widely across the country.After testing whether linear measures of threat employed in recent research on immigration policies predict the level of exercised discretion, the analyses examine whether the outcome follows a nonlinear function: My main explanatory factors (percent Hispanic and its exponent) are followed by Z, a set of correlates of restrictive immigration policies and related measures: minority population growth; Republican vote shares; timing of Secure Communities activation; presence of local restrictionist measures; a criminal justice capacity index; and unemployment. 7Y = 0 + 1 Percent Hispanic + 2 Percent Hispanic 2 + Z + Counties are the relevant unit of analysis because sheriff departments are elected to run jails and can decide whether to turn arrestees over to immigration authorities.Central city police departments regularly transfer noncitizen inmates to sheriff-administered jails (Koralek, Pedroza, & Capps, 2010).Of course, analyzing county data challenges the assumption of independent observations in linear regressions.In response, standard errors are clustered across 24 regional jurisdictions designated by DHS, and state fixed effects account for policy variation between states.On balance, the analyses account for interdependence among counties while leveraging program data to contribute to policy research.

Results
Table 1 presents results from a series of models employing two common measures of threat (minority shares and growth rates) for two groups (Hispanics and immigrants).The alternate specifications are included to determine whether the relationship between, for example, Hispanic growth rates or the foreign-born share of a county is a reliable predictor of the level of exercised discretion across models.None of the existing (linear) measures employed in the literature on immigration policymaking are statistically significant, and the direction of the foreign-born population coefficients is inconsistent across models.In sum, linear measures of threat offer little information when predicting exercised levels of discretion to deport.
Table 2 presents estimates of the association between Hispanic concentration and discretion and shows that Hispanic shares are nonlinearly related to the level of exercised discretion.The relative size of the Hispanic population predicts discretion differently along escalating levels of Hispanic concentration. 8A county where Hispanics comprise a small (5 percent) share of the population is expected to have deported more than one-fifth of noncitizens in custody (exercised discretion score between 0.77 and 0.79 in models 2 and 3).A county where one-quarter of residents identify as Hispanic is predicted to have deported only one out of six noncitizens under arrest (or an exercised discretion score of 0.84).Predicted discretion is higher (i.e., less restrictive) in counties where Hispanics comprise 35-40 percent of a county (discretion score between 0.85 and 0.86); which means county jails generally transferred one-sixth or one-seventh of noncitizen arrestees to immigration agents.The level of discretion then reverses course and was more restrictive where Hispanics approach more than half of the population (Figure 2).This relationship implies a protective relationship at above-average levels of Hispanic shares, a relationship which then weakens at the highest levels of Hispanic concentrations.Specifically, where Hispanics reach 20 percent of the population, discretion is predicted to exceed 0.83 but then tapered off and below 0.85 where Hispanic residents exceeded 40 percent of a county.The inverted, U-shaped curve runs counter to the hypothesized results according to a racial threat perspective.
If percent Hispanic is a contextual proxy for influence over deportation outcomes, then a curvilinear relationship should prove most reliable when measuring the concentration of minorities with potential clout and minorities most affected by deportations.The following analyses employ alternative specifications and are consistent with the tiered influence hypothesis. 9First, the inverted, U-shaped relationship remains consistent when substituting percent Hispanic with Hispanics with economic and political resources: (i) the Hispanic share of the labor force; (ii) Hispanic adults as a share of the population, or (iii) Hispanic U.S. citizens as a share of the county.Predicted discretion peaks (0.85-0.86)where Hispanic workers comprise 30-45 percent of workers; Hispanic adults are 25-35 percent of a county; and Hispanic U.S. citizens are 25-40 percent of the population.
Second, deportation discretion is related to the concentration of Hispanics with more clout than vulnerable Hispanic groups.Hispanic youth (under age 18), Hispanic noncitizens, and Hispanics not in the labor force are less likely, in general, to be in a position to advocate for the rights of noncitizens under arrest than Hispanic adults, workers, and U.S. citizens.Consistent with a tiered influence account, a curvilinear relationship between discretion and percent Hispanic youth is less pronounced than the above results: predicted discretion is similar (0.83-0.84) when comparing counties where Hispanic youth concentration was low, medium, or high (5, 10, and 15 percent of a county, respectively).Furthermore, discretion is unrelated to proportions of Hispanic noncitizens and Hispanics not in the labor force.Third, previous research has established that the presence of Hispanic officers is related to less restrictive outcomes (Pedraza & Calderon, 2017).Consistent with the tiered influence perspective, the concentration of Hispanic law enforcement officers is related to higher discretion scores, but only up to a point.The relationship is also less precise than when measuring the concentration of Hispanic residents.Furthermore, a positive relationship between deportation discretion and percent Hispanic officers should vary along different concentrations of Hispanic residents.Indeed, after introducing an interaction term (percent Hispanic × percent Hispanic officers), percent Hispanic residents and percent Hispanic officers are positively related to discretion, except where the concentrations of Hispanic residents and officers were both high.
Fourth, tiered influence should not apply to groups not as readily associated with deportation.Indeed, the relationship is unique to the share of Hispanic residents rather than the shares of non-Hispanic black residents or the foreign-born population.Previous research finds a curvilinear effect on legislative action as a function of Hispanic and black population shares (Jacobs & Tope, 2007).However, in the context of deportations, the percent of black residents and percent black 2 is not significant after accounting for the curvilinear relationship of Hispanic shares.Furthermore, modeling discretion as a curvilinear function of immigrant shares does not yield substantively similar results.As discussed previously, foreign-born shares are not expected to predict the level of discretion because a county's immigrant population excludes U.S.-born Hispanics in households affected by deportation and includes immigrant groups unlikely to face (or be expected to face) deportation.When predicting discretion as a function of percent immigrant and its exponent, the coefficients are statistically significant.Although the relationship is consistent with the racial threat hypothesis, the estimates are less precise and inconsistent when using different baseline years to measure population growth.
In addition to the alternative specifications above, the inverted, U-shaped curve holds only when predicting deportation discretion, and the relationship is not affected when including other controls.Notably, the nonlinear association of Hispanic shares applies to exercised discretion but not rates of deportation (i.e., removals and returns adjusted for the noncitizen population), where patrol officers decided whether to arrest someone but may have had no control over whether the arrestee was transferred to DHS.Finally, adding a control for the unauthorized share of a county's noncitizen population does not alter the results predicting deportation discretion.Discretion is lower in counties where unauthorized immigrants comprise more than half of all noncitizens, which is likely due to the broader range of deportable offenses for unauthorized detainees compared to green card holders (Rosenblum & Kandel, 2012). 10Discussion I examine whether the exercised level of discretion under Secure Communities responds to variation in threat measures.Linear proxies for racial threat yield contrasting and imprecise estimates, echoing the varying results in previous research on the role of minority shares and growth rates as predictors of immigration policymaking.I show the relationship between Hispanic concentration and deportation discretion is not linear but curvilinear.Divergent theoretical literatures support competing hypotheses for the direction of the nonlinearity.The results support the tiered influence account, which suggests the political clout amassed by Hispanic populations builds, but opposition to restrictionism eventually dissipates when the population gets too large.Therefore, the results are not surprising if we consider that the relative size of the Hispanic population is a proxy for tiered influence rather than threat.
The analyses above focus on county-level determinants of deportation activity, so this paper does not represent a definitive account of the organizational-or individual-level mechanisms driving variation in deportations.Nevertheless, the results suggest the functional form and direction of the relationship between Hispanic concentration and discretion is consistent with a theory of tiered influence rather than racial threat alone.Only the tiered influence account correctly predicted county jails would limit cooperation with DHS where Hispanic concentration was neither too large nor too small.Although I find little support for a threat curve, and evidence of racial threat in the recent literature on immigration policymaking is mixed, racial threat has been shown to hold under different circumstances.As Tolnay and Beck (1992) cautioned, the conditions under which we observe support for a threat curve-such as punitive electoral votes or imprisonment rates (Jacobs & Kleban, 2003;Jacobs & Tope, 2007)-may not extend to other exclusionary outcomes.
Next, I discuss possible reasons for the relationship between Hispanic concentration and deportation discretion.We observed low levels of exercised discretion among counties where the Hispanic share of the population is low (below 20 percent; N = 2,338 counties).Notably, nearly one-third of the Hispanic population in the study sample lives in these counties, and these places by far outnumber counties with large concentrations of Hispanics.In these locations, Hispanics remain less visible than other locations, and elected sheriffs routinely complied with requests to turn noncitizens over to DHS authorities.If Hispanic concentration is a proxy for clout, it is not surprising that we find low levels of exercised discretion in counties with small Hispanic proportions.After all, if sheriffs made decisions regarding whether to cooperate with DHS in response to the influence of Hispanics, then counties with relatively few Hispanics could wield limited influence over deportation decisions.
According to the racial threat hypothesis, counties above a certain threshold should provoke hostility.The results suggest the opposite when we compare a cross-section of counties where Hispanics proportions were either below and/or above 20 percent of a county.Sheriff departments generally helped deport a lower share of noncitizens under arrest if Hispanics comprised a substantial but not overwhelming (20-40 percent; N = 194 counties) share of the local population.In these places, county jail officials generally transferred smaller fractions of noncitizens to immigration authorities.Hispanic group size might predict less restrictionism for a number of reasons.Hispanics may have leveraged immigrant-serving organizations (Steil & Vasi, 2014) to advance the interests of a minority group; namely, Hispanics at risk of deportation.In addition, sheriff departments may have felt constituent pressure to represent the interests of immigrants in counties with a formidable Hispanic presence because such concentrations could mobilize against restrictionist policies (Avery et al., 2017).These groups may have also organized to elect sheriffs committed to less restrictive immigration enforcement (Filindra & Pearson-Merkowitz, 2013).This analysis does not pinpoint the relative importance of these potential sources of influence.The cross-sectional evidence suggests deportation discretion is responsive to concentrations of certain groups (e.g., percent Hispanic adults, workers, and U.S. citizens) but not others (e.g., percent Hispanic youth, percent black, percent foreign-born, percent Hispanic noncitizen).However, unmeasured determinants of deportations may explain both why discretion varies across the country and why discretion appears to be related to Hispanic concentration.Future research should explore how the civil society context might differ where Hispanics are a substantial minority versus the majority (Appendix Table A1).
As anticipated by the tiered influence account, exercised discretion plummets in counties with the largest concentration of Hispanics (over 40 percent; N = 137 counties).DHS disproportionately relied on these counties to reach record-high deportations during the period of study.Elected sheriffs in these places were exceedingly likely to comply with detainer requests in majority-Hispanic counties rather than exercise discretion to release noncitizen arrestees.As discussed above, Hispanic residents may have coalesced to advocate for less restrictive contexts where Hispanics are a sizable minority group.Where Hispanics are most concentrated, including counties where Hispanics are the majority, pressure to advocate for the interests of noncitizen arrestees appears muted and opposition to restrictionism appears to have ebbed.It seems Hispanic concentration is related to less restrictive deportation decisions as long as Hispanics are both sizable and a minority proportion of a county.This account is consistent with Tolbert andHero's (1996, 2001) research that finds support for restrictive policymaking in counties with the largest Hispanic concentrations.Related explanations may also account for this pattern of restrictiveness in the most Hispanic-dense counties.Even if Hispanics in these counties did not hold particularly strong views about immigration policy, it is possible immigration issues are a lower priority in such places (Valenzuela & Stein, 2014), which might preclude efforts to advocate for the interests of Hispanic noncitizens.Moreover, high concentrations of Hispanic elected officials may not offset Hispanics from restrictive policymaking (Liang, 2018).

Conclusion
Noncitizens under arrest for low-level offenses faced starkly different odds of being transferred to DHS depending on where they were booked into jail.This paper examined two theoretical predictions whereby specific thresholds of Hispanic concentration are related to the level of exercised deportation discretion.Both approaches anticipate policy outcomes should be different in contexts with low versus high concentrations of minority groups.The accounts part ways in where they expect group size to translate into protective outcomes: racial threat predicts less restrictionism when minority group concentration is at its highest, unlike tiered influence.
The evidence presented is not in line with the racial threat scenario, whereby rising Hispanic proportions trigger a threat response followed by acquiescence to pressure from Hispanics in places where they comprise the largest shares of a county's population.Instead, sheriff departments administered the highest levels of exercised discretion where Hispanic concentration was neither too small nor too large (i.e., between 20 and 40 percent).In sum, the ability of Hispanic minorities to influence Secure Communities outcomes through mid-2013 highlights the possible entrenchment of Hispanics' tiered influence over elected sheriffs, who exercised relatively low levels of discretion in all but a narrow group of counties.
This paper also offers lessons for analyzing how demographic contexts shape immigration policymaking.I argue in favor of measuring minority shares and their exponent, especially when analyzing sub-state variation or continuous outcomes.Further, following Filindra (2018), studies should test whether results are sensitive to competing measures of minority composition and alternate model specifications more generally.
Given their contrasting measures, it comes as no surprise that previous research comes to competing conclusions about the role of demographics when predicting state-level policymaking data and zero-bound counts of legislative activity.However, researchers should not only test for nonlinear relationships and alternate measures in cross-sectional data.In order to fully leverage state-and local-level variation in minority composition as well as account for pre-existing trends, researchers should look to panel data wherever possible to examine changes in states' and localities' demographic makeup in the same places over time (Commins & Wills, 2017;Creek & Yoder, 2012;Reich, 2018;Ybarra et al., 2015) and conduct definitive tests of the conditions under which outcomes are a function of nonlinear effects, as recommended elsewhere (Stults & Swagar, 2018;Tolnay & Beck, 1992).
Juan Manuel Pedroza is assistant professor of demography, migration, and inequality in the sociology department at the University of California, Santa Cruz.His research concerns the vast inequalities present in immigrants' access to justice, the social safety net, and poverty.His latest work examines how and where deportation and immigration enforcement initiatives exacerbate these inequalities and leave imprints in local communities.

Notes
Many people have lent detailed and helpful suggestions.I thank Aliya Saperstein, Tomás Jiménez, Michael Rosenfeld, John Meyer, David Grusky, Florencia Torche, Ariela Schachter, Michel Grosz, Alex Stanczyk, Katie Vinopal, Mitch Downey, Paul Chung, Emily Carian, Amanda Mireles, and members of graduate research workshops in the sociology department at Stanford University.The paper benefited from valuable feedback from anonymous reviewers and conference participants at the Population Association of America; the Western Political Science Association; the Law and Society Association; the Politics of Race, Immigration, and Ethnicity Consortium; the Berkeley-Stanford Immigration Conference; the Blurring the Border conference; and the Berkeley Demography Department.Any errors or oversights in the paper are my own.Fellowships from the Ford Foundation and Stanford University's Center for Comparative Studies in Race and Ethnicity provided funding support.
2. Secure Communities data exclude deportations under the purview of Customs and Border Enforcement, whose discretion is unclear (Vega, 2017) compared to the Secure Communities program.
3. Available Secure Communities data are limited to the above measures of matches and deportations.The Transactional Records Access Clearinghouse publishes county-level data on DHS requests to county officials to hold noncitizen detainees.However, the data appear to cover detainer requests across enforcement programs, including programs where discretion plays a limited role.As such, the data in this paper remain the most unambiguous measure of exercised discretion for the purpose of examining the competing hypotheses proposed in this paper.
4. The data exclude more than 400 counties with no matches, which are home to 5 percent of the nation's Hispanic population.Nineteen counties with missing covariate data are also excluded, and these are mostly in Alaska where election data do not conform to county boundaries.Alaska had 400 matches and 1 deportation as of May 2013.
5. Denying DHS detainer requests was common among "sanctuary cities" (Congressional Research Service, 2006;Ridgley, 2008) and became more common after the summer of 2013.By 2015, over 300 counties limited the transfer of noncitizens arrestees (Immigrant Legal Resource Center, 2016).Sanctuary designation diffused via policy networks akin to a theory of polarized change and issue entrepreneurs in research on restrictionism (Gulasekaram & Ramakrishnan, 2015).Sanctuary designation alone did not guarantee higher levels of exercised discretion, however, and the determinants of such policy adoptions warrant further study.
7. The analyses use weights to ensure the estimated relationships between discretion and independent variables are adjusted for a county's Hispanic population size.Results are substantively the same when using noncitizen weights.The models use analytic weights because the contextual factors are mean county characteristics rather than a probability sample.

Figure 1 .
Figure 1.Anticipated Shape and Direction of Relationship between Percent Hispanic (X) and the Level of Exercised Discretion under Secure Communities (Y).

Figure 2 .
Figure 2. Curvilinear Relationship between the Level of Exercised Discretion and Relative Size of Hispanic Population.
(Cox & Miles, 2013;Jung, 2015)r variation in the timing of program adoption, the models account for early (N = 699), middle (1,113), and late (N = 857) adopters of the program(DHS, 2013).Early adopters began participating in Secure Communities within 2 years of the program's launch (October 2008-October 2010), and late adopters activated the program during the final year of its roll-out (January 2012-January 2013).Previous research has shown that the length of time since program activation is positively correlated with Hispanic concentration and restrictive deportation outcomes(Cox & Miles, 2013;Jung, 2015).
Additional ContJoyner, 2018;King, Massoglia, & Uggen, 2012;s for other possible explanations of the level of exercised discretion.An index of criminal justice capacity adjusts for counties with a vast capacity to conduct policing activities compared to counties with meager capacity.6In addition, results also account for unemployment rates (Department of Labor, 2013) because downturns can influence immigration policymaking(Hopkins, 2010;Joyner, 2018;King, Massoglia, & Uggen, 2012;

Table 1 .
Linear Models of the Level of Exercised Discretion (2,669 Counties With Noncitizen Arrestees) Note: Robust standard errors clustered across DHS jurisdictions.Models control for Republican vote share, existing restrictive laws, the timing of program activation, criminal justice capacity, unemployment rates, and state fixed effects.

Table 2 .
Nonlinear Models of the Level of Exercised Discretion (2,669 Counties With Noncitizen Arrestees) Table 2 improve fit over models without state dummies (R 2 : 0.44) and confirm the important role of state contexts.Absent state fixed effects and clustered standard errors, the results are substantively similar.Variance inflation factors (VIF) have a mean of 1.4 in models without squared terms or state-level indicators, and no VIF exceeds 1.7.9. Results available upon request.10.Using unauthorized population figures (Migration Policy Institute, 2016), I create a categorical variable to identify counties where unauthorized immigrants are more than half of noncitizens or less than half.Counties with no unauthorized population estimate are the reference.