The Economic Impact of Lockdowns: A Persistent Inoperability Input-Output Approach

: The COVID-19 pandemic has forced governments around the world to implement unprecedented lockdowns, mandating businesses to shut down for extended periods of time. Previous studies have modeled the impact of disruptions to the economy at static and dynamic settings. This study develops a model to fulﬁl the need to account for the sustained disruption resulting from the extended shutdown of business operations. Using a persistent inoperability input-output model (PIIM), we are able to show that (1) sectors that su ﬀ er higher levels of inoperability during quarantine period may recover faster depending on their resilience; (2) initially una ﬀ ected sectors can su ﬀ er inoperability levels higher than directly a ﬀ ected sectors over time; (3) the economic impact on other regions not under lockdown is also signiﬁcant.


Introduction
The COVID-19 pandemic continues to disrupt the world as the number of cases continues to escalate. While some countries have managed to bring the outbreak under control in the past months, others are still experiencing a continuous increase in the number of new cases. Several countries in Europe are now experiencing a second wave. In the absence of a vaccine, there is a need to "flatten the curve" to avoid overwhelming each country's healthcare system (Flaxman et al. 2020). Governments have adapted non-pharmaceutical interventions (NPIs) to control the transmission of the disease. Extreme measures such as lockdowns and mandatory business and school closures have been implemented in most countries (Ullah and Khan 2020). In addition to causing direct economic losses during the closure, the extended lockdowns pose the socioeconomic risk of irreversible closure of businesses, with the attendant ripple effects. Travel restrictions remain (International Air Transport Association 2020), causing airlines to incur losses. Tourism-intensive economies have experienced increasing unemployment resulting from the decline in tourism demand (United Nations Conference on Trade and Development 2020). Commercial establishments have observed mandatory closures during the lockdown period. Limited availability of public transportation services has caused mobility and accessibility problems for consumers and workers alike (Suman et al. 2020). Amid school closures, businesses largely dependent on students and school employees as their clientele, especially in college towns, may have to close (Wong 2020). In the United States alone, a total of 72,842 establishments listed on Yelp have permanently shut down (Pesce 2020). Close to two-thirds of small businesses, which account for nearly half of American employment, are at risk of permanent closure resulting from the Santos et al. (2013) considered the impact of the 2009 H1N1 that had two waves over a 42-week interval. These studies were able to identify the critical economic sectors during a pandemic. El Haimar and  proposed a stochastic recovery model that factors inoperability and economic losses as risk metrics with a possible surge in the pandemic. The current pandemic has gone on longer than imagined, with a global scope and no commercially available pharmaceutical intervention to date. The world has resolved to adapt non-pharmaceutical measures that have severely affected the global economy.
This work develops a persistent inoperability input-output model (PIIM), which models the reduced capacity of sectors that persist during a lockdown period mandated by the government. Unlike previous models, the PIIM will provide insights on the impact of prolonged inoperability in various sectors of the economy. This model builds on the input-output model as discussed in Section 2. Section 3 introduces the PIIM model. The PIIM models the sectoral impacts of persistent disruptions to the economy as a whole and does not account for differences of impact on individual firms. Section 4 provides a demonstration of how the model can be implemented using the Philippines as a case study. Section 5 presents the conclusions and areas for future research.

Input-Output Foundations
Input-output (I-O) modeling has been used to capture the interdependencies that ripple through the economic sectors across an economy. Leontief (1936) developed a system of linear equations to represent the transaction flows between each sector in the economy as given in Equation (1): where x is the output vector, A is the technical coefficients matrix and c is the final demand vector. The total output vector, x, is the sum of the intermediate consumption, Ax, and final demand, c. Haimes and Jiang (2001) developed a physical representation of the I-O model for critical infrastructure systems with the introduction of inoperability, or the inability of a system to operate at its full capacity. The initial inoperability input-output model (IIM) was reformulated into a demand-reduction IIM that can be used with standard I-O tables expressed in monetary terms (Santos and Haimes 2004); this step allowed the IIM concept to be operationalized and calibrated using readily available statistics. The demand-reduction IIM provides two useful metrics for estimating the impact of an external disruption on an economic system-inoperability and economic loss. Inoperability is specified as: where q is the inoperability vector, A * is the interdependency matrix, and c * is the initial demand perturbation vector. The inoperability vector is defined as the vector of normalized economic losses and can be derived as q = [diag(x)] −1 x −x , where x is the as-planned level of output andx is the degraded level of output and its elements have values between 0 and 1. The interdependency matrix, A * , contains elements, a * ij , which show the additional inoperability that sector i contributes to sector j. It can be derived as The product of the interdependency matrix and the inoperability vector, A * q, yields the intermediate inoperability. The initial demand perturbation vector, c * , is the normalized degraded demand vector derived as c * = [diag(x)] −1 c −c , where c is the as-planned level of final demand andc is the degraded level of final demand resulting from the exogenous system disruption. Economic loss is computed using Equation (3): where EL i is the economic loss of sector i resulting from the total inoperability level, q i , multiplied by the as-planned output level, x i . These two metrics differ such that the inoperability metric is a dimensionless metric that measures the functional impact on the economic system while the economic loss yields the monetary value lost resulting from the external disruption. Lian and Haimes (2006) extended the IIM to account for time dynamics and recovery. They introduced the dynamic inoperability input-output model (DIIM) which is specified as: where q(t + 1) is the inoperability vector at time t + 1, and K is the industry resilience coefficient matrix. K is a diagonal matrix which has elements, k ii , that represent the inherent ability of sector i to recover from the disruption. Despite the significant number of publications that extended the theory and methodology in support of the inoperability-based IO model, it has not become immune to criticisms pertaining to issues ranging from novelty (Dietzenbacher and Miller 2015) to plausibility (Oosterhaven 2017). Nonetheless, the concept of inoperability-which has been integrated to the basic I-O model-has served as the unprecedented bridge between traditional economic analysis and other fields like engineering reliability and disaster risk management. Okuyama and Yu (2018) have defended the IIM and emphasized its merits, particularly in the context of disaster resilience modeling. The practicality and intuitiveness of the IIM have paved the way to a myriad of articles that continue to explore and extend inoperability-based theories and applications. Miller and Blair (2009) discuss the simple location quotient (SLQ) approach to derive regional I-O tables. Most countries collect I-O data at the national level, and SLQ is a way to estimate regional I-O tables using location-specific economic data, such as industry production outputs. SLQ for region r is defined as: where SLQ r i is the simple location quotient for sector i in region r, x r i is the total output of sector i in region r, x r is the total output of all sectors in region r, x n i is the national total output of sector i, and x n is the national total output of all sectors. The elements of the regional technical coefficient matrix, a rr ij , can be obtained by: where a n ij is the technical coefficient from the national input-output table. When sector i in region r is self-sufficient or an exporter of goods for other regions, the regional technical coefficient for sector i is assumed to be the same as the technical coefficient at the national level. However, if it is not self-sufficient and relies on other regions to satisfy its demand for sector i, the national technical coefficient is multiplied by the SLQ for sector i.
The interregional trade component is accounted for through the introduction of the interregional trade coefficients matrix, T, which is written as: where each submatrix T rs shows the proportional consumption of region s of commodities produced in region r with p number of regions. Each submatrix is an n × n diagonal matrix with the ith element specified as: where t rs i is the proportion of commodity i consumed by region s produced by region r, z rs i , in relation to the total consumption of commodity i by region s produced by all regions, y s i . The multiregional input-output model is defined as: and this can be extended to account for inoperability (Crowther and Haimes 2010) as: where q is an nm × 1 vector of inoperability, T * is an nm × nm matrix computed as . . x m , A * is an np × np matrix with diagonal submatrices of n × n dimension interdependency matrices for m regions and c * is an nm × 1 vector of demand perturbation vector.
The dynamic representation of the multiregional inoperability input-output model (MRIIM) is given as:

Persistent Inoperability Input-Output Modeling
Community quarantines and countries under lockdown have forced several sectors in the economy to remain inoperable at certain levels for a period of time. This means that inoperability remains constant for sectors initially affected by the lockdown. This paper measures the persistency of the inoperability through Equation (12): where q p is the persistent inoperability vector, c * (0) is the demand perturbation at the onset of the community quarantine or lockdown, and d is the number of days that the lockdown or community quarantine is enforced. The persistent inoperability vector quantifies the inability of a sector to recover despite its inherent ability to cope with disruptions. Sectors that should have recovered, but are unable to do so, are said to be in a state of persistent inoperability. Equation (13) illustrates how persistence of inoperability is introduced into the dynamic MRIIM model where t ≤ d. The persistent inoperability vector is added to the dynamic MRIIM in Equation (11) to ensure that inoperability for the initially affected sectors remain at a constant level. It can be noted that the first part of Equation (13) is the same as the dynamic MRIIM model specified in Equation (11). Hence, Equation (13) can be rewritten as: When the lockdown or community quarantine is lifted, t > d, the persistent inoperability becomes a zero vector, thereby reverting to the dynamic MRIIM formulation. Economic sectors are allowed to recover as businesses strive to revert back to business-as-usual levels. However, if a more relaxed lockdown is implemented, another lockdown period is introduced, d 2 , and As more lockdown variations are introduced at different time periods, more levels of persistent inoperability can be observed.

Case Study
The Philippines is one of the countries that implemented a lockdown to control the spread of the COVID-19 disease. Most of the cases during the start of the pandemic were from the National Capital Region (NCR). The NCR is the political and economic hub of the country. Although it occupies only 0.2% of the country's total land area, it accounts for 37% of the USD 390 billion national gross domestic product (GDP) (Philippine Statistics Authority 2020a) of a country with a population of 13.8 million (Philippine Statistics Authority 2019a). Thus, an enhanced community quarantine (ECQ) was imposed for the NCR from 15 March to 15 May 2020; this ECQ was then relaxed to a modified enhanced community quarantine (MECQ) from 16-31 May 2020. Economic losses mounted as the lockdown extended for much longer than originally planned. With the worsening economic situation, the government decided to allow more businesses to operate under a general community quarantine (GCQ), which was implemented from 1 June until 3 August 2020. The increasing number of COVID-19 cases in the region forced the government to revisit its lockdown policy, and it reverted back to a MECQ for the period of 4-31 August 2020. Although the number of COVID-19 cases continued to increase, the government decided to relax the quarantine restrictions back to GCQ for the period of 1 September until 31 October 2020. Table 1 presents the definition of the different quarantine scenarios as given in the guidelines published by the Philippine Inter-Agency Task Force for the Management of Emerging Infectious Diseases.

Quarantine Scenario Definition
ECQ "Implementation of temporary measures imposing stringent limitations on movement and transportation of people, strict regulation of operating industries, provision of food and essential services and heightened presence of uniformed personnel to enforce community quarantine protocols" (Philippine Inter-Agency Task Force for the Management of Emerging Infectious Diseases 2020).
MECQ "Transition phase between ECQ and GCQ, when the following temporary measures are relaxed and become less necessary: stringent limitations on movement and transportation of people, strict regulation of operating industries, provision of food and essential services and heightened presence of uniformed personnel to enforce community quarantine protocols" (Philippine Inter-Agency Task Force for the Management of Emerging Infectious Diseases 2020).

GCQ
"Implementation of temporary measures limiting movement and transportation of people, regulation of operating industries, and presence of uniformed personnel to enforce community quarantine protocols" (Philippine Inter-Agency Task Force for the Management of Emerging Infectious Diseases 2020).
The prolonged lockdown led to a 16.5% drop in national GDP in the second quarter of 2020, with a large share of the losses being incurred in the NCR (Philippine Statistics Authority 2020b). The NCR services sector, which includes transportation, trade, finance, real estate, private services and government services sectors, is a major contributor to the national economy, accounting for 52.82% of the Philippine services GDP (Philippine Statistics Authority 2019b). Furthermore, NCR's share of the trade sector is 62.19% of national trade (Philippine Statistics Authority 2019b). Therefore, the lockdown measures imposed on the NCR have had a significant impact on the nation's economy.
This study uses a 14-sector Philippine I-O table that is disaggregated into two regions, the NCR and the rest of the Philippines (ROP) 1 . The regional acronyms are used as prefixes to the sector codes provided in Table 2 as identifiers. Communications and Storage S10 Trade S11 Finance S12 Real Estate and Ownership of Dwelling Palaces S13 Private Services S14 Government Services Initial inoperability estimates were based on National Economic and Development Authority (2020) estimates of the impact on GDP. The affected sectors are NCR's manufacturing, construction, land transportation, water transportation, air transportation, trade, finance, and private services sectors. Figure 1 illustrates the levels of persistent inoperability sustained by the initially affected economic sectors. It can be observed that during the initial ECQ, the persistent inoperability level was very low. This was mainly because the lockdown was preventing the affected sectors from recovering. The level of inoperability that persisted on a daily basis was only the supposed recovery for that day. However, upon allowing some sectors to reopen, recovery was not instantaneous and sectors suffered higher levels of inoperability compared to what would be expected from the more relaxed lockdown. Hence, the level of persistent inoperability was the difference between the higher level of inoperability that it was recovering from and the more relaxed lockdown inoperability level. This difference represents an "economic inertia". For example, since the initial inoperability that the NCR trade sector experienced was quite high, the persistent inoperability that it suffered during the first MECQ was initially higher relative to other sectors. During the first GCQ period, the NCR trade sector had the fastest reduction in persistent inoperability, as it continued to recover. This means that sectors are still experiencing inoperability as a residual impact of the previously tighter lockdown. During the second MECQ in August 2020, persistent inoperability spiked for several sectors due to the tighter lockdown; however, this was immediately flattened as the level of inoperability that persisted was only the supposed recovery for that day as in the case of the initial ECQ scenario. Hence we can see that as coming from tighter forms of lockdowns, the persistent inoperability is evident and will take time to decline. If there was no lockdown or the previous type of lockdown was more relaxed or, as in the case of the ECQ from 16 March-15 May 2020 and the MECQ from 4-31 August 2020, persistent inoperability would remain flat during that period. Each sector has a different rate of recovery which is attributable to its inherent resilience and at the same time its interdependence with other sectors. For example, the NCR manufacturing sector has the highest industry resilience coefficient; however, Figure 1 shows that the NCR manufacturing sector exhibited the slowest rate of recovery compared to the rest of the affected 1 The data are available upon request from the authors. sectors. NCR manufacturing has a strong dependence on other sectors; thus, the inoperability from the other sectors caused inoperability to persist for longer periods as evidenced in the graph. On the other hand, the NCR water transportation sector has the lowest industry resilience coefficient; however, it does not depend too much on other sectors for inputs to provide services, thus it exhibited the fastest rate of decline in terms of persistent inoperability.  Figure 2 presents the ten most affected sectors in terms of inoperability. It can be seen that sectors most affected by the lockdown already had high inoperability levels at the onset and they are unable to recover until lockdowns are relaxed. It can be noted that all sectors in this graph belong to the NCR. Although there is continuous demand for goods produced by the NCR manufacturing sector, raw materials may not necessarily be readily available as some firms may be sourcing raw materials from abroad and the closures of banks delays release of these items from ports (Jiao 2020). The NCR air transportation sector, which connects the Philippines to the rest of the world as it houses the country's main international airport, has canceled and reduced the number of flights. In addition, the public transportation sector is operating at reduced capacity with less passenger demand and with mandatory reduced vehicle occupancy as a social distancing measure. Local public utility vehicles such as "jeepneys" which provide a transportation service on local routes, are not allowed to operate during ECQ and MECQ. Lack of access to public transport has hindered workforce mobility, causing further disruption even in partially operational sectors (Rey 2020).  Figure 2 presents the ten most affected sectors in terms of inoperability. It can be seen that sectors most affected by the lockdown already had high inoperability levels at the onset and they are unable to recover until lockdowns are relaxed. It can be noted that all sectors in this graph belong to the NCR. Although there is continuous demand for goods produced by the NCR manufacturing sector, raw materials may not necessarily be readily available as some firms may be sourcing raw materials from abroad and the closures of banks delays release of these items from ports (Jiao 2020). The NCR air transportation sector, which connects the Philippines to the rest of the world as it houses the country's main international airport, has canceled and reduced the number of flights. In addition, the public transportation sector is operating at reduced capacity with less passenger demand and with mandatory reduced vehicle occupancy as a social distancing measure. Local public utility vehicles such as "jeepneys" which provide a transportation service on local routes, are not allowed to operate during ECQ and MECQ. Lack of access to public transport has hindered workforce mobility, causing further disruption even in partially operational sectors (Rey 2020).
Sectors that were not initially affected by the quarantine scenarios such as NCR electricity, gas, and water, and NCR communications sectors, have experienced increasing levels of inoperability as the lockdown has progressed. As the labor force shifted to working from home and students shifted to online learning, these sectors suffered an unprecedented surge in demand for their services. NCR has experienced rotating power outages during the lockdown period (Lectura 2020). Internet connectivity was also disrupted due to a network logjam resulting from the shift to telecommuting and online learning. Business process outsourcing (BPO) firms have made similar arrangements for their employees, going as far as purchasing desktops and providing loans to their employees. However, international clients have slowly been pulling out due to a business slowdown in their own countries, which may affect employment (Macaraeg 2020). houses the country's main international airport, has canceled and reduced the number of flights. In addition, the public transportation sector is operating at reduced capacity with less passenger demand and with mandatory reduced vehicle occupancy as a social distancing measure. Local public utility vehicles such as "jeepneys" which provide a transportation service on local routes, are not allowed to operate during ECQ and MECQ. Lack of access to public transport has hindered workforce mobility, causing further disruption even in partially operational sectors (Rey 2020).  The healthcare sector has also experienced inoperability due to different reasons as front-line personnel are continuously exposed to high viral loads, and are thus at a disproportionately higher risk of contracting COVID-19. Even if they do not contract the disease, they may need to undergo self-isolation as persons under monitoring (PUM) or patients under investigation (PUI), thus removing them from the active workforce. In addition, if a member of their household is classified as a PUM or PUI, or worse, contracts the disease, they may have to tend to personal matters, which contributes to absenteeism (Santos et al. 2014). Other essential sectors that have remained open, such as supermarkets, banks, and restaurants, among others, are faced with similar predicaments. This situation is alarming as the NCR provides more than one-third of total employment in the Philippines. Table 3 provides a summary of the NCR employment share of national employment for each sector in 2018.  Figure 3 presents the ten most affected sectors in terms of economic losses. The overall economy of the Philippines is estimated to lose PHP 2.1 trillion (approximately USD 42 billion) resulting from the pandemic, accounting for ripple effects. The NCR trade, NCR manufacturing and NCR private services sectors are the hardest hit sectors, accounting for 29.19%, 18.03%, and 13.11% of total economic losses respectively. In terms of economic loss, the ROP land transportation sector and ROP agriculture sector are also significantly affected. With the closure of NCR from incoming and outgoing travel, the ROP land transportation sector has been affected as provincial bus trips are cancelled. In addition, ROP agriculture is significantly affected as traders are unable to go to the trading posts to purchase produce which is largely sold to the NCR, which resulted in farmers throwing out their truckloads of products (Soriano 2020). The inoperability in the NCR economy results from a mix of supply reduction and demand reduction perturbations. Supply reduction perturbations result from supply chain disruptions, as well as workforce reduction due to either travel restrictions or absenteeism. Demand reduction perturbations result from a drop in total purchases of goods resulting from the ECQ. The combination of multiple perturbations increases the complexity of modeling and analyzing the economic impacts associated with scenarios with persistent inoperability, like the prolonged lockdown in the Philippines. Furthermore, these estimates do not include impacts on the informal sector of the NCR economy, but it is plausible to assume that similar losses are incurred there as well. The Philippines has implemented Republic Act 11,469 through formulating the Philippine Program for Recovery with Equity and Solidarity (PH-PROGRESO) which includes programs for various economic sectors (Philippine Department of Finance 2020). However, there is a need to expand the coverage of such programs as required.

Conclusions
This work has developed a model to estimate the impact of varying degrees of lockdowns on the sectors in an economy. Results show the degree by which each sector is affected and how much economic loss they incur. Furthermore, we have illustrated that inoperability can persist over time despite the implementation of less stringent lockdowns. Such information will be essential in developing strategies for recovery. This includes developing measures such as extending employment support through businesses to ensure employment retention post-pandemic and optimizing the stimulus packages across various sectors. Future research can explore the integration of our lockdown scenario modeling with optimization models (Baghersad and Zobel 2015;Aviso et al. 2015) to ensure efficient allocation of stimulus packages across sectors. Governments are faced with the problem of choosing between suppressing the number of cases and pursuing economic survival. Despite efforts in implementing social distancing in public places, most developing countries have high population density in places with limited access to clean water. This poses further challenges in controlling the spread of the virus. Workplace reassignment within a firm can The inoperability in the NCR economy results from a mix of supply reduction and demand reduction perturbations. Supply reduction perturbations result from supply chain disruptions, as well as workforce reduction due to either travel restrictions or absenteeism. Demand reduction perturbations result from a drop in total purchases of goods resulting from the ECQ. The combination of multiple perturbations increases the complexity of modeling and analyzing the economic impacts associated with scenarios with persistent inoperability, like the prolonged lockdown in the Philippines. Furthermore, these estimates do not include impacts on the informal sector of the NCR economy, but it is plausible to assume that similar losses are incurred there as well. The Philippines has implemented Republic Act 11,469 through formulating the Philippine Program for Recovery with Equity and Solidarity (PH-PROGRESO) which includes programs for various economic sectors (Philippine Department of Finance 2020). However, there is a need to expand the coverage of such programs as required.

Conclusions
This work has developed a model to estimate the impact of varying degrees of lockdowns on the sectors in an economy. Results show the degree by which each sector is affected and how much economic loss they incur. Furthermore, we have illustrated that inoperability can persist over time despite the implementation of less stringent lockdowns. Such information will be essential in developing strategies for recovery. This includes developing measures such as extending employment support through businesses to ensure employment retention post-pandemic and optimizing the stimulus packages across various sectors. Future research can explore the integration of our lockdown scenario modeling with optimization models (Baghersad and Zobel 2015;Aviso et al. 2015) to ensure efficient allocation of stimulus packages across sectors. Governments are faced with the problem of choosing between suppressing the number of cases and pursuing economic survival. Despite efforts in implementing social distancing in public places, most developing countries have high population density in places with limited access to clean water. This poses further challenges in controlling the spread of the virus. Workplace reassignment within a firm can be done using optimization modeling to minimize the impact of prophylactic absenteeism during crisis conditions (Aviso et al. 2018). Extensions on analyzing the impact on supply chain networks across countries (Arto et al. 2015;MacKenzie et al. 2012;Lei et al. 2019;Yu et al. 2020a) may also be explored. This can be coupled with the reassessment of public health expenditure programs (Eissa 2020) in managing the impact of the pandemic on the economy. Further research should be done to estimate the impact of social security programs and stimulus packages of governments to ensure minimal impact on the welfare of their citizens.
Vaccination has been identified as a cost-effective measure to control the spread of pandemics and to minimize economic losses (Prosser et al. 2011). With the recent news of vaccines with significantly high efficacy (Cohen 2020), future research should integrate efficient production and distribution of the vaccine globally (Yu et al. 2020b). This can contribute to mitigating further economic damages and pushing the economy back on track to recovery.