Urban resilience as a mitigating factor against economically driven out-migration during COVID-19: The case of Eilat, a tourism-based city

Abstract

The COVID-19 pandemic has created an ongoing global crisis. The unprecedented shock has been particularly devastating for tourism-based cities and has tested their resilience. This study addresses the mitigating role of urban resilience in the interplay between acute crises and the phenomenon of urban outmigration. Leveraging a unique dataset collected during the first national lockdown that followed the outbreak of COVID-19 in the city of Eilat (Israel)—a geographically isolated single economic sector-based city with no feasible options to commute—we offer here a new conceptual framework and an empirical framework for measuring perceived resilience. Using validated psychometric questionnaires and employing the nested hierarchical modeling approach, we estimate the impact of perceived resilience on the decision to migrate from the city. We find that even though Eilat has all the attributes to experience significant out-migration, its residents are not inclined towards migration due to its prior investment in resilience measures, which strengthened the local community and created a unique credo shared by its residents. These findings call for policymakers to focus on long-term resilience schemes directed at increasing the appeal that cities have for their residents and ensuring their endurance in times of extreme hardship.

1. Introduction

The COVID-19 pandemic has created a sudden, rapid, and unprecedented crisis, affecting almost every aspect of our lives. The International Monetary Fund (IMF) estimates that the global economy shrunk by 4.9% in 2020 and labeled the decline the worst one since the Great Depression. Despite the recent development of vaccines, the possibility of further lockdowns and limitations remains a valid threat, and delays in the rollout of vaccines suggest an even more gradual recovery than previously forecasted (IMF, 2020).

While the economic demise is felt across most sectors, the tourism industry suffers disproportionately from a reduction in ground and air traffic, stringent border controls, and mandatory social distancing. New variants of the virus—discovered in recent months—have forced many countries to re-introduce tighter travel restrictions. According to UNWTO (2021), international tourist arrivals declined by 74% during 2020, translating into a 1 billion international arrivals loss and approximately USD1.3 trillion in export revenues from international tourism. This loss in receipts is 11 times the loss recorded in 2009 due to the subprime crisis and is responsible for more than 100 million tourism jobs so far.

Amid the immense hardship experienced by the entire tourism sector, this crisis has had a devastating effect on tourism-based economies (e.g., Macao, Seychelles, and the Maldives, where about two-thirds of GNP originate from tourism; World Bank, 2016). A destination affected by a disease may suffer in the long-term from a negative image that deters travelers (Cooper, 2005), whereas the most destructive force is the collective memory of its route (Speakman & Sharpley, 2012). At the micro-scale of cities and communities whose economic basis depends on tourism, a crisis such as COVID-19 may lead to substantial negative net migration and deterioration of urban centers. In extreme cases, cities can turn into ghost cities, a term usually used to describe a phenomenon in which boomtowns, created by a single activity or resource, are abandoned once the resource is depleted (Detroit was nicknamed a ghost city due to the urban decay caused by the deindustrialization of the automobile companies, depopulation, and abandoned buildings; Alesawy, 2019). When a city is geographically isolated and lacks connectivity to other urban centers—thus excluding commuting as an option—the risk of out-migration following a significant crisis increases.

The severity of this risk depends on the interplay between the severity of the global and consequent local disaster, the city's resilience, the extent of external support and aid provision, and past experience with disasters. The role of resilience in disaster and crisis management continues to gain attention from both researchers and practitioners. Specifically, given the devastating impacts of disasters on local communities' viability and the realization that disasters have a significant social dimension, the interest in the nexus between social resilience and disaster management has been growing in the last two decades (Aldunce et al., 2015). This discourse has brought to the fore concepts such as social resilience, community resilience, and social cohesion, all related to “understanding the response of human systems to change” (Wilson, 2012; p. 1218).

This study quantitatively addresses the impact of urban resilience in a city in which a global disaster (COVID-19) has resulted in and intertwined with a local secondary disaster due to a halt in tourism activities that threatens the city's economic basis. As noted by Guo et al. (2018), there is a lack of empirical analysis, and thus understanding, of the drivers of resilience and vulnerability in tourism-based communities, which in turn leads to the failure to effectively design community resilience. The outbreak of the COVID-19 pandemic and its long-lasting impacts have created an opportunity to fill this gap.

This paper leverages this opportunity by focusing on the city of Eilat- the southernmost city in Israel, and the most peripheral city in the country. Drawing on the literature on crises, disaster management, and urban resilience, we aim to study the impact of COVID-19 on the city of Eilat as a unique model of an urban system. The rationale for considering Eilat as a pertinent test case that can yield generalizable implications is twofold; a. its geographical isolation and b. its reliance on a single sector—tourism in this case—as an economic engine. Specifically, we aim to explore empirically, using advanced econometric and psychometric methods, how the emergence of COVID-19, perceived resilience, and inherent pull and push factors of the city to operate and interact with each other to evoke or restrain intentions to migrate from the city to the major population centers further north. Understanding the mechanisms of residents' perceived resilience is crucial for recovery from disasters, as well as for strengthening the community's adaptive capacity to manage future disruptions.

In light of the characteristics of Eilat as an isolated urban system that relies heavily on tourism, urban resilience plays a crucial role in preventing a collapse. However, since urban resilience is a multifaceted concept germane to conditions across social, ecological, economic, and institutional systems, the process through which urban resilience is operationalized and the way it interacts with the various aspects of a global pandemic such as COVID-19 are unclear (Sharifi & Khavarian-Garmsir, 2020). We tackle this challenge by examining the relationships between the impacts of COVID-19 and different facets of urban resilience, simultaneously with examining the relationship between these aspects and the risk of outward migration from the city.

The contribution of our work lies in two main aspects: (a) conceptually: we offer a synthesis of several theories, drawing from the urban resilience and catastrophe management theories. While a crisis may strike any city or community, recovery and survival mechanisms may not be sufficient to prevent residents' intentions to out-migrate, especially in prolonged crises such as COVID-19. Community resilience, built over the long haul via a dynamic process, can serve as a mitigating mechanism for undesired results such as intentions and actual out-migration, which for some cities, may be disastrous. To our best knowledge, this work is the first to integrate these fields of knowledge into a unified conceptual framework. (b) empirically: this study employed an advanced econometric approach to estimate the relationships between the discussed constructs while considering mediation effects and latent variables. In fact, this is one of very few papers, that empirically estimate perceived urban resilience.

To achieve these goals, the study makes use of a unique dataset that was collected amid the ongoing crisis, i.e., it was collected during the first lockdown in Israel, which brought the country's economy to a complete halt. During the first lockdown, the city of Eilat, given its peculiarities, resembled a post-apocalyptic town, with zero visitors, empty streets, and abandoned attractions and shops on its promenade. Nevertheless, our study demonstrates positive and optimistic beliefs of Eilat's residents in the city's ability to cope and overcome this crisis and an overall negative tendency to out-migrate. Empirical evidence clearly indicates that the city's community resilience is sound and that residents are altogether satisfied with the general attributes of the quality of life offered by Eilat. When measured as predictors of out-migration, these factors served as mitigating factors against such undesired processes. In particular, their impact on the propensity to leave Eilat was negative and significant, i.e., they decreased the risk of outward migration from Eilat.

2. Literature review and hypotheses development

We first delineate the conceptual framework of our research. Since our study synthesizes ideas from several research fields, we hereafter review canonical literature in the fields of urban resilience, catastrophe management in tourism, and economically driven out-migration. We highlight the connection between these subjects, and finally present our own synthesized conceptual framework of urban resilience as a preventive measure against out-migration in times of extreme crises, followed by economic aftershocks.

2.1. Urban resilience

The concept of resilience was first introduced in a seminal paper by Holling (1973) in the context of ecological systems, with resilience defined as a measure of the ability of an ecosystem to absorb changes and persist. According to this definition, resilience is a mere property of a system, while stability is defined as the ability of a system to return to equilibrium after temporal shocks. These concepts, however, became enmeshed in modern urban resilience literature, and are now intertwined in a single canonical concept (Cariolet et al., 2019; Folke, 2006; Masnavi et al., 2019; Meerow et al., 2016).

We adopt here the following contemporary definition of resilience in the context of urban studies: “Urban resilience refers to the ability of an urban system—and all its constituent socio-ecological and socio-technical networks across temporal and spatial scales—to maintain or rapidly return to desired functions in the face of a disturbance, to adapt to change, and to quickly transform systems that limit current or future adaptive capacity” (Meerow et al., 2016, p. 39). This definition gives rise to three main attributes of resilience: the ability to recover, adapt, and transform. Recovery strategies refer to the ability of an urban system to withstand disasters and recuperate from acute shocks, whilst either planning for them or accruing sufficient resources in order to face a wide array of unknown factors (Ahern, 2011; Lamond & Proverbs, 2009). Adaptability, as an intermediate mechanism between recovery and transformation, is defined as an urban system's ability to adjust to changing conditions (Alberti et al., 2008; Godschalk, 2003; Pickett et al., 2004). In contrast to recovery, it simply allows the urban system to reallocate resources in order to maintain functionality and prevent its demise when facing specific threats (Brown et al., 2012). Transformation calls for complete restructuring to prepare for anticipated and unanticipated shocks and disturbances (Ernstson et al., 2010). It involves the integration of resilience as an everyday practice adopted by policymakers, planners, and communities in order to both predict calamities and embed resilience practices (e.g. safety measures, emergency plans, etc.) in their modus operandi (Coaffee, 2013).

The literature reviewed in this subchapter provides broad scope into the various mechanisms underlying the vague and challenging measure of the concept of urban resilience. These concepts, however, remain mainly theoretical, since the empirical study in the field is scarce (Bottero et al., 2020; Cote & Nightingale, 2012; Sharifi, 2020; Vale, 2013). While many studies in the fields of urban planning and climatology discuss and examine alternatives towards building resilience in cities, the literature has yet to offer a quantitatively applied, universally agreed index/measure for resilience, in terms of social stamina, well-being, and quality of living (Therrien et al., 2020; Woodruff et al., 2021; Yumagulova & Vertinsky, 2021). In addition. There is a dearth of empirical data on disaster conditions which hinders the ability to quantify and estimate key determinants of resilience (Chen et al., 2021).

2.2. Urban resilience and disaster management

Although the field of disaster management developed earlier than that of urban resilience, the interconnectedness of the two in urban contexts is evident. Disasters can occur at the micro-level or on a global scale. However, the consequences of global disasters are not equally distributed among the world's regions, among the countries within regions, or the cities within countries (Jayarathne & Babu, 2017).

Many cities have particular vulnerabilities that expose them to city-level disasters, mainly due to their geographical dimensions. Some cities are exposed to storms and floods; others are susceptible to wildfires, earthquakes, or volcano eruptions. In other cases, cities suffer catastrophes as part of a national, regional, or global event. Cities whose main economic engine is tourism are more vulnerable when a global disaster occurs due to the tourism industry's high vulnerability to disasters (Becken et al., 2014). In fact, most disasters have an immediate effect on the tourism industry, either directly (as in the case of earthquakes or tsunamis) or indirectly (as in the case of decreased tourist flows following terror events or economic crises). Given the growing prevalence of events such as terrorist attacks, natural disasters, and epidemics, the field of crisis and disaster management in tourism research and practice is surging. and the development of adaptive capacity in tourism-based communities has become an essential issue in tourism research and practice (Biggs et al., 2012; Calgaro et al., 2014; Espiner et al., 2017; Luthe & Wyss, 2014).

In recent years, resilience has become a focus of tourism research as part of an effort to understand the tourism sector's ability to cope with disasters (e.g., Bec et al., 2016; Orchiston et al., 2016). In particular, increasing the resilience of a tourism community is important for truly sustainable tourism development (Hartman, 2016; Pyke et al., 2016; Tsao & Ni, 2016). Having said that- as noted by Chen et al. (2021), in a literature review on tourism crisis and disaster management, only 5% of the studies focused on resilience (Ritchie & Jiang, 2019), also, the literature offers mostly theoretical frameworks, and little empirical work (Bangwayo-Skeete & Skeete, 2021; Chen et al., 2020; Filimonau & De Coteau, 2020).

2.3. Epidemiological crises and disasters

While sometimes used interchangeably, disasters and crises do not necessarily overlap. Disasters are largely defined as sudden unforeseen events over which there is little control, whereas crises are abnormal situations that threaten a wide array of stakeholders (Al-dahash et al., 2016).

Studies of crises and disasters in the tourism industry generally defined them based on their origins, roughly divided into socioeconomic causes (e.g. terror attacks or war) versus natural and technological causes (e.g. floods or transport disasters) (Santana, 2004). However, this distinction may also be based on an event's severity rather than its cause (Laws & Prideaux, 2008).

Since the beginning of the millennia, the tourism industry was hit by several epidemics and pandemics (i.e. the severe acute respiratory syndrome (SARS) in 2003, the swine flu (H1N1) in 2009, and the Middle East Respiratory Syndrome (MERS) in 2015). These epidemics and pandemics affected local markets as well as global ones, depending on the spread of the disease and the attention given to it by the media. Yet, none of these outbreaks was termed a “super-shock” for world tourism as COVID -19 did (Dolnicar & Zare, 2020). This limits the effectiveness of managerial implications and experience accrued after health crises before COVID-19. The analyses and inferences provided in this study can be integrated into a well-structured learning mechanism, based on pre-preparedness and general resilience of the economy and community and cooperation from different stakeholders (Mair et al., 2016; McCartney et al., 2021).

2.4. Economically driven out-migration

While a plethora of factors may contribute to mass out-migration, a main generator of such processes is a fundamental change to the structure and base of the economy, either within the city, state, or country, or globally (Alves et al., 2016). The effect of such changes, and the rate of urban deprivation, is ten times greater in economies based on a single sector, than in diverse economies (Wang et al., 2020). Perhaps the most prominent example of such a change is the one undergone by the formerly major industrial cities of Detroit and Pittsburg during the shift of the United States to a services-based economy (Fol & Cunningham-Sabot, 2010). These metropolitan areas, and other cities located on the American Rust Belt, experienced mass migration, followed by neglect, a decrease in the urban quality of living, and rising crime rates. These, in turn, fueled a destructive positive feedback loop, and generated additional migration flows (Döringer et al., 2019; Haase et al., 2016).

2.5. Synthesis of reviewed theories and hypotheses

Considering the literature reviewed in this chapter, we propose the following conceptual framework. As illustrated in Fig. 1 : Urban resilience, catastrophe management, and economically driven out-migration are intertwined, creating a feedback loop, where a change in one factor results in a change in all others, whilst impacting the probability of a negative outcome of outmigration of residents from the urban system. Urban resilience enables urban systems to manage better and regulate catastrophes and disasters since it endowed them with inherent stamina stemming from the city's investment in these mechanisms. Survival mechanisms allow cities to promptly return to a normal daily routine and minimize secondary damages caused by external shocks. Adaptation mechanisms ensure operational flexibility in light of sudden changes, which may turn into long-term catastrophes. Finally, when facing disasters, transformation mechanisms ensure the city's survival in the long haul since they enable and encourage ingenuity and innovation. These three resilience schemes may prove crucial in the COVID-19 era since the pandemic caused immediate interruptions to daily lives and long-term effects on the economic flow of people and goods and overall well-being. While catastrophes of these scales are rare, they challenge and test the urban system's ability to cope with disasters and may, in turn, influence its residents' perception of the system's resilience. While it is still too early to determine if and how the pandemic affects cities long term resilience, it is possible to measure its effect on the propensity of residents to out-migrate in light of the fallout.

Fig. 1.

Conceptual framework of the relationship between the research factors and out-migration.

In light of the literature reviewed in this chapter, we claim that the rate of outward migration is directly related to urban systems' resilience and their ability to manage multifaceted catastrophes and cope with their outcomes. Resilient cities maintain and develop adaptation and transformation mechanisms in order to cope with sprawling and abrupt shocks and disturbances; hence, they are more capable of preventing mass outmigration of their residents. This is especially so when the crisis hits hard on the city's economic basis, and commuting is very limited or impossible. When facing crises or disasters, these cities maintain a sense of safety, cohesion, and inclusion whilst preserving the urban quality of living and infrastructures. The COVID-19 pandemic serves as a unique opportunity to test for such a hypothesis, especially in urban systems where out-migration is already a risk factor, due to their inherent weaknesses, such as remoteness, single sector-based economy, and enhanced secondary shocks due to this ongoing crisis. We, therefore, hypothesize the following:

h1

The structure of the work market has a significant effect on the propensity to out-migrate.

In our study, this hypothesis is tested under extreme conditions; the economy of the studied city is based almost solely on tourism (a sector that suffered a fatal blow during 2020) in a remote urban city where commuting is not an option. In light of the literature surveyed, we expect these factors to increase the propensity to out-migrate.

h2

The effect of the actual state of the economy is confounded by the belief in the ability of the city to survive an economic turmoil.

While catastrophes may lead to economic distress, these hardships may turn out to be temporary, and residents are willing to endure and wait out the hardships if their belief in the city's ability to manage and assuage them is sound. When testing for this hypothesis in a tourism-based economy it is important to take into consideration that this effect may even be boosted since tourism-based cities are accustomed to seasonal fluctuations in demand for their product.

h3

perceived resilience suppresses and prevents economic outmigration.

Since residents have only partial access to the information regarding the true resilience of the city they live in, signals such as social cohesion, quality of urban living, sense of belonging and opportunities for personal growth cultivated by the city itself may buffer intentions to out-migrate. In the case of COVID-19, this hypothesis may even prove stronger since economic conditions are poor on a nationwide scale. As an alternative, residents may choose to stay, despite economic conditions, if they believe the city can offer them added values that other cities lack.

3. Data and methods

3.1. The data

Our research employs data collected from a convenience sample of 750 residents of Eilat. The survey was distributed via social networks (i.e., Facebook and WhatsApp) during the first lockdown in Israel between April 16th and May 4th, 2020. The sampling process was exhausted when we reached a representative sample of the city's population in terms of demographic and socio-economic metrics. Our data includes approximately 50% males and 50% females aged 18–80, all residing in Eilat. Sampled residents' educational attainment ranged from high school graduates (considered low attainment in Israel), through vocational schools' graduates, to professors at the local university. The distribution of education is right-skewed, meaning most residents have lower than average education, in line with the city's lower than the national average educational attainment level. In terms of economic metrics, average household income was relatively low, again in line with the city's population attributes, and the proportion of self-employed individuals was above the national average; however, fit the nature of employment in the city, and the National Bureau of Statistics' yearly indices for Eilat (Central Bureau of Statistics, 2020b).

3.2. Research design

Our survey covered a wide range of subjects, designed to measure the current state of Eilat residents and their belief in the city's resilience systems and its odds of recovery. The questionnaire consisted of five main resilience questionnaires, all of which required the individual to rank items on a Likert scale of 1 to 5. The questionnaires were the following: Economic resilience- was Divided into two subscales: (a) survival and adaptation, and (b) transformation; Community resilience- the measure of social cohesion and social participation, using a mixture of validated questionnaires previously used in the social cohesion literature (Dupuis et al., 2017; Forrest & Kearns, 2001; Schmeets & Coumans, 2013; Zimet et al., 1988; Zimet et al., 1990); Self-resilience the ability of the individual to ‘bounce back from stress’, as measured using the abridged version of the CD-RISC scale (Connor & Davidson, 2003; Windle et al., 2011); Push and pull factors- the individual’s willingness to introduce into the city's economy more diverse economic sectors (e.g., manufacturing, high-tech and R&D, etc.); Satisfaction with city life-the individual’s satisfaction with municipal services, urban quality of life and the city's appearance. The questionnaires were later transformed into scales using a reliability analysis scheme. All scales proved reliable, with alpha values greater than 0.7.1 The survey also included a sociodemographic questionnaire, including general and specific attributes of residents of a city that correlate with the tourism industry and the city of origin of the respondent (25% of Eilat residents are seasonal workers). Respondents were also asked to rank the measure of disturbance by the crisis, the need for an inherent change in the city's tourism industry, and their belief in the city's ability to recover from the crisis. The dependent variable in our study was the respondent's answer to the binary question: ‘Given that the current state continues, will you consider emigrating from Eilat?’

3.3. The statistical model

Since our main model measures the propensity to emigrate from Eilat, we employed a technique of logistic regression model approximation. However, since our explanatory variables may be correlated and dependent on each other, our model should provide sufficient robustness in order to avoid biases related to confounding variables and multicollinearity. To control for such biases, we employ a nested hierarchical GLM regression model, using blocks of variables, and a forward stepwise method for entering variables within each block. The hierarchical model allows for the introduction of both micro and macro level data into the regression model where the response variable is predicted as a function of both influences while controlling for joint effects and interactions between them. In particular, a nested blocks model introduces in each step an array (i.e., a ‘block’) of variables to be estimated together, yet independently from previously estimated blocks of variables. This method allows the following desired statistical properties: (1) The contribution of each block to the model can be measured and estimated separately, and one may test for the significance of wide phenomena using multiple variables, while measuring their joint effect on the response variable. (2) Multicollinearity, or the existence of confounders, is controlled using this method, since each block is estimated using the remaining variance of the response variable, given the explanatory power of previously added blocks.

Property (2) is particularly appealing when estimating regression models using psychometric techniques, since scales used in the analysis are—more often than not—highly correlated with one another, but not necessarily correlated with the response. In particular, when building a model using subject-based blocks, there is a higher risk of introducing confounders into the model, since these usually have a stronger (yet spurious) correlation with the dependent variable. To avoid such pitfalls, we introduce each regressor, within each block, using a forward stepwise method. We apply the Forward LR rule since it is the least prone to error out of the commonly used selection methods.

For elaboration on hierarchical models and the forward LR algorithm, please refer to Appendix A.

3.4. The study area

The urban system studied in this work is the southernmost city in Israel, located on the gulf of the Red Sea, near the Jordanian and Egyptian border, 250 km south of the nearest urban center, and approximately 350 km south of the center of Israel. It is worth noting that since Israel is merely 600 km long, and travel distances between major urban areas do not exceed 100 km, Eilat's location is considered extremely isolated. Moreover, in contrast to other metropolitan areas in Israel, Eilat is not connected to other cities by train or any major highways. Therefore, commuting to and from Eilat is done either by a long drive on a narrow, one-lane road or by a 45-minute flight from the Tel Aviv greater metropolitan area to the new airport located 45 min from Eilat (the old airport in the center of Eilat, established in 1949, was closed in 2019). In addition, the regional council of Eilot, adjacent to Eilat, is populated by only 4000 residents in rural communities (Central Bureau of Statistics, 2020a), hence, Eilat is not considered a metropolitan area; it has no satellite cities or suburbs, and is, in fact, a standalone city. Geographical attributes of Eilat, including its location, main roads leading to and from the city, and the spread of international airports in Israel, are shown in Fig. 2 .

Fig. 2.

Map of Israel.

NOTE: the map includes names of the four major metropolitan areas in the country, as well as the research case.

The city of Eilat was founded in 1952, and its few residents were mostly port employees, military personnel, and convicted felons exiled by the court's instructions. The city's population did not grow beyond 10,000 residents until the middle of the 1960s, despite government efforts to encourage migration to Eilat (Cohen & Shiller, 1993). The stagnation in its population and economic growth finally reversed during the 1970s, due to the development of a thriving tourism industry, based on Eilat's unique climatic conditions and rare coral beaches (as well as other natural assets). Tourism has been integrated into the urban economy and gradually grew into the pillar industry of the city. October 10th of 1985 remains a major milestone in the city's history, when it was announced a ‘Free Trade Area’, turning Eilat into the shopping capital of Israel, and catalyzing an economic boom during the 1990 (RIC, 2015). By then, the city's population more than doubled, and developers began building a new residential area, which offered high standards of living, in suburban-like neighborhoods. As of 2021, Eilat's population consists of 52,787 residents, and it is ranked 35th in the Urban Hierarchy Index. Its population is considered homogenous in terms of religion, with 95% of its population being strictly Jewish. Eilat is ranked rather low in terms of socioeconomic indices (154 out of 255 municipal authorities in Israel), with an average wage lower than the national average, as well as a significantly lower proportion of households earning 4 times the average wage (0.8%, in comparison to 2% nationwide) (Central Bureau of Statistics, 2020a; National Insurance Institute of Israel, 2019).

With the tourism industry being the city's major employer for most of its' existence, its economy heavily depends on it. In addition to the tourism sector, another major employer (although ten times smaller than the tourism industry) is the Red Sea Port. Eilat currently has two branches of Israel's major universities, 3 academic colleges, and a marine research institute, all of which offer academic attainments in only a few fields of study. The lack of employment diversification and the scarcity of academic opportunities generate a steady and persistent trend of negative migration, with most of the emigrants from Eilat being people aged 30 or older (Israeli Parlement, 2015).

The outbreak of COVID-19 in Israel in March 2020 marked the beginning of a year of dramatic events, each of which, in turn, eroded the city's financial stability. First, the domestic airport in Tel-Aviv, which served many residents of Eilat commuting to Israel’s larger metropolitan areas (Israel Airports Authority, 2015), closed. Next, a severe storm caused damage estimated at USD29 million to the city's coastal infrastructure (Ministry of Environmental Protection, 2020). Finally, the proliferation of COVID-19 cases led to a lockdown being imposed on Israeli residents, robbing Eilat of its core economic driver—the tourism sector. With a soaring 70% unemployment rate in April 2020, the city was at major risk of becoming a ghost city. In line with the taxonomy offered by Ritchie and Jiang (2019), we define the storm that hit Eilat in March 2020 as a disaster, and the COVID-19 pandemic as a crisis.

Despite its inherent disadvantages, Eilat stands out for its immense, ongoing, investment in and promotion of environmental-oriented and community-wise projects. Over the past two decades, the city has won numerous awards for its appearance and infrastructure, municipal services, landscaping projects, use of renewable energy, and investment in communal projects and facilities. To name a few, Eilat has won the highest award given by The Council for a Beautiful Israel every year since 1995 (Rashuyot, 2021); it was the first city to pass bills prohibiting the use of plastic disposable goods on its beaches in 2019 (State of Israel, 2020a); it has the highest rate of renewable energy use in Israel since 2007 (70–100% during the daytime; Eilat- Eilot Renewable Energy, 2020); it currently ranks 2nd in the Israeli Smart Cities Index (IDC, 2020); and it introduced a maverick anti-violence educational program in 2004 that is now the benchmark for all other municipalities in Israel (RIC, 2010).

The choice of an isolated city, which is not impacted by spillover effects from nearby localities, as a test case, allows for a broader discussion of the effectiveness of the proposed statistical method. This is since the sampling space in this work is largely free of statistical background noise, which may create bias due to the existence of additional metropolises and high connectivity between metropolitan areas. As such, the measurement of factors influencing the degree of potential urban contraction is carried out under “laboratory conditions”. The independence of the economy and its social systems make the city of Eilat a kind of microcosm, thus inferences from this study may be applied to the meso scale.

4. Results

Descriptive statistics for the dependent and independent variables and items from questionnaires (a)–(i) which proved statistically significant for our analysis, are reported in Table 1 .

Table 1.

Descriptive statistics for variables used in this study.

Variable	Type	Description	Mean	Std. Dev
Socioeconomic
Age	Continuous		42.57	13.71
No. of children	Continuous		1.76	1.38
Above-average income	Dummy	1 = if the respondent's income is above average	25.22%
Fixed income	Dummy	1 = if the respondent's source of income is fixed (government sector, tertiary sector, retired, etc.)	25.24%
Born in Eilat	Dummy	1 = if the respondent has lived in Eilat since childhood	43.10%
COVID-19 direct effect on income	Ordinal 1–5	The extent to which COVID-19 affected the respondent's income	4.15	1.48
Propensity to emigrate
Leave Eilat	Dummy	1 = the respondent considered emigrating from Eilat if the economic crisis continued	37.61%
Belief in Eilat's recovery ability
Transform tourism	Ordinal 1–5	The extent to which the respondent believes that the city should transform its touristic product to recover	4.36	1.02
Eilat's recovery ability	Ordinal 1–5	The extent to which the respondent believes that Eilat can recover from the COVID-19 crisis given that the damage from the storm is repaired	3.57	1.31
Perceived resilience scales
Community resilience	Continuous	On a scale from 1 (low) to 5 (high)	4.06	0.73
Self-resilience	Continuous	On a scale from 1 (low) to 5 (high)	4.12	0.81
Push factors	Continuous	On a scale from 1 (low) to 5 (high)	4.50	0.46
Satisfaction with city life	Continuous	On a scale from 1 (low) to 5 (high)	3.45	0.69

Table 2 presents the results for the hierarchical nested model. We used SPSS25 and R studio to run the models and simulations in this work. The dependent variable is a binary variable which equals 1 if the respondent reveals an intention to leave the city. All coefficients are presented in their $exp\left\{\widehat{\beta }\right\}$ form, to allow easier interpretation of the incremental contribution of each variable to the propensity to emigrate from the city.

Table 2.

Results of the hierarchical logistic nested blocks models.

Model	(1)	(2)	(3)	(4)	(5)	(6)
Const	2.53⁎⁎	3.20⁎⁎	0.63	0.89	0.67	0.45
Age	0.98⁎⁎	0.98⁎	0.98	0.98⁎	0.97⁎⁎	0.96⁎⁎⁎
Above average Income(D)	0.46⁎⁎	0.47⁎⁎	0.50⁎	0.48⁎⁎	0.46⁎⁎	0.49⁎
No. of children	0.76⁎⁎	0.77⁎⁎	0.77⁎⁎	0.78⁎⁎	0.73⁎⁎	0.77⁎⁎
Fixed income(D)		0.29⁎⁎⁎	0.46⁎⁎	0.47⁎	0.47⁎	0.47⁎
COVID-19 direct effect on income			1.37⁎⁎⁎	1.39⁎⁎⁎	1.36⁎⁎⁎	1.50⁎⁎⁎
Born in Eilat				0.57⁎⁎	0.45⁎⁎⁎	0.38⁎⁎⁎
Transform tourism					1.55⁎⁎⁎	1.67⁎⁎⁎
Eilat's recovery ability					0.72⁎⁎⁎	0.76⁎⁎
Community resilience						0.47⁎⁎⁎
Self-resilience						1.53⁎⁎
Push factors						2.02⁎⁎
Satisfaction with city life						0.55⁎⁎
Accuracy	0.75	0.69	0.68	0.69	0.74	0.77
-2loglikelihood	362.11	348.39	339.53	355.14	315.36	177.22
Nagelkerke R2	0.13	0.18	0.22	0.23	0.31	0.43
Omnibus χ2	29.32⁎⁎⁎	43.04⁎⁎⁎	51.89⁎⁎⁎	56.29⁎⁎⁎	76.07⁎⁎⁎	114.21⁎⁎⁎

NOTE: Variables are presented by entry order in each block from top to bottom. Variables denoted by a subscript (D) are dummy variables.

First, we note that the estimation results, in terms of goodness of fit and predictive power, are highly satisfactory. The accuracy of the model exceeds 70%, while the sensitivity and specificity of the model are 57.7% and 87.8% respectively. As for the -2LL statistic, it steadily decreases as blocks and terms are added to the model, indicating that the model is robust in predicting the decision to leave. As for the significance of each step of the model, omnibus test results indicate that the introduction of additional blocks into the model significantly increases the model’s chi-squared ability (χ ² values for each step within the nested models are not presented here, since variables were selected based on their conditional predictive power; hence, omnibus test results for these steps are always significant). As for the pseudo-R ² values, the Nagelkerke R ² value increases as more variables are added into the model, reaching a value of 43.3% in the final model. It is worth noting, as highlighted in Fig. 3 , that the relative improvement in all three indices sharply increases when the resilience scales are introduced into the model.

Fig. 3.

Goodness of fit and predictive power indices for the six regression models.

When examining the effect of the sociodemographic variables, younger respondents are slightly more prone to emigrating, and the more children they have the less likely they are to do so, whereas those whose income is average or less are twice as likely to leave Eilat. The effect of the source of income is also quite strong: those who do not have a steady and guaranteed income are twice as prone to emigrate. As for the direct effect of the COVID-19 crisis on respondents' income, results show that the more severe it is, the likelier it is for respondents to consider emigration. The effect of being born in Eilat is also strong; respondents who migrated to Eilat as adults are 2.5 times more likely to consider leaving the city. As for the different metrics of belief in the city's ability to bounce back from each crisis, two had contributory power to our model, with a reverse effect: the more a respondent believed that a change is needed in the tourism base of the city, the more likely the respondent was to leave, whereas the more a respondent believed in the city's ability to recover from the COVID-19 crisis, the less likely the respondent was to leave. Out of 6 resilience scales, 4 had significant contributory power to the model. As hypothesized, the economic resilience scales were found insignificant in the model and had no statistical power in explaining the propensity to migrate, in comparison to all other resilience factors. Both community resilience and satisfaction with city life had a negative effect on the propensity to emigrate, with a marginal impact of approximately 50% for a single unit increase in these scores. The self-resilience scale had a positive effect, such that a marginal increase in this score corresponds to 1.5 times more risk of leaving Eilat. As expected, the effect of the push factors scale is also positive, and more dramatically so, with twice the likelihood of leaving for each marginal increase in its score. Out of the 4 scales in our model, the community resilience one was the most powerful in terms of its influence on the decision to migrate from Eilat. The mean and median probabilities of migrating per resilience level are shown in Fig. 4 .

Fig. 4.

Predicted propensity to emigrate from eilat versus groups of resilience levels used in the regression model

*The blue Xs and red triangles denote the median and average propensity to emigrate within each unified level of resilience, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5. Discussion

Although Eilat is considered a medium-to-large city in Israel, in global terms, Eilat is a small city. So are other well-known tourism cities including Dubrovnik, Mantova, Pattaya, Dambulla, La Rochelle, Grenoble, Ibiza, Benidorm, Southampton, and many more. According to the State of EU cities report (2016), cities below 250,000 residents account for 33% of city residents in Africa, 28% in Europe, and 17% in North America. Of those small cities, the case of Eilat applies to cities that are at high risk of outmigration in times of prolonged crisis that shakes their economic basis, due to the combination of two essential elements (1) reliance on a vulnerable single-economic basis and (2) remoteness, i.e., lack of commuting possibilities. These characteristics result in structural economic vulnerability.

Our conceptual framework and empirical approach developed using the context of Eilat could be applied to those small and remote cities, that rely on a single and vulnerable economic basis (including, but not limited to tourism) around the globe who need to crucially adjust or rebuild their resilience against future disasters. Our work opens the door to other empirical studies on the subject, in other cities with these- as well as other- unique attributes. Moreover, since the city functions as a separate unit from the rest of the country, with infrastructure and facilities usually built only in large cities (such as hospitals, universities, airports, district courts, and utility companies), it can be considered as ‘a state within a state’, allowing us to examine the nexus of ‘major crisis’ and ‘urban resilience’ with no spillover effects from nearby cities, or other adjacent metropolitan areas.

Unlike other tourism cities, the isolation and remoteness of Eilat and its operation as a ‘state within a state’ helped, and are still helping it, to endure the crisis and to survive a full collapse of its economy. This was largely supported by the city's investment in several elements of resilience that proved to be highly effective in mitigating residents' intention to out-migrate. This is despite the fact that residents of remote and peripheral cities may have a stronger tendency to migrate when disaster strikes, compare to residents of large metropolitan areas who can commute and compensate for their economic loss (Pritchard & Frøyen, 2019; Yang, 2020). In the latter case, the city as an urban unit continues to exist, however, solidarity and sense of community weaken (Jakubec et al., 2019; Wickes et al., 2019). The test case of Eilat demonstrates that proactive stances in favor of improving the overall quality of urban living, enhance resilience and overall coping ability when disasters strike.

In particular, the econometric analysis affirms our three main hypotheses: (1) Job stability and economic soundness have a significant impact on out-migration; (2) the local community's belief in the city's economy depends on perceptions of its soundness; and (3) perceived community resilience and quality of life metrics have a significant and robust effect on out-migration. These results lead us to conclude that trust in— the economic system, the community's resilience, and the city's ability to provide its residents with high-quality services—is key factor in preventing out-migration. While cities may face times of crisis and distress, their residents are willing to endure such times when their connection to their city is strong. This connection extends well beyond financial considerations and includes the residents' sense of belonging, their satisfaction with city life, and the city's ability to maintain, protect, and improve their quality of life.

Upon the outbreak of COVID-19 and the consequent lockdown that started in Israel in March 2020, the city of Eilat was amid an ongoing crisis, with both the southern storm and the closing of the domestic airport in Tel-Aviv already severely affecting the city's connectivity to the rest of the country and threatening its tourism sector. The current crisis, unprecedented in scope, brought the unemployment rate in Eilat in April 2020 to 69%. With a minuscule number of COVID-19 patients recorded in Eilat, it seems that the city suffered from all the economic symptoms of the pandemic, but not the disease itself (Israel Ministry of Health, 2021). During the first lockdown, the press and social media in Eilat reflected the despair among Eilat's residents and their concern that if government support was not forthcoming within a short span of time, Eilat may not emerge from the greatest crisis in its history. While the government-approved financial aid to Eilat in April 2020 (Cabinet Secretariat, 2020; Israeli Parliament, 2020), as of August 2021, only a negligible share of this support had arrived at its destination. The uncertainty regarding if (and when) these much-needed funds will be granted, demonstrates that a gap exists between community expectations that, following disasters, governments will take responsibility and governments' actual actions. This further highlights the important role of existing urban systems in responding to such crises that may result in out-migration.

This idea is further emphasized in light of the ‘Green Islands’ initiative approved in November 2020 (the State of Israel, 2020b). A major proactive stance was taken by the local governance created enough leverage to convince the government to greenlight a unique and maverick pilot program in which Eilat is to be a controlled area where most tourism activities continue to operate, and all visitors are required to present a negative COVID-19 test upon entrance. This program is a well-adjusted response to the ‘new normal’ formed by the COVID-19 era and was made feasible by the local government's ability to adapt considering the circumstances. Although the program was short-lived, due to a third lockdown announced in January 2021, Eilat is the only city in Israel with a ready-to-use plan in place for the day after the lockdown is lifted. It is also the only city in Israel that transformed its disadvantages (e.g., remoteness and isolation) into virtues during this era. In this study, we tested for the interplay between urban resilience and catastrophe management, and their impact on out-migration. Eilat serves as a sound test case of a city that relies almost entirely on a single economic driver and is exposed to a greater risk of out-migration when experiencing an abrupt disaster.

5.1. Limitations and avenues of future research

Our study is a novel attempt to quantify the relatively new concept of urban resilience, and aims to test for it during a complicated era, in a city that is unique in terms of its properties. These facts present us with a few limitations, although they also open the door to further research in the field of the urban resilience of tourism-based economies.

The first limitation is the unique nature of our data, which may not be easily reconstructed in a different country, or even in a different city in Israel. Eilat as a case study may even be regarded as a state of its own, being remote and completely independent of most services provided by the state. When the lockdown began in March 2020, most cities experienced some disturbances in commuting and interacting with other cities; however, no city was as completely and utterly detached from the rest of the country as Eilat. This fact may heavily influence the local residents' sense of community, as well as strengthen the effect of their belief in Eilat's sole economic sector. In contrast to many other cities, residents of Eilat cannot commute to a different city in order to seek short-term job opportunities and are completely dependent on the resilience of the local economy. This, in turn, affects their propensity to turn to extreme measures such as migrating, since their ability to continue living in Eilat while working in a different sector is limited.

An additional limitation is the severity of the lockdown imposed by the government during the first outbreak of COVID-19. As a result, Israelis soon found themselves in a complete lockdown and quickly saw a plunge in daily new cases. These steps may have led respondents to believe that while the situation was severe, the local tourism industry would soon recuperate. While this was indeed the case for a short while, and Eilat experienced its most prosperous summer in years, Israel is now recovering from its third lockdown, and the positive atmosphere may have changed during this time. Hence, it is worth re-examining Eilat's perceived resilience a year into the COVID-19 crisis to re-affirm its soundness.

To the best of our knowledge, our study is the first to measure perceived urban resilience using psychometric tools. Our robust results highlight the need to further pursue quantitative studies in the field and increase the number of tools used in measuring resilience. We also call for the development of additional measures of resilience that can accommodate both perceived and measured resilience, especially in the field of tourism. Our results show the important role of perceived resilience in single-sector economies, and the more analytic tools that are developed to accommodate perceived resilience, the greater their contribution could be to local policymakers.

6. Conclusion

This work contributes to the body of literature on urban resilience in the following manner: While many studies stress the significance of economic and physical factors in urban resilience, few consider empirically the influence of social factors including social participation, sense of belonging to a community, and social inclusion on community resilience (Aldrich & Meyer, 2015; Calgaro et al., 2014). In this study we offer a quantitative measure of perceived community resilience and present a robust method for measuring its impact on out-migration. We also provide evidence for the moderating effect of intense investment in residents' quality of living, regardless of the effect of any exogenous shocks to the system. The fact that the municipality's persistent investment in the city's appearance significantly decreases the propensity to emigrate indicates that cities ought to consider adopting quality-of-life measures as part of their resilience strategies. Our work also opens the door to other empirical studies on the subject, in other cities, with other unique spatial, economic, or social attributes.

6.1. Recommendations and policy implications

Most of our recommendations below can be applied to other small cities, that rely on a single and vulnerable economic engine, and in particular on tourism.

It has been argued that small cities have a stronger potential to create a sense of community and life satisfaction than large cities, and that the connection between sense of community and life satisfaction is more robust in small cities (e.g., Prezza & Costantini, 1998). We show that realizing this potential pays off; a sense of belonging and life satisfaction has been translated into willingness to endure a major crisis which was accompanied by mass fear and despair. Thus, our key implication is that in order to mitigate citizens' inclination to leave the city when disaster strikes, it is important to build community stamina by strengthening the sense of engagement in the community, and the city's living appeal.

Having said that, it is important to create a sense of belief and trust in the city's economy via the state of its main economic engine, as they mitigate intentions to out-migrate. In the case of tourism cities, our findings are in line with the works of Romão (2020) and Weidenfeld (2018), that also found that residents' trust is gained by signaling to the local community that the industry is at the top of its game. Unlike some economic sectors which may not survive prolonged crises or those that incurred by disruptive innovation, the tourism industry proved its ability to bounce back following major crisis (e.g., after the global recession of the subprime crisis in 2008, worldwide tourism demand started to grow again Lim & Won, 2020). Residents of tourism cities, who are experienced with fluctuations of the industry following crises, expect the local economy to recuperate after the crises subsides and life returns to its course. Thus, the more trust they have in their local touristic product, the more willing they are to endure times of hardship and uncertainty, believing that their economy will emerge stronger from the other side. Therefore, strengthening the belief of residents in the city's tourism product is pivotal in alleviating out-migration.

Obviously, these should not be standalone measures. A truly resilient city cannot base its economy on a single sector alone. Cities like Eilat must diversify their economic basis and lessen their dependence on a single sector. While some cities who face a similar risk get a second chance (e.g., El Paso in Texas witnessed its soldier population decreases by half due to the decision to close Fort Bliss military installations. Eventually the decision was reversed, and the city joined the 100 Resilient Cities partnership in search of diversification opportunities [Hegar, 2019]), for other cities, there may not be a second chance. This is especially important for tourism-based cities like Eilat which attract temporary young and unprofessional workers. By offering opportunities to those temporary migrants who may wish to pursue higher education and permanent positions in the workforce, these cities can experience growth that comprises highly skilled and educated residents.

CRediT authorship contributino statement

LG conceptualized the ideas, the overarching research goals and aims, developed the conceptual framework, developed the questionnaire, collected the data, designed the methodology and performed the formal, econometrical analysis, applying statistical and mathematical techniques. She wrote the first draft and reviewed the final version.

AT helped formulating the goals and aims as well as designing the questionnaire, critically reviewed, comment and edit the first and final drafts, supervised and administered the project.

SS helped with the data curation, contributed from his knowledge on crisis management in tourism and reviewed the first draft.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Mathematical appendix

We use definitions, vocabulary, and annotations as suggested by Nelder and Wedderburn (1972) and elaborated on by Wong and Mason (1985). In order to introduce the discussed model and avoid further complications related to mathematical notation, we assume, WLOG, that the model consists of K micro variables, and a single macro variable, with J levels. Under these assumptions, the hierarchical model is in fact a series of J logit equations, using K regressors, for N observations of the dependent variable. Hence, we may start by introducing the statistical properties of each equation, and afterwards elaborate on the properties of the joint set of J equations.

We start by estimating at the micro level, i.e. estimating Y _j, an n _j × 1 vector of responses for each j level of the 1, …, J contexts. Since our response variable is dichotomous, we assume for each j-th category of the macro variable the following distribution of the i-th observation:

$$Y_{\mathit{ij}}\mid p_{\mathit{ij}}\stackrel{i.d.}{~}B\left(p_{\mathit{ij}}\right)$$

Where p _ij = ℙ(Y _ij = 1), meaning that the probability that the i-th micro observation pooled from the j-th category of the macro variable is assigned the value 1. Assuming an array of K micro variables within each level of macro variables, the matrix representation of the logit function is:

$${\omega }_{\mathit{ij}}=log\left[\frac{p_{\mathit{ij}}}{1-p_{\mathit{ij}}}\right]={\mathit{X}}_{\mathit{ij}}^T{\mathit{\beta }}_j$$

Such that $X_{\mathit{ij}}^T\in {\mathbb{M}}_{K1}$ are the K measurements of the micro variables for the i-th observation, and β _j = (β _j1,  β _j2, …β _jK)^T is the vector of micro coefficients of these variables at the j-th level of the macro variable.

At the macro level, in order to capture the variability of the J micro coefficients over each one of the K micro variables, we employ an additional set of regressors:

$${\beta }_{\mathit{jk}}={\mathit{G}}_{\mathit{jk}}^T{\mathit{\eta }}_k+{\alpha }_{\mathit{jk}}$$

$${\alpha }_{\mathit{jk}}\stackrel{i.d.}{~}N\left(0,{\gamma }_{\mathit{kk}}\right)$$

$$\forall j\in \left\{1,\dots ,J\right\}$$

$$\forall k\ne k^{\prime },\mathit{cov}\left({\alpha }_{\mathit{jk}},{\alpha }_{j^{\prime }{k}^{\prime }}\right)=\left\{\begin{array}{c}{\gamma }_{k{k}^{\prime }}\mathit{if}j=j\text{'}\\ 0\mathit{else}\end{array}\right)$$

Where G _jk are the observations on the l _k macro variables and η _k is the vector of macro regression coefficients. This means that, at a macro level, the compact notation of the system of equations is:

$${\mathit{\beta }}_j={\mathit{G}}_j\mathit{\eta }+{\mathit{\alpha }}_j$$

$${\mathit{\alpha }}_j\stackrel{i.d.}{~}N\left(\mathbf{0},\mathbf{\Gamma }\right)$$

Where ${\mathit{G}}_j=\mathit{diag}\left({\mathit{G}}_{j1}^T,\dots ,{\mathit{G}}_{\mathit{jK}}^T\right)\in {\mathbb{M}}_{\mathit{KL}},L=\sum _{t=1}^k{l}_t$, and η = (η ₁, …,  η _K)^T, and the variance-covariance matrix applies in a vector space of: $\mathbf{\Gamma }\in {\mathbb{M}}_{\mathrm{KK}},{\left\{\mathbf{\Gamma }\right\}}_{k{k}^{\prime }}={\gamma }_{k{k}^{\prime }}$.

The general case assumes a flat prior on the macro coefficients where:

$$\mathit{\eta }~N\left(\mathit{\kappa },{\mathbf{\Sigma }}_{\eta }\right),{\mathbf{\Sigma }}_{\eta }^{-1}\overrightarrow{a.s.}\mathbf{0}$$

While this assumption may not necessarily hold in the specific case discussed, the convergence property of the variance-covariance matrix allows for such modifications in the model, without departing from the assumptions of the ‘plain vanilla’ model.

We may interpret the model discussed above in one of two ways: It is either a specification of a classic discrete mixed model with fixed (η) and random (α _j) effects, or a Bayesian model with specified exchangeable priors (α _j) and standard vague priors on the fixed effects (η). In either case, the estimation procedure for the parameters is conducted using maximum likelihood estimators (MLE). This method first maximized the marginal likelihood involving the variance-covariance matrix of the model, and then used it in order to obtain estimates of the different effects.

Estimation methods for the MLE of Γ are well beyond the scope of this paper, and are nowadays performed automatically using statistical software, using numerical approximations. However, it is worth noting that once an approximation exists, the full posterior model may be estimated, as elaborated on hereafter.

We denote:

$$\mathit{\pi }\mathit{=}\left[\begin{array}{c}\mathit{\eta }\\ \mathit{\alpha }\end{array}\right]\mathit{,}\mathit{\alpha }\mathit{=}\left[\begin{array}{c}{\mathit{\alpha }}_{\mathbf{1}}\\ \mathit{⋮}\\ {\mathit{\alpha }}_{\mathit{j}}\end{array}\right]\mathit{,}\mathit{Y}\mathit{=}\left[\begin{array}{c}{\mathit{Y}}_{\mathbf{1}}\\ \mathit{⋮}\\ {\mathit{Y}}_{\mathit{j}}\end{array}\right]$$

Hence, the prior distribution of Y under logit assumptions may be re-written as:

$$f\left(\mathit{Y}|\mathit{\pi }\right)=\prod _{i,j}\frac{exp\left(-{\mathit{X}}_{\mathit{ij}}^T{\mathit{G}}_j\mathit{\eta }-{\mathit{X}}_{\mathit{ij}}^T{\mathit{\alpha }}_j\right)}{1+exp\left(-{\mathit{X}}_{\mathit{ij}}^T{\mathit{G}}_j\eta -{\mathit{X}}_{\mathit{ij}}^T{\alpha }_j\right)}exp\left\{\left(\sum _j{\mathit{Y}}_j^T{\mathit{X}}_j{\mathit{G}}_j\right)\mathit{\eta }+\sum _j{\mathit{Y}}_j^T{\mathit{X}}_j{\mathit{\alpha }}_j\right\}$$

Deriving the prior density of π from the distribution of β _j, α _j, and η, and multiplying it by the prior density of Y ∣ π, we obtain the posterior distribution of π:

$$f\left(\mathit{\pi }|\mathit{Y}\mathbf{,}\mathbf{\Gamma }\right)\propto \prod _{i,j}\frac{exp\left(-{\mathit{X}}_{\mathit{ij}}^T{\mathit{G}}_j\mathit{\eta }-{\mathit{X}}_{\mathit{ij}}^T{\mathit{\alpha }}_j\right)}{1+exp\left(-{\mathit{X}}_{\mathit{ij}}^T{\mathit{G}}_j\eta -{\mathit{X}}_{\mathit{ij}}^T{\alpha }_j\right)}exp\left\{\left(\sum _j{\mathit{Y}}_j^T{\mathit{X}}_j{\mathit{G}}_j\right)\mathit{\eta }+\sum _j{\mathit{Y}}_j^T{\mathit{X}}_j{\mathit{\alpha }}_j-\frac{1}{2}\sum _j{\mathit{\alpha }}_j^T{\mathbf{\Gamma }}^{-1}{\mathit{\alpha }}_j\right\}$$

The marginal likelihood of Γ (neglecting constant factors) is now given by:

$$\mathcal{L}\left(\mathbf{\Gamma }|\mathit{Y}\right)={\left|\mathbf{\Gamma }\right|}^{-\frac{J}{2}}\int f\left(\mathit{\pi }|\mathit{Y},\mathbf{\Gamma }\right)d\mathit{\pi }$$

WLOG, we assume a single block model with K = {1, 2, …,  J} candidate regressors. The pseudo- algorithm for selecting a subset K′ ⊆ K is:

• a.Estimate the ‘null model,’ where no regressors are introduced into the model, and estimation of the intercept is based on the dependent variable’s 1st and 2nd central moments.
• b.Test for the likelihood ratio of the model using each of the J regressors separately.
• c.
  Choose j ^∗ ∈ K such that:

  $$j^{\ast }=\underset{j\in K}{\text{argmax}}\left\{l\left(\widehat{\beta }\right)-l\left(\widehat{{\beta }_{-j}}\right)\right\}$$

Where $\widehat{\beta }$ is the unconstrained MLE, s.t.: $\widehat{\beta }=\underset{\beta }{\text{argmax}}l\left(\beta \right)$, and l(∙) is the log likelihood function, which, in its simplest state, reduces to: $l\left(\bullet \right)=ln\left(\genfrac{}{}{0pt}{}{n}{k}\right)+\mathit{kln}\left(p\right)+\left(n-k\right)ln\left(1-p\right)$.

• d.Test for the significance of the LR calculated (assuming $\mathit{LR}\stackrel{d}{\to }{\chi }^2$). If PV is sufficiently small, introduce regressor j ^∗ into the model.

Repeat steps b–d for subset K _(−j^∗). Stop when PV exceeds the desired threshold.