Modeling of Complex Non-Full-Availability Systems

This article presents an analytical model of complex non-full-availability telecommunications systems. The high degree of accuracy of the model is demonstrated by a comparison with the results of simulation experiments. Due to the introduction of an availability parameter, this model may be used in the future for analyzing real systems, such as, for example, cloud computing infrastructure. This will be possible provided that the function combining the physical structure of the system and the availability parameter is specified. This problem will be addressed in our future work and will constitute the next stage of research undertaken by the authors. Keywords—analytical model, availability, non-full-availability systems.

Introduction
From the traffic engineering perspective, telecommunications and computer systems that are currently under development are characterized by a peculiar but rarely noticed property, namely they constitute non-full-available systems. Non-full-availability is based on the fact that calls arriving at the input end of a system have no access to all of the system's resources. Instead, they only have access to a certain subset of those resources. In the literature, this subset is referred to as availability [1], [2]. Basically, systems of this type have existed in telecommunications from the very inception of the domain. Over time, however, the source of non-full-availability has changed. Originally, non-fullavailability resulted from the limited nature of telecommunication networks' resources, e.g. outputs of communications networks and telephone exchange systems, where the number of such outputs exceeded the capacities of output groups. Today, non-full-availability of a system results primarily from the individual traffic management mechanisms that are used by networks operators to optimize the use of the available resources (e.g. resource reservation, compression, priorities and queuing) and, very frequently, from the wide area or distributed nature of the physical infrastructure. Non-full-availability of a system may be illustrated with an example of a dynamic resource reservation system [3], [4]. Its operating principle is based on the system's occupancy limit (boundary) adopted which, when exceeded, causes the resources of the system to be available only to certain pre-defined calls, at the expense of the remaining calls.
Concurrent use of a number of mechanisms means that the degree of dependence between the amount of resourcesavailable to a given call and the system occupation level becomes even higher. Physical infrastructure of a cloud computing system may serve as the best example of a modern non-full-availability solution. A high number of devices, the distributed nature of the system, the mechanisms used to optimize of the utilization of resources in cloud computing, the mechanisms that guarantee safe provision of the services, the algorithms employed to reduce power consumption, as well as the nature of the services offered [5]- [8] all make it possible for new calls to be supported and serviced by the resources in the cloud. There is a number of models available in the literature concerned with analyzing current telecommunications systems. As a rule, however, these models deal with a single traffic management mechanism, while a real system is approximated by a model of a full-availability system (historically known as a full-availability group model), e.g. shown in [9]- [15]. Models of non-full-availability systems, such as the limited-availability group model (LAG) or Erlang's ideal grading (EIG), are used for that purpose less frequently [16]- [19]. Non-full-availability systems belong to a group of the socalled state-dependent systems [20], [11]. This dependence may result from the existence of the function that relates the number of busy resources in a system to the calls that arrive at the input, or, alternatively, dependence between the number of occupied system resources and the decision to admit a new call for service may exist. In the former case, we deal with systems with a state-dependent call stream. In the latter case, we deal with systems with a state-dependent service process. [20] presents general rules applicable to modeling this type of systems with the use of a one-dimensional Markov process, after the so-called state transition coefficient has been taken into account. This coherent methodology makes it possible to model very complicated systems as well, providing that the relevant transition coefficients may be determined. This article presents an analytical model of a complex nonfull-availability system. The structure of the system shows some non-full-availability features, i.e. it is composed of a group of separated resources that are non-full-availability systems themselves. It is the authors' opinion that the model may be relied upon, in the future, to model the physical infrastructure of cloud computing solutions. The authors of the article are currently conducting research on the conditions under which this may become feasible. The remaining part of the article is structured as follows. Section 2 presents the main assumptions for modeling statedependent systems. Section 3 provides a description of the structure of this complex non-full-availability system and the corresponding analytical model proposed. On account of the approximate nature of the model, Section 4 presents a comparison between the results obtained with the analytical model and the results obtained during simulation experiments. The article is summarized in Section 5.

Resources and Traffic in Telecommunications Networks
Today's telecommunications networks are primarily packetswitched networks based on the IP protocol. The analysis of a network at the packet level is complicated and time consuming. Papers [9], [21], [22] prove that it is possible to analyze packet networks at the call level, where calls correspond to packet streams (with constant or variable transmission rates) that are sent between a given source and the receiver. Thus, the network traffic represented has the properties of Poisson traffic flow. Thanks to this operation, it is possible to express the amount of resources of the system in dimensionless units, i.e. in resource allocation units (AU). This transition from dimensional units to dimensionless units is known as discretization. The said operation increases versatility of models, since the scope of their operation is not limited to the analysis of the link bit rate (in bps), but is expanded to include other system resources, such as storage memory, RAM memory or processors [23]. The above-mentioned discretization process will be illustrated with an example of a network resource (e.g. a link between routers) with the capacity of C bps. This resource services constant bit rate (CBR) streams and variable bit rate (VBR) streams. In the discretization process, the VBR streams are represented by streams with a constant bit rate, with the transmission speed equal to the so-called equivalent bandwidth (EB). EB for individual call classes may be determined either on the basis of the maximum bit rates or on the basis of heuristic algorithms, in line with the principle that the result of a VBR call service in the network is the same as the result of a CBR call service with the bit rate equal to EB [24]. Most frequently, these algorithms take into account such traffic parameters and networks system parameters as the maximum and the average bit rate of a call, bit rate variance, acceptable delay, jitter and quality of service (QoS) parameters adopted for a given service, etc. It is worth emphasizing at this point that the determination of the EB value on the basis of the maximum bit rates makes it possible to analyze the system under consideration for the worst conditions, i.e. for the highest offered traffic. The knowledge of EB values (the manner in which EB is determined for individual packet streams is beyond the scope of the present article) for all traffic classes offered to the system makes it possible to determine the resource allocation unit of the system, as the traffic class is composed of all packet streams with similar parameters. The general assumption is that 1 AU is equal to the greatest common divisor of the equivalent bandwidths of all traffic classes that are offered to the system: where c i (bps) is the equivalent bandwidth of class i, whereas m is the number of traffic classes offered to the system. The parameter c AU determines the bit rate per a single AU.
After the determination of c AU it is possible to express the capacity of resource V and the demands of individual traffic classes t i in the AUs, where C is the resource capacity: Call classes are described by: this parameter characterizes the frequency at which new calls arrive, this parameter characterizes call service time, • a i average intensity of traffic of class i (in relation to calls): To simplify the analysis of modern networks, an additional assumption may be made that 1 AU corresponds to the bit rate of 1 bps (or 1 kbps): This choice of the AU value causes the demands of individual classes -Eq. (3) and the capacity of the system -Eq. (2) to be equal, in terms of their value, with the demanded bit rates and the total capacity of the system:

General Model of State-dependent Systems
The general method for modeling state-dependent systems by a one-dimensional Markov process is presented in [20]. The dependence of a system on its state (i.e. resource occupancy) may be a result of the following: • limited number of traffic sources -in this case, we deal with systems with a state-dependent call stream -a single source can generate a new call only when it is unoccupied. As a consequence, the ration the number of calls that arrive at the input of the sys-between tem within a given time unit and the number of calls admitted earlier is changed. For instance, for Engset traffic, this number decreases along with an increase in the number of occupied traffic sources; • system structure -in this case, we deal with a system with a state-dependent service stream. The structure of the system and the call service process may cause only a part of the resources to be available, just as it is the case with switching networks, for example. The structure of the connections within the network and the calls that are currently serviced may then affect the setting up of a connection between a free input and a free output of the network, rendering it impossible; • algorithms operating the call admission control function -similarly as in the former case, we deal with a state-dependent service stream. Call admission control algorithms may prevent new calls from being serviced under certain operating conditions, e.g. based on a dynamic resource reservation in relation to the total number of busy AUs in the system.
In state-dependent systems, the transition between states depends not only on the parameters λ i and µ i , but additionally on the so-called conditional transition coefficient σ i (n), where i is the number of a call classes, and n is the number of busy AUs in the system. This is presented, in a simplified form, in Fig. 1. It is proved in [20] that in the case of systems in which state-dependence is the result of a number of different and independent sources, the total conditional transition coefficient may be determined in the following way: where: • [σ i (n)] R is the conditional transition coefficient of class i in occupancy state n, resulting from the properties of a call stream of this class, • [σ i (n)] A is the conditional transition coefficient of class i in occupancy state n, resulting from the structure of the system, • [σ i (n)] P is the conditional transition coefficient of class i in occupancy state n, resulting from the function of new call admission in the system.
The knowledge of the values of all σ i (n) parameters makes it possible to determine occupancy distribution within the system with the use of the following formula [20]: where [P n ] V is the probability of occupancy n AUs in the system.

Model of a Complex
Non-full-availability System

Structure of Complex Non-full-availability Systems
The analytical model proposed in the article was developed for a system that is presented, in its simplified form, in Fig. 2. The assumption was that the system was composed of k separated resources (subgroups) with the capacity of f AUs. The total capacity of the system is: The division of all AUs within the system into separated full-availability resources renders the system a non-fullavailable solution. The literature of the subject describes its analytical model, known as the limited-availability group model [25]. In this paper, we assumed that each of k separated resources shows the properties of a non-fullavailability system. Non-full-availability of a single separated resource may stem from its internal structure or from the call admission control algorithm. The literature presents a small number of analytical models pertaining to non-full-availability systems, e.g. Palm-Jacobeus formula, modified Palm-Jacobeus formula or the EIG model [1].

Fig. 2.
Simplified diagram of the structure of a complex nonfull-availability system.
In analytical models, non-full-availability of resources is characterized by a parameter knowns as availability d i (1 ≤ i ≤ m) [1], [26]. This parameter determines the number of AUs in the system to which calls of a given class have access. It is unique for each class of calls (and it may assume different values for each of those classes), while its value is based on the structure of the system and on the call admission control mechanism. It should be stressed that if calls of class i have availability equal to d i AUs of the system, this does not necessarily mean that all of them have access to the same AUs. Typically, they have access to different AUs of the system. Calls or, to be more precise, their sources that have access to the same AUs in the system are called a load group. In EIG, the number of load groups (for calls of class i) is equal to the number of choices of d AUs from V : In real world systems, this number is typically lower. Figure 3 shows a simple single-service system with the capacity of 3 AUs and availability of d = 2 AUs that illustrates the idea of availability and presents an example of a blocking state. The assumption is that in the complex non-full-availability system under consideration, new calls are admitted according to the following algorithm. Assume that a call of class i that demands t i AUs for service arrives at the input to the system. In the first instance, the number of unoccupied AUs in the entire system is checked. If the number of free AUs in the entire system is lower than t i AUs, then the call is lost. When this is not the case, a further check is performed to verify whether in a single separated resource there exist at least t i unoccupied AUs. This condition is particularly important, as calls may be supported only by AUs that belong to one separated resource. If such resources are not available, then the call is rejected. In the case where the system has separated resources that have at least t i free AUs available, one of the available resources is chosen randomly and the system checks whether the resource may admit the call under consideration for service. The absence of a possibility to admit a new call may result from the fact that this new call has no access to (i.e. cannot occupy) free AUs in the resource. If the selected separated resource does not offer such a possibility, then the next one is selected. In the worst case, all k separated resources will be checked. If none of k resources can service the new call, the call is lost again.

Analytical Model
To determine occupancy distribution in the system under consideration, as given by Eq. (8), and, in consequence the blocking probability, it is necessary to determine the values of the conditional transition coefficient σ i (n) for all call classes offered and for all system occupancy states. The state-dependence of the service stream and, consequently, the non-full-availability in the system under consideration, results from two factors: • all AUs in the system are divided into k identical separated resources (subsystems), while a call may be completely serviced by one separated resource only, • each separated resource has limited access to its own AUs which leads, in consequence, to a situation in which -despite a sufficient number of free AUs -the call cannot be admitted for service due to the lack of access to free AUs.
On the basis of Eq. (7), we can write: where [σ i (n)] SZ is the transition coefficient that results from the division of the AUs of the system into the separated resources, whereas [σ i (n)] S results from the non-fullavailability of a single separated resource.

Now, let us consider the manner in which parameters
[σ i (n)] SZ and [σ i (n)] S may be determined. The values of the coefficient [σ i (n)] SZ may be determined as follows. Since calls may be completely serviced only by a single separated resource, this resource has to have at least t i unoccupied AUs. To satisfy this condition, an appropriate distribution of free AUs between all separated resources is required. An unfavorable distribution of free AUs within the system may be followed by new calls being rejected, as presented in Fig. 4. The said figure shows the distribution of three free AUs in a system that is composed of two separated resources. If, at the input to this system, a call that demands 3 AUs arrives, then it may be admitted for service only in the case of 2 from 4 potential distributions of unoccupied AUs within the entire system. To determine the conditional transition coefficient, the dependence proposed in [25] can be used: where the function F(x, k, f ) is given by: Parameter [σ i (n)] SZ V is calculated based on the assumption that separated resources are of the full-availability variety. This assumption is based on the new connection setup algorithm implemented. According to this algorithm, the separated resources are checked for free AUs first, without checking whether there is access to them. Each of the separated resources may be the source for nonfull-availability as well. Systems in which calls have limited access to their own AUs may be modeled by EIG [26], [1]. In this model, the conditional transition coefficient is determined with the use of the following formula: where: In order to substitute Eqs. (12) and (14) into Eq. (11), two problems have to be solved first. Firstly, the occupancy of a single separated resource changes from 1 to f , while the occupancy of the whole of the system changes from 1 to V . Secondly, the call admission algorithm allows all separated resources that have at least t i free AUs to be checked. In the proposed analytical model, the first problem was solved in the following way: since the assumption was that the choice as to the separated resources was random, then it could be adopted that approximately (rough estimate) each of them had equal loads and, what followed, the average number of occupied AUs in each resource was equal to n k , where n was the occupancy state in the entire system. The other problem, in turn, was solved thanks to the adoption of the assumption that since service admission of a new call depends on the state of each of the separated resources, then product dependence must exist between the transition coefficients in each of the separated resources and the resultant transition coefficient [σ i (n)] S . The proposed Eq. (15) was defined as follows: since the call admission algorithm for new calls assumes the possibility of checking all separated resources, then the admission of a new call is possible if such a possibility exists in just one of them: By taking into consideration Equations (12), (14) and (15), we can ultimately write:

Results
To verify the proposed analytical model, the results obtained with the use of the model were compared with the results of the simulation. For this particular purpose, a simulation model of the non-full-availability system under consideration was devised and implemented in the C++ language. The simulator used the event scheduling methodology. To determine a single measurement, 5 series of simulations with 1,000,000 calls of the class that demanded the highest number of AUs for series each, were performed. The results obtained are presented in the form of a function of traffic offered to a single AU of the system: Another assumption was that the total traffic offered was divided between individual call classes in the following manner: a 1 t 1 : a 2 t 2 : ... : a m t m =1 : 1 : ... : 1. Figure 5 shows the result for the following system: k = 3, f = 25 AUs. The system was offered three classes of calls (m = 4) that demanded 1, 2, 3 and 4 AUs for service, respectively, while the availabilities were 8, 10, 12 and 15 AUs (Case 1). Figure 6 shows the result for the following system: k = 3, f = 15 AUs. The system was offered three classes of calls (m = 3) that demanded 1, 2 and 3 AUs for service, respectively, while the availabilities were 6, 8 and 10 AUs (Case 2). Figure 8 shows the result for the following system: k = 3, f = 21 AUs. The system was offered three classes of calls (m = 3) that demanded 1, 2

Fig. 5.
Blocking probability in a complex non-full-availability system (Case 1).

Fig. 6.
Blocking probability in a complex non-full-availability system (Case 2).

Fig. 7.
Blocking probability in a complex non-full-availability system (Case 3). and 5 AUs for service, respectively, while the availabilities were 7, 10 and 18 AUs (Case 3). The model presented is an extension of the research described in article [27]. The previous model, in the scenario with low availability for the class requesting the least number of resources, showed some significant inaccuracies. Figure 5 shows the results obtained using models described in [27], [4], and the model described in the current article in connection with the following system: k = 3, f = 24 AUs. The system was offered three classes of calls (m = 3) that demanded 1, 3 and 4 AUs for service, respectively, while the availabilities were 5, 10 and 13 AUs (Case II). Thanks to the modification, the problem of inaccuracies in the youngest class has been eliminated. The analytical model proposed in the article is of the approximate variety. However, the presented results of the study show that the model is efficient at approximating the non-full-availability system under consideration. The highest error rate under investigation occurs for the class that demands the lowest number of AUs. However, this inaccuracy is much lower than that in the model presented in [27]. This error is based on a certain underestimation of the blocking probability, but the repeatability of this error makes it possible to introduce a relevant adjustment to the model. The accuracy of the model, as confirmed in the study, makes it possible rely on the model for modeling non-full-availability systems, such as those used in cloud computing. This will be feasible, however, only when appropriate equations that make it possible to determine the availability in such systems are proposed. This will be the subject of further research the authors intend to conduct.

Summary
This article presents the architecture of a complex non-fullavailability system and its analytical model developed by the authors, enabling to determine loss coefficients and the blocking probability in this system. Though the proposed model is of the approximate nature, the results obtained in the study clearly indicate that is its highly accurate. The approximation errors that occur in the results, and are reported in the investigation, are of the fixed nature, which makes it possible to introduce simple corrections and adjustments that would nullify these differences during the further development stages. The authors are of the opinion that further research into complex non-full-availability systems is of utmost importance due to the dynamic growth of IT services and increasingly more sophisticated systems that are offered to users. The model presented in the article may become, in the future, a useful tool in modeling real telecommunications systems, such as data centers or cloud computing solutions. The fact that it requires a small amount of computer resources to perform calculations and is characterized by a relatively short time of operation is an additional advantage of the model presented.


Democracy, State Capacity, and COVID-19 Related School Closures

This paper investigates the institutional determinants of the timing of COVID-19 related school closures around the world, focusing on the role of democracy and administrative state capacity. Relying foremost on Cox proportional hazard models of up to 166 countries observed daily between February and April of 2020, the paper ﬁnds that other things being equal, democratic countries tended to implement school closures quicker than those with a more authoritarian regime, while countries with higher government eﬀectiveness tended to take longer than those with less eﬀective state ap-paratuses. A supplementary analysis that distinguishes between the two democratic dimensions of contestation and participation indicates that it is the existence of fair and competitive elections that prompts democratic leaders to respond more rapidly. Lastly, auxiliary evidence indicates that demography and family systems may also help determine countries’ pandemic responses.

Introduction
The recent weeks have seen governments across the world respond rapidly and with unprecedentedly disruptive measures to address the spread of coronavirus disease 2019 , including non-pharmaceutical interventions such as school closures, travel restrictions, curfews and quarantines. Yet, there is also considerable variation in terms of the timing and stringency of countries' response strategies (Hale and Webster 2020). As questions about how to understand and handle the pandemic and its aftermath now surge on the research agendas across academic disciplines, a key task for political scientists will be to explain why different governments responded the way they did.
Although it is still too early for any all-encompassing analysis of the crisis responses around the world, it is possible to analyze one non-pharmaceutical measure that has already been remarkably widely implemented and for which comprehensive and comparable data is already available (UNESCO 2020), namely school closures. As shown by the data reported in Figure 1 for 178 countries enjoying at least some degree of functional and/or formal sovereignty, the four weeks that followed after COVID-19 related school closures occurred in China and Hong Kong on February 16 saw a striking 112 additional countries following suit. After two more weeks the growth leveled of, as a total of 167 countries had implemented a localized or national school closure. Although 11 countries had still not seen a school closure by April 7, it is clear that we have already witnessed the vast majority of potential initial closure decisions.
The widespread implementation of school closures may not come as a surprise, given that they may help slow the spread of the virus by increasing social distancing and the likelihood that exposed individuals develop their symptoms while not in school (CDC 2020;Jackson et al. 2013;WHO 2019). However, depending on when and for long they are implemented, school closures may also put older relatives at higher risk, have detrimental effects on student performance and well-being, and decrease the workforce in health care and other important capacities as more parents stay home with children (Brown et al. 2011;CDC 2020). Thus, given that the timing of school closures appears be of critical importance for their outcomes, and that political and institutional factors have previously been found to influence how governments respond to pandemics and other crises (Salajan et al. 2020), it is of interest to investigate whether such factors also systematically mattered for the timing of countries' decisions to implement school closures in response to . Besides being of interest in their own right, the results from such an investigation may also serve to inform scholars' expectations when analyzing other types of pandemic interventions going forward. 16feb2020 26feb2020 07mar2020 17mar2020 27mar2020 06apr2020 School closure National school closure

Democracy, State Capacity, and the Timing of School Closures: Theoretical Considerations
This paper focuses on two institutional factors of longstanding interest to social scientists, which have also been brought up in the nascent conversation on COVID-19, namely democracy and administrative state capacity (e.g., Fukuyama 2020). For neither of them it is clear from previous research whether we should expect it to make countries more likely to adopt a precautionary strategy, through which the entire population is led to make sacrifices for the sake of vulnerable individuals-which in this case would imply a rapid school closure-or a more proportional strategy, where school closures are postponed in favor of less disruptive measures, such as interventions to isolate individuals that are vulnerable or infected (Baekkeskov and Rubin 2014).

Democracy
Consider first democracy, which is commonly conceived as the extent to which rulers and the policy choices they make are responsive to citizens, as achieved through fair and competitive elections combined with wide suffrage and extensive political involvement (Dahl 1971;Miller 2015). On the one hand, according to a political survival logic (de Mesquita Bruce et al. 2003), leaders in democratic countries should be more likely to quickly adopt a precautionary strategy in times of national crisis, especially in cases where an election is imminent. Existing crisis management research points to two reasons (Baekkeskov 2016). First, democratically accountable leaders should have stronger incentives to respond promptly to avoid the threat of electorally harmful blame, whether from the opposition or the mass media (Baekkeskov and Rubin 2014;Besley and Burgess 2002). Second, democratic governments have been found to use emergencies as an opportunity to demonstrate their value to contested constituencies (Healy and Malhotra 2009;Reeves 2011). Furthermore, in democratic countries the freedom of expression improves the quality of information available to governments, which may enable a quicker crisis response (Kahn 2005;Persson and Povitkina 2017). In addition, to the extent that a more rapid response indeed reflects a greater commitment to public health, we should expect democracies to act faster as they tend to put higher priority on safeguarding the population's well-being (Besley and Kudamatsu 2006;Cronert and Hadenius forthcoming). However, there are also arguments for why we should expect a null or even negative effect of democracy on the timing of school closures. To begin with, authoritarian regimes may also be worried about the possible damage that a slow or unnoticeable crisis response could do to popular support for the government, especially considering that such damage may simultaneously challenge the legitimacy of the entire political regime (Baekkeskov and Rubin 2017). It is furthermore possible that a measure as disruptive as a school closure is more difficult to enact in a democratic country where a larger share of the population-many of whom will be personally and immediately affected by the measure-are able to have a say in politics, whether individually or through civil associations. For a formal argument along these lines, applied to the case of mass vaccination, see Ahlskog (2017). Lastly, given that we should expect a higher degree of public deliberation on pandemic response policy in democracies (Baekkeskov and Öberg 2017), we should perhaps also expect that it takes longer for democratic governments to decide on their preferred strategy.

Administrative State Capacity
It is also not obvious what impact to expect of administrative state capacity, by which we typically refer to the extent to which competent, efficient and impartial administrative agencies enable the state to take action in an appropriate and effective manner (Bäck and Hadenius 2008;Cronert and Hadenius forthcoming). On the one hand, drawing on earlier research about the importance of government effectiveness for a successful response to natural disasters as well as pandemics, one might expect that high state capacity enables countries to prepare for and implement school closures more rapidly (DSB 2011;Kahn 2005;Persson and Povitkina 2017;Raschky 2008).
On the other hand, it is possible that countries with more well-functioning state agencies also have a larger set of policy tools available for consideration, and thus are in a better position to suspend drastic precautionary measures like school closures longer in favor of a more proportional strategy with less disruptive initial responses. Such a reasoning was, for instance, provided by the Singaporean minister of education when explaining the government's decision to keep schools open: "We still have options. We are not like many countries, where they are forced into sudden school closures" (Teng and Davie 2020). This is not to suggest that epidemiologists and other experts at the national public health agencies cannot make different judgments about the appropriateness of different strategies (cf. Baekkeskov 2016). The point is simply that when such agencies are able to exert more influence on governments' pandemic responses, we should expect decisions about school closures to be guided relatively more by criteria related to necessity and proportionality than by a presumed political pressure for a precautionary response (for evidence on the prominence of necessity and proportionality considerations in public health officials' decisions on school closures during the 2009 H1N1 influenza outbreak in the US, see Kayman et al. 2015).
Lastly, another way in which the existence of a competent and effective administrative apparatus may lead to later school closures is by making it possible for political leaders to shield themselves from potential blame for a slow response, by shifting the responsibility for the strategy to the certified expertise (Baekkeskov and Öberg 2017). The Swedish response to COVID-19 may illustrate this mechanism. When other European democracies began closing schools in early March, the powerful Public Health Agency defended the country's deviating strategy with reference to the large disruptions and to the importance of timing, while government representatives made it "somewhat of a mantra" to state that they were following the agency's recommendations (Rothschild 2020). On March 18, Sweden enacted a partial national closure, only affecting upper secondary schools and universities (UNESCO 2020).

Empirical Analysis
In the following, I investigate the role of democracy and administrative state capacity in determining the timing of COVID-19 related school closures around the world. This is done first by means of a simple graphical illustration, and second by means of regression analyses in a survival analysis (event history) framework. In the interest of making these analyses as comprehensive as possible, efforts have been made to include all countries that enjoy at least some degree of functional and/or formal sovereignty as defined by the Varieties of Democracy (V-Dem) Institute (Coppedge et al. 2020). Out of these 179 countries, 10 (5.5 %) must be excluded altogether since they lack the essential data on COVID-19 cases reported by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University 1 (CSSE 2020).
To enable a meaningful comparison of timing, we need to define a common starting point for the analyses. To reconcile comparability and inclusiveness, I have chosen two different starting points. For the graphical analysis, the point of reference is the day of the first confirmed case of COVID-19, as reported by the CSSE (2020) 2 . However, given that a considerable number of countries closed schools already before having their first confirmed case, this starting point is inappropriate for the survival analyses. To include as many countries as possible in these analyses, their starting point for all countries is February 16, the day that school closures where implemented in China and Hong Kong (UNESCO 2020). Accordingly, omitting these two countries as well as Mongolia where a school closure was implemented already on January 27, this set of analyses includes at most 166 countries, 159 of which had implemented a school closure by April 7 when the period of observation ends.

Key Variables
To measure a country's level of democracy in 2019, I primarily rely on the electoral democracy index provided by the V-Dem Institute, which is based on sub-indices that measure freedom of association, clean elections, freedom of expression, elected officials, and suffrage (Coppedge et al. 2020). As an indicator of administrative state capacity, I use the Worldwide Governance Indicators' (WGI) 2018 estimate of government effectiveness, which considers the quality of public service provision, the quality of the bureaucracy, the competence of civil servants, the independence of the civil service from political pressures, and the credibility of the government's commitment to policies (Kaufmann et al. 2011  Data on daily incidents of school closures are retrieved from UNESCO (2020), while daily data on logged confirmed cases of COVID-19 come from the CSSE (2020). A number of additional control variables are included in the various models and are discussed subsequently. See the Appendix for details regarding definitions and sources.

Descriptive Evidence
Let us begin by considering some graphical descriptive evidence. For all countries except China, Figure 2 plots the number of days between the country's closure (or April 7 for right censored observations) and the day of the first confirmed case against the country's government effectiveness rating. The color and shape of the markers indicate whether the country has a below-median (red circles) or above-median (green triangles) democracy rating.
Two observations can be made from the two lines that represent quadratic predictions fitted to the two subsets of the data. First, the positive slopes show a clear positive relationship between administrative state capacity and time to school closure. Second, judging from the positive difference between the red and the green line at most values of government effectiveness, it appears that less democratic countries tended to implement school closures somewhat later than more democratic countries.

Cox Proportional Hazard Models
The cue from the graphical exercise above is that democracies appears to have implemented school closures more quickly than more authoritarian countries as a response to the spread of COVID-19, while countries with more effective governments tended to take longer than those with more limited state capacity. As it turns out, similar results are retrieved from the survival analyses that are summarized in Figures 3 and 4 and reported in full in the Appendix, Table 1. These analyses are based on the Cox proportional hazards model, which unlike parametric duration models does not require an assumption about the shape of the baseline hazard. The data are structured as country-date panels, beginning for each country on February 16 and ending on the day of the first school closure event or on April 7. Exploratory analyses indicate that no country-specific frailties are needed, but for the proportional hazard assumption to be satisfied the observations are stratified by the day of the country's first confirmed case of COVID-19 to account for the fact that those hit later by the pandemic have a higher baseline hazard of school closure. The baseline Cox model applies the V-Dem Institute's democracy index and the WGI government effectiveness indicator as the key independent variables. As controls, it includes the daily (logged) number of confirmed domestic COVID-19 cases as well as six region dummies based on the World Bank's categorization, which serve to absorb regional shocks such as different exposures to the pandemic. It furthermore adds a measure of (logged) GDP per capita, which is correlated with both democracy and state capacity and was found positively associated with state-level implementation of social distancing policies in one of the first studies on the timing of COVID-19 responses among US states (Adolph et al. 2020). Lastly, the baseline model adds a time-varying dummy indicating country-specific weekend days, considering that a school closure should be much more likely to begin on a working day.
The results from the baseline model (A) indicate that other things being equal, democratic countries are likely to implement school closures sooner than those with a more authoritarian regime. The hazard ratios reported in Figure 3 indicate that an increase in democracy by one unit (on a 0-10 scale) is associated with an increase in the relative risk of school closure of around 17 percent. As to administrative state capacity, a one unit increase in the WGI indicator is associated with a 19 percent lower relative risk of school closure. Both results are statistically significant at conventional levels. There is furthermore a significant positive relationship between confirmed COVID-19 cases and the relative risk of school closures, while the association of GDP per capita is negative and insignificant.
Model (B) includes a number of additional control variables, which may be correlated with democracy and state capacity, and which may also affect the time to school closure. The first is a measure of the population health (healthy life expectancy), which may reduce the urgency of precautionary measures. The second is the share of the population aged 0-14 and is meant to capture that a larger youth population might make a school closure costlier and more difficult to implement. The third is a measure of urbanization, which might make school closures both more urgent and easier to implement. The fourth variable is meant to capture the core features of a country's family system, and measures the proportion of its current population whose ancestors resided in nuclear or stem families, rather than polygamous or community families (Giuliano and Nunn 2018). In countries with a tradition of nuclear and stem families, households tend to be smaller (Rijpma and Carmichael 2016), people report more freedom of choice within the family (Rijpma and Carmichael 2016), pre-primary and primary school enrollment tends to be higher , and retirement ages tend to be higher. All these are factors that may make school closures more costly to implement and sustain, but   Table 1. since reliable data is lacking for a sufficiently large number of countries, I instead rely on this family system based proxy.
The results from model (B) indicate that a younger population and a nuclear or stem family system are indeed associated with a significantly lower relative risk of school closure. However, since including these control variables reduces the sample size by 9 countries while increasing the coefficients for both democracy and state capacity, I retain the more encompassing and conservative baseline model as my preferred specification.
Acknowledging that state capacity is a multi-dimensional concept, model (C) adds two indicators commonly used to capture the extractive (fiscal) and coercive capacities of the state respectively (Hanson 2018). The first is a measure of taxes (including social contributions) as share of GDP and the second is the Political Terror Scale, an index of violations of physical integrity rights carried out by states or their agents (Gibney et al. 2019;Teorell et al. 2020). While the coefficients for both variables are negative, neither is statistically significant and the results from the baseline model are intact. Lastly

Substantive Interpretation of the Baseline Model
To help interpret the baseline model in policy-relevant terms, Figure 4 reports the marginal changes in expected time to school closure given a change in democracy or state capacity from the 25th to the 75th percentile respectively, estimated using the Cox ED procedure (Kropko and Harden 2020). These estimates indicate that such an increase in the level of democracy-roughly equivalent to a change from that of Turkey to that of Chile-corresponds to a reduction in the average expected time to school closure by approximately 5.4 days. A change in government effectiveness of an equivalent size-i.e., from that of Egypt to that of Italy-is associated with an increase in expected duration of around 4.2 days. These estimates can be compared to the average expected time to school closure of 36 days after February 16.

Which Aspect of Democracy Expedites Response?
As discussed above, democracy is a multi-faceted concept, the full realization of which is commonly seen as requiring both a high degree of electoral contestation and a high degree of popular participation (Dahl 1971;Miller 2015). In an effort to elucidate which of these two characteristics of democracies that drives their quicker response, I conduct a supplementary analysis which substitutes the V-Dem democracy indicator for the two indicators of contestation and participation developed by Miller (2015). Two shortcomings of these indicators should be noted upfront: they are only available for 149 countries and for no later years than 2003/2004, which means that they are likely marred by some inaccuracy. As reported in Figure 3, the model in question (E) indicates that it is the presence of free, fair and contested elections that increases the relative risk of school closures, although the coefficient does not quite reach statistical significance (p=0.071). Interestingly, extensive participation-measured by suffrage and voter turnout-is instead negatively associated with the relative risk of school closures. It should be noted that in this model the effect of government effectiveness disappears, at least partly as a consequence of the depressed sample.
To illustrate the substantive implication of these results, I estimate the expected time to school closure for three fictive regime types: a closed authoritarian regime with relatively low (25th percentile) values on both dimensions (similar to Egypt), a democratic regime with high (75th percentile) values on both dimensions (e.g., South Korea), and an electoral authoritarian regime with low contestation but high participation (e.g., Belarus). 3 The estimated differences between the closed authoritarian regime and the two others are reported in Figure 5. These suggest that while the democratic regime is expected to take two days less to close its schools, the electoral authoritarian regime is expected to take two days more.
The diverging responses to COVID-19 by the neighbouring countries Poland and Belarus are consistent with these results. In Poland, in which a relatively competitive presidential election is scheduled for May 10, 2020, the government quickly adopted a precautionary strategy, including a school closure and a lock-down within two weeks after the first confirmed case. Possibly out of concern that the incumbent president Duda's re-election prospects will deteriorate if the election were to be postponed until a later stage of the pandemic aftermath, the governing party has insisted on conducting the election as soon as possible (The Associated Press 2020). By contrast, in Belarus where elections are inclusive but non-competitive, long-time president Lukashenko has rejected any precautionary measure to tackle COVID-19-including school closures-despite facing a presidential election in August 2020 (Karmanau 2020).

Concluding Remarks
This paper has investigated how two institutional factors-democracy and administrative state capacity-help determine the varying timing of countries' implementation of school closures as a response to the spread of COVID-19 in the spring of 2020.
Overall, the evidence from Cox proportional hazard models of up to 166  Table 1. countries indicates that a higher level of democracy in a country is associated with a several days' shorter time to school closure, whereas a higher level of state capacity is associated with a more delayed implementation. In addition, auxiliary evidence suggests that factors related to demography and family systems may also help determine countries' pandemic responses and may deserve more attention in future analyses of COVID-19 interventions. A few caveats are warranted here. First, although including up to 94 percent of all formally and/or functionally sovereign countries, the analyses leave out a few countries for which no data on COVID-19 cases are reported. Second, among countries that do report cases, the quality of the information is likely to vary in a non-random manner. This might affect the results in various ways, given the importance of the case-related variable in all models. In an attempt to assess the sensitivity of my results to this issue, I have conducted a supplementary analysis which assumes a two-day delay of the first COVID-19 case in each of the 10 percent least democratic countries and found that the results remain intact (see the Appendix, Table 1, model F). Third, I want to underscore that the analyses reported here are not intended to evaluate, nor do they say anything about, the appropriateness or effectiveness of any particular school closure strategy.
Lastly, it should be emphasized that school closure is only one among many types of government responses to COVID-19, and it is not clear how the patterns observed here travel to other types of more or less precautionary and disruptive measures. As more data become available-for instance through the Oxford COVID-19 Government Response Tracker (Hale and Webster 2020)-comparing different types of responses will be a crucial research endeavor. Given that the findings herein suggest that different aspects of democracy and state capacity may be differently related to the pandemic response, it appears crucial that future theoretical and empirical work involving these concepts makes sure to take their multi-dimensionality to heart.
• Weekend: A dummy for days that are not working days, as listed on Wikipedia.
Saturday-Sunday is assumed if information is missing.
• GDP per capita (logged): Measured in in current US dollars. Source: The World Bank's World Development Indicators, retrieved primarily from Teorell et al. (2020).
• Urbanization (2016) • Nuclear/stem family system: Defined based on Rijpma and Carmichael (2016) as the proportion of a country's contemporary population whose ancestors resided in nuclear or stem families, rather than polygamous or community families, divided by 1 less the share for which data is missing. Computed using variables v8_grp1-v8_grp9 in the etnhnographic database provided by Giuliano and Nunn (2018).
• Taxes  • Democratic Contestation: Index that captures the extent and fairness of electoral competition between parties and distinct interests. Pertains to 2004, although for ten countries, values for 2003 are used. Source: Miller (2015).
• Democratic Participation: Index that captures the extent of popular electoral involvement across the citizenry. Pertains to 2004. Source: Miller (2015). Coefficient estimates and 95% confidence intervals from pooled Cox models of school closures between February 16 and April 7, 2020. Observations are stratified on date of first confirmed COVID-19 case. For a description of models A-E, see the main text. Model F replicates model A but assumes that the ten percent countries with the lowest democracy score registered their first case two days earlier. Robust standard errors in parentheses. * p < 0.10, * * p < 0.05, * * * p < 0.01.


Mechanisms of stimulating activities in banking participation in the development of construction industry and national economy at all

The development of the real sector is crucial to ensure the growth of the national economy of any state. The main institution working with money in the economy are banks. They serve the cash flows of companies in real sector, and also serve as one of the sources of investment for them, which are provided in the form of bank loans. Given that the task of stimulating the growth of the real sector is not only facing the banking system, but also the economy as a whole, the approach to solving it should be comprehensive and systemic. In this regard, it is especially important to develop a list of measures that provide a differentiated approach to the support system for companies in the real sector of the economy. The implementation of such measures should include the active participation of development institutions, and therefore the active participation of banks in the system of implementation of national projects. Particularly important in this regard is the improvement of legislative regulation of issues of interaction between banks and business entities, as well as the development of new financial instruments that contribute to building up the financial potential of the real sector of the economy. The article analyzes the participation of banks in lending to the real sector of the Russian economy, considers the key features of lending to the construction industry. A number of measures are proposed, both at the macro and the micro level, ensuring not only the coherence of the economic interests of companies and banks, but also significantly reducing costs.

Introduction
The development of construction and other sectors of the real economy is extremely important for ensuring the growth of the entire national economy. And since the growth of the well-being of all economic entities depends on this, all of them should contribute to the development and positive dynamics of this process as much as possible. Growth requires cash, which is the main source of investment in expanded reproduction and construction, which is the source of economic growth.
The main institution that works with money in the economy is banks. They serve the monetary turnover of companies working in the construction sector and other sectors of the real economy that make up its nonfinancial sector, and also serve as one of the sources of investment for them, which are provided in the form of Bank loans.
Analyzing the debt structure of the non-financial sector, it can be noted that domestic borrowing is 70%, having increased by 5% since 2013. The share of loans in the domestic borrowing system has decreased slightly, but today it reaches 84%. At the same time, the rubledenominated debt accounts for more than 65% of the non-financial sector's domestic borrowings, which once again highlights the relationship between the banking sector and the real economy.
The volume of loans provided by banks to legal entities and individual entrepreneurs, which make up the real sector of the economy, has a positive trend in the long-term perspective. Over the past 10 years, in absolute terms, it has grown more than 3.65 times (from 1,502,062 million rubles in March 2010 to 5,485,236 million rubles in March 2020).
At the same time, in the dynamics of loans over 10 years, the volume of loans issued has significant fluctuations during the year. This is more clearly and clearly visible on the chart in a shorter time interval. Of course, this is determined by the seasonal nature of activity, taking into account the peculiarities of the geographical location of the Russian Federation and the length of its borders, as well as the features of the economic cycle of enterprises in the real sector of the economy.
These fluctuations are related to the seasonality of business in the main sectors of the economy and the seasonal need for investment in the form of Bank loans in the maintenance and development of businesses and entrepreneurs. However, the main part of Bank loans received by enterprises is used to solve current financial issues related to solving current production tasks, which are seasonal in many industries. To ensure the growth of the real sector of the economy, it is necessary not only to solve the current financial issues of enterprises, but also, most importantly, to invest in their fixed capital.
It should be noted that the role of banks in the process of activating investment activities of companies is extremely small. At the beginning of 2008, the share of Bank loans in the structure of investments in fixed assets was fixed at 10.4 %. As part of the Concept of long-term socio-economic development of the Russian Federation for the period up to 2020, adopted in 2008, it was supposed to grow by 2 times by 2020. However, due to the global financial crisis of 2008 and its consequences, as well as due to economic sanctions imposed against Russia since 2014, banks were forced to solve their own financial problems. Therefore, by 2016, this indicator fell to 8.1 %, which corresponds to the level of 2006. After that, according to state statistics and the Bank of Russia, the indicators of banks ' participation in the structure of investments in fixed assets have consistently increased. At the end of 2016, it reached the level of the beginning of 2008 and amounted to 10.4 %. At the end of 2017, it increased to 11.2 %. However, in 2018, after its reduction in the first half of the year to 8 %, it remained at the level of 11.2% at the end of the year.
However, it is important to take into account not only the quantitative changes in the participation of banks in the investment process, but also to monitor the qualitative changes that ensure the growth rate of individual sectors of the economy. Project financing is a tool that contributes to the development of the construction industry today. Despite the turmoil caused by the pandemic, banks confirm the stability of the situation with the financing of developers who switched to escrow accounts.

Methods
Bank loans failed to play the role they were assigned in increasing the share of investment in fixed assets of enterprises and thus ensuring the conditions for growth of the real economy. To solve these problems, enterprises are increasingly forced to rely on their own resources and resources. The share of equity in investments increased in the first half of 2018 compared to the first half of 2014 by 7.2 % (from 52.5% to 59.7 %). In this regard, enterprises began to invest less in other enterprises and the share of borrowed funds from other enterprises in the investment structure decreased from 6.8 % to 4.1 %. the Share of budget funds remained at a level slightly higher than 12 %, since budget funds are also directed to solving other problems that are often more acute.
The share of Bank loans in this indicator decreased from 10.3% to 8.0% over the specified period. This happened for several reasons.
First, as mentioned above, banks were dealing with their own financial difficulties caused first by the global financial crisis in 2008, and then by the economic sanctions imposed in 2014.
Second, it has become very burdensome for many companies to take out Bank loans. This is due to the fact that loan rates rose sharply in December 2014 following the increase in the key rate. After that, they gradually change in the direction of reduction, following changes in the key rate. At the same time, many organizations are forced to spend their profits, and often take out new loans to repay their previously taken loans and interest on them at high rates. In addition, along with the reduction in loan rates, the profitability of most enterprises also decreased due to the economic downturn in the country and the reduction in real incomes of both the population and the enterprises themselves. In this regard, many companies cannot take out large and long-term loans necessary to invest in their development, even at the currently reduced rates.
Third, due to the above-mentioned financial difficulties, along with the growth of loan arrears, the volume of overdue loans and their share in the total amount of debt is also growing. The first jump in the share of overdue debt occurred in early 2009 and is related to the economic consequences of the 2008 crisis. The second, which occurred in early 2015, is related to the introduction of economic sanctions in 2014, which essentially blocked the possibility of receiving investment from abroad. Despite the fact that after this, the share of overdue loans began to decrease, in 2019 it began to grow again. In this regard, banks were forced to tighten requirements for potential borrowers, which made it more difficult for them to obtain new loans, especially for a long time in conditions of economic uncertainty. This had the expected effect and the share of overdue debt began to decrease starting from the end of 2019. And all this is happening against the background of a serious reduction in the key rate, which in April 2020. it was 5.5%. It would seem that everything is being done to make the main sources of funding cheaper and reduce the burden of interest payments on loans. Apparently, the solution to this issue lies not only in the field of monetary regulation, and it is worth paying attention to the issues of investment attractiveness of enterprises in the real sector of the economy. In this regard, Russian companies must first meet the regulatory values of financial stability indicators and increase the parameters of business value. It is not possible to implement this task for the majority of small and medium-sized enterprises due to the unsatisfactory balance sheet structure and the threat of bankruptcy.
Fourth, the reduction in the number of banks in connection with the process of clearing the Russian banking system of unscrupulous players conducted by the Bank of Russia does not contribute to the growth of the use of Bank loans as a source and method of supporting the growth of the real sector of the economy. First of all, this applies to small banks, which, according to the Bank of Russia's plans, should focus on lending to small and medium-sized businesses.
In this regard, it is necessary to solve the problem of finding effective mechanisms to stimulate the banking sector to support the real sector of the economy and stimulate its growth, while creating conditions for the development of the internal potential of Russian companies. Successful implementation of this task is possible if there is sufficient investment attractiveness of Russian companies. This requires not only consistency of economic interests of banks and organizations, but also a healthy investment climate. The investor should see the immediate prospect of implementing their projects. It provides stable profit indicators for the company, which means stable sales markets provided by effective demand and healthy competition.
It is also important to take into account that the process of interaction between banks and enterprises is associated with a high degree of risk, which requires new integrated approaches to risk management. As a condition for expanding effective Bank lending to the real sector, a reduction in credit risk should be assumed. An effective system of internal banking control plays an important role in ensuring that the interests of enterprises and banks are aligned.
The modern organization of the Bank lending system creates unequal conditions for commercial and industrial enterprises. Those areas of business where the cost of paying interest on a loan can be transferred to buyers of services, while taking into account the high turnover of working capital, contribute to an increase in the interest rate. For industrial enterprises, this policy becomes ruinous. As a result, such business areas as trade, mining, as well as the production and distribution of water, gas, and electricity in General can afford to take out a loan in the current conditions. As a result, industrial enterprises lose their ability to organize the reproduction process and reduce their competitiveness. In this regard, a well-thought-out state industrial policy is necessary. In the framework of the implementation of such policy banks should use a differentiated approach to the loan. In particular, the interest rate should vary depending on the object of lending. Such a role can be performed by development institutions today, performing certain tasks within the framework of national projects, including providing the opportunity to saturate the economy with long-term money that banks do not have. In any case, the algorithm of interaction between banks and development institutions should already take into account interest rate differentiation.

Results
Considering the mechanisms for stimulating the involvement of banks in lending to the real sector of the economy and supporting its growth, we see the following tasks that need to be solved at the micro level: -introduction of a wide range of Bank refinancing mechanisms, including those that take into account existing foreign and domestic experience; A number of Central banks have experience in providing banks with so -called "economic" loans, which are secured by the obligations of real sector enterprises (bills of exchange and credit requirements of enterprises) along with the usual type of security of the first category (highly liquid securities-government securities, as well as securities listed on major stock exchanges, etc.). Such loans are provided to banks by Central banks of a number of European countries (Germany, France), the United States and other developed countries. Implementation of this practice will require an adequate legal framework and an extensive system of institutions that are responsible for the implementation of collateral rights and the liquidation of enterprises. The experience of such lending is available in Russia. However, it requires wider application.
-formation of a system for monitoring collateral for loan debt; The list of objects can be expanded for high-tech companies in terms of using intellectual property objects (IPOs) as collateral. Given that the value of an IPO can be much higher than the value of the entire enterprise's property-equipment, raw materials, current stocks of finished products, and in some cases may even correspond to the value of the company, this object can now freely act as a collateral instrument. It is also necessary to take into account the fact that the IPO pledge is almost the only security tool for start-up hightech companies today. In this case, the collateral agreement must function in conjunction with the loan agreement. Moreover, the pledge agreement must clearly define the point about whether the exclusive right to the result of intellectual activity is pledged, and to what extent. Moreover, the subject of the pledge agreement itself must be determined as accurately and correctly as possible. Exclusive rights to a particular item may consist of separate entitlements. To do this, a whole Institute of assessment and admission to the use of various OIS should be created.
Providing loans secured by the obligations of enterprises will require significant work to collect and evaluate data on enterprises whose obligations can be accepted as collateral for a Bank of Russia loan. In this regard, it is necessary to create a database on organizations in the non-financial sector for refinancing banks against the obligations of enterprises. It is possible to form a so-called "collateral pool" that is actively used abroad.
-reengineering of companies ' business processes; The need to develop project financing is associated with the implementation of the long-term lending process. In this regard, the introduction of Bank representatives in the management of funded organizations will not only make it possible to organize the credit process more efficiently, but also ensure the rational functioning of the business in the company. It is also possible for the Bank to join the capital of financed enterprises and thus create financial and industrial groups, the success of which is confirmed by both Russian and foreign experience. This can be a solution to bad debts and at the same time revive real production.
Emerging FGS will be a conglomerate (vertical or horizontal) in terms of production and economic integration, intersectoral in terms of industry affiliation, multidisciplinary in terms of diversification, and regional in terms of scale of activity. At the same time, banks are becoming even more involved in the work of enterprises in the real sector of the economy, and therefore interested in their growth. However, it is necessary to work out the banking legislation regarding restrictions on lending by banks to affiliated entities.
-use of new financial instruments; In accordance with the procedure for applying the new tool, equity holders ' funds will be accumulated in special Bank accounts-escrow. The developer will be able to use the money of shareholders only after the construction is completed. Thus, banks will lend to the developer and their role in ensuring the development of the construction industry will increase. This scheme will significantly change the financing mechanism of the construction industry. Major banks prepare products for project lending to developers based on the use of flexible interest rates and convenient credit conditions.
The result of implementing this tool is that a third of the housing under construction in Russia is now sold through escrow accounts. Today, more than 90% of applications received by Sberbank from developers are applications for project financing with escrow. The possibility of using escrow accounts revealed a serious contradiction in the pricing system, where banks take the position of restraining the growth of the price per square meter, stimulating demand.
-reducing the number of documents requested by the Bank from the borrower; The list of documents requested by the Bank must comply with the basic principles of lending, without reducing the ability of the borrower to take out a loan. In addition, these documents should provide a qualitative assessment of the borrower's creditworthiness in accordance with the requirements of the Bank of Russia, both for issuing loans and for creating reserves for them. This is especially true for long-term loans and loans to small and medium-sized businesses, where the preparation and submission of the requested documents to the Bank requires distracting employees from their main activities or forces them to hire new employees, thereby increasing the company's expenses. Under these conditions, it is possible to create business centers with the support and participation of banks that can provide consulting, marketing, and audit services for enterprises in the real sector of the economy. These centers can operate on the principle of the Bank of Russia's regulatory sandbox, or even within it. In addition, electronic document management and other modern financial technologies that have been actively developed and implemented recently as part of the digitalization of the economy can be used to facilitate and reduce paper document flow between banks and borrowers. business community and relations with society as a whole; The development of partnership relations between banks and business incubators will contribute to more active involvement of banks in lending and financing of start-UPS, which are now drivers of economic growth in many countries and are actively gaining momentum in Russia. Their lending under the current legislation and banking rules is very difficult, since they have no financial history or any security, but only ideas and a desire to implement them. Therefore, we need to correct the current legislation in this direction.
-formation of long-term funding sources; In addition to attracting funds from private investors, as mentioned earlier, it is necessary to work out a mechanism for banks ' access to long-term sources of financing, such as free funds from the state, state corporations, pension funds and insurance companies. This will allow banks to manage resources more boldly and confidently, giving businesses more long-term loans, which is important for businesses to invest in their future development and growth.
Summarizing the above, the system of measures to enhance interaction between banks and companies can be presented in the following form (table 1).
Participation of banks in various public programs that are not purely commercial, but also social and cultural in nature will help to improve the attitude towards banks and increase confidence in them. And thanks to this, banks will be able to actively develop cooperation with enterprises and citizens, attracting money from them and providing loans to enterprises and individual entrepreneurs, which will contribute to the development and growth of the real economy.

Discussions
Given that the task of stimulating the growth of the real sector is not only for the banking system, but also for the entire Russian economy as a whole, the approach to its solution should be comprehensive and systematic at different levels.
At the macro level, there are several ways to solve the problem of stimulating the growth of the real sector of the economy.
It seems appropriate to involve banks more actively in the implementation and financing of national projects. It is necessary to make banks active participants in the implementation of national, as well as related Federal and regional projects. The level of the program that the Bank is involved in should be linked primarily to the Bank's financial capabilities. At the same time, it makes sense to consider the Bank's participation in a particular project individually, taking into account, in addition to its financial capabilities, its role in the region's economy, territorial, cultural and historical features. In addition to servicing the enterprises involved in these projects, banks need to be involved in financing these enterprises. Moreover, this funding should be based on the principles of public-private partnership (PPP). In other words, part of the money will be allocated to banks from the Federal or local budget that finances the project, and placed in the Bank for further lending to real sector enterprises within the project. And the banks will have to allocate the other part from their own funds. Thus, banks become interested in the successful implementation of the project and the growth of the real sector of the economy directly or indirectly associated with it. At the same time, the state, represented by the Ministry of Finance, the Bank One of these projects is the national project "Housing and urban environment", approved in December 2018. Its main key goals are to provide affordable housing for middle-income families, increase the volume of housing construction, improve the comfort of the urban environment, reduce the housing stock that is unsuitable for housing, etc. This will contribute to the growth of the welfare and housing conditions of Russian citizens, and will be achieved through the development of construction and other related industries.
It is also possible to work out issues on granting tax and other benefits to banks that lend to enterprises from priority sectors of the economy. Moreover, this lending can be carried out by banks as part of participation in the financing of national, Federal and regional projects, or completely at their own expense.
Another issue of stimulating the banking sector to support the growth of the real economy, which needs to be addressed at the macro level, is the creation of a favorable and trust-based economic environment. The scale of investment in the real economy and its development in the market economy of the West relies on an army of institutional investors, financial intermediaries the network of financial markets, carefully designed legislation and developing for many decades-way trust of wide layers of private investors (i.e. of the population) to all named institutions. Private investors, especially in the context of economic sanctions and the closure of foreign sources of financing, should become an important source of financing for the growth of the real economy. This financing should be carried out through various financial institutions, including banks, which should turn the funds of private investors placed with them into loans to the real sector of the economy. Therefore, the state should create legislative conditions that will help increase the confidence of private investors in banks. To do this, in particular, the Bank of Russia should set time limits for completing the active process of improving the Russian banking sector and clearing it of unscrupulous players, and establish clear and understandable criteria for classifying banks as such players. This will increase confidence in the banking system as a whole, since neither private investors nor businesses in the real sector will be afraid to cooperate with a particular Bank for fear of revoking its license.
To form a comprehensive mechanism for active involvement of banks in the lending process and support the growth of the real economy, it is necessary to combine regulatory and tax incentives, as well as a set of measures aimed at reducing investment and credit risks.