Abstract We develop a theoretical model of a network of intermediaries whose optimal behavior is jointly determined, leading to heterogeneous financial norms and systemic vulnerabilities. We apply the model to the network of U.S. mortgage intermediaries from 2005 to 2007, using a data set containing all private-label, fixed-rate mortgages, with loan flows defining links. Default risk was closely related to network position, evolving predictably among linked nodes, and loan quality estimated from the model was related to independent quality measures, altogether pointing to the vital importance of network effects in this market. In a recent paper, Stanton, Walden, and Wallace (2014) establish the existence of strong empirical network effects in the U.S. residential mortgage market, with clearly demarcated segments of connected firms subject to differing amounts of default risk. A recent theoretical literature also highlights the potential A previous version of this paper was circulated under the title "Securitization Networks and Endogenous Financial Norms in U.S. Mortgage Markets." We are grateful for financial support from the Fisher Center for Real Estate and Urban Economics. We thank Stijn Van Nieuwerburgh (the editor); two anonymous referees; and seminar participants at the 2015 meeting of the Western FinanceAssociation, the 2015 NBER Summer Institute conference on Risks of Financial Institutions, the Consortium for Systemic Risk Analytics (MIT) importance of network connections between intermediaries and institutions in explaining financial market risk. 1 These studies show that financial networks may create resilience against shocks in a market via diversification and insurance, but the network interconnections also expose market participants to additional sources of risk. Network structure can thus be a crucial determinant of the riskiness of a financial market. Abstract These theoretical studies of networks and risk in financial markets typically focus on ex post effects: how the network redistributes risk between participants, and the consequences for the system's solvency and liquidity after a shock. Particularly in the mortgage market, ex ante effects also should be important: the presence and structure of a financial network should affect-and be affected by-the quality choices (e.g., the resources devoted to screening and monitoring loans) and other actions of individual intermediaries and financial institutions, even before shocks are realized. The focus of our study is to build a model that can both explain the empirical findings of Stanton, Walden, and Wallace (2014) and help us to understand the equilibrium interaction between network structure, the quality choices made by market participants, and the market's riskiness. Abstract We introduce a model with multiple agents-representing financial intermediaries-who are connected in a network. Network structure in our model, in addition to determining the ex post riskiness of the financial system, also affects-and is affected by-what we call the financial norms in the network, inspired by the literature on influence and endogenous evolution of opinions and social norms in networks (see, e.g., Friedkin and Johnsen 1999; Jackson and López-Pintado 2013; López-Pintado 2012). Financial norms in our model are defined as the quality and risk decisions agents make, which are, in turn, influenced by the actions of other agents in the network. Abstract Our model is parsimonious, in that the strategic action space of agents and the contract space are limited. Links in the network represent risk-sharing agreements, like in Allen, Babus, and Carletti (2012) . Agents may add and sever links, in line with the concept of pairwise stability in games on networks (see Jackson and Wolinsky 1996) , and also have the binary decision of whether to invest in a costly screening technology that improves the quality of the projects they undertake. Abstract The equilibrium concept used is subgame perfect Nash. In an equilibrium network, each agent optimally chooses whether to accept the network structure, as well as whether to invest in the screening technology, given (correct) beliefs about all other agents' actions and risk. Shocks are then realized and distributed among market participants according to a clearing mechanism 1 See, for example, Acemoglu, Ozdaglar, and Tahbaz-Salehi (2015) , Allen, Babus, and Carletti (2012) , Allen and Gale (2000) , Babus (2016), Cabrales, Gottardi, and Vega-Redondo (2014) , Chang and Zhang (2015) , Di Maggio and Tahbaz-Salehi (2014), Elliott, Golub, and Jackson (2014), and Glasserman and Young (2015) . A growing literature deals with trading networks in OTC markets, for example, Babus and Kondor (2013 ), Gofman (2011 ), and Zhong (2014 , but risk exposure is not the focus of this literature. Eisenberg and Noe (2001) . Like in Elliott, Golub, and Jackson (2014), we assume that costs are associated with the insolvency of an intermediary, potentially creating propagation of shocks through the clearing mechanism, and thereby making the market systemically vulnerable. The model is simple enough to allow us to analyze the equilibrium properties of large-scale networks computationally. Our model has several general implications. First, network structure is related to financial norms. Given that an agent's actions influence and are influenced by the actions of those with whom the agent interacts, this result is natural and intuitive. Importantly, an agent's actions affect not only his direct counterparties but also those who are indirectly connected through a sequence of links. As a consequence, a rich relationship between equilibrium financial norms and network structure suggests a further relationship, between the network and the financial strength of the market, beyond the mechanical relationship generated by shock propagation. Abstract Second, heterogeneous financial norms may coexist in the network in equilibrium. Thus, two intermediaries that are ex ante identical may be very different when their network positions are taken into account, not just in how they are affected by the other nodes in the network but also in their own actions. Empirically, this suggests that network structure is an important determinant not only of the aggregate properties of the economy but also of the actions and performance of individual intermediaries. Abstract Third, proximity in the network is related to financial norms: nodes that are close tend to develop similar norms, just like in the literature on social norms in networks. This result suggests the possibility of decomposing the market's financial network into "good" and "bad" parts, and addressing vulnerabilities generated by the latter. Abstract Fourth, the behavior of a significant majority of nodes can typically be analyzed in isolation, while a small proportion of nodes affect the whole network through their actions. Such systemically pivotal nodes are especially important, suggesting a "too pivotal to fail" characterization of the systemically most important intermediaries in the market, rather than a "too big to fail" focus. Abstract Fifth, the financial norms of a node are related to the size and connectedness of its own connections. All else equal, nodes that are connected to other nodes that are larger and/or less connected tend to be of lower quality. Abstract We analyze the mortgage origination and securitization network of financial intermediaries in the United States, using a data set containing all fixed-rate, private-label mortgages (i.e., mortgages not securitized by either Fannie Mae or Freddie Mac) originated and securitized between 2005 and 2007. We use loan flows to identify the network structure of this market and ex post default rates to measure performance, and use the model to estimate the evolution of risk and financial norms in the network. Abstract We document a strong relationship between network position and performance, in line with the predictions of our model, which is present even after controlling for other observable characteristics like type and geographical position of the lender. We also find a positive relationship between predicted and actual out-of-sample default rates of the firms in the market. Finally, we compare estimated firm quality with labor intensity, which we argue is a proxy for how much firms invested in monitoring of loans, and again find an economically and statistically significant positive relationship. Abstract The precrisis residential mortgage origination market comprised thousands of firms and subsidiaries, including commercial banks, savings banks, investment banks, savings and loan institutions (S&Ls), mortgage companies, real estate investment trusts (REITs), mortgage brokers, and credit unions. These had various roles in handling the loan flows from origination to ultimate securitization. Except for the closure of the Office of Thrift Supervision in 2011, the types of firms in the market are largely the same today. Abstract A major driver of the subprime mortgage crisis was increased credit supply, as shown by Mian and Sufi (2009 , who study heterogeneous loan performance at the ZIP-code level and show that performance was closely related to credit availability. Other authors (see, e.g., Bernanke 2007; Di Maggio and Kermani 2014; Kermani 2014; Rajan 2010) have argued that the cumulative effect of low interest rates over the decade leading up to the financial crisis lowered user costs and increased the demand for credit to purchase housing services. Others have argued that the rapid expansions in the precrisis mortgage market arose due to widely held beliefs concerning continued house price growth (see, e.g., Cheng, Raina, and Xiong 2014; Glaeser and Nathanson 2017; Shiller 2014) Alternative explanations have focused on how mortgage securitization led to the expansion of mortgage credit to risky or marginal borrowers (see, e.g., Demyanyk and Van Hemert 2011; Loutskina and Strahan 2009; Nadauld and Sherlund 2013) . Palmer (2015) suggests that vintage effects were important in explaining heterogeneous loan performance: mortgages originated earlier had more time for house price appreciation in the booming market, which created a cushion against default. Our focus complements this literature, since as we shall see, precrisis network effects were also important in explaining heterogeneous loan performance in the securitized residential mortgage market. Figure 1 presents the market structure for loan sales, decomposed into three levels. Loans flow from the mortgage originator of record to the aggregator of the loans, and then to the securitization shelf and to the holding company that owns it. 2 Figure 1 portrays two possible holding-company types. The lefthand side of the schematic, shown in yellow, represents bank or thrift holding 2 When private-label issuers file a registration statement to register an issuance of a REMIC security, they typically use a "shelf registration," which is owned by a shelf holding company. The shelf registration includes a "core" or "base" prospectus, which outlines the parameters of the various types of REMIC Abstract The residential mortgage market structure Loan sales within affiliated firms (gray arrows) versus loan sales between unaffiliated firms (blue arrows). Abstract company operations, while the right-hand side of the schematic, shown in green, represents investment bank or large independent mortgage company operations in the precrisis period. The gray arrows represent loan sales between entities that are subsidiaries (they may or may not be fully consolidated) of the same holding company and the blue arrows represent loan sales between two unaffiliated firms and holding companies. 3 The graph of the gray arrows represents two trees. However, since loans in the market also flow between these entities, represented by the additional blue arrows in the figure, the market is really a network. 4 The network structure of the market is important, because it suggests complex interactions between intermediaries, potentially affecting their behavior and providing a channel through which shocks can spread. Abstract Note that the arrows in Figure 1 are double-headed, representing bidirectional links in the network. In 2006, the preponderance of loan sales into the pools, typically organized as real estate mortgage investment conduits (REMICs), occurred within 60 days of the origination date of the loan due to the contractual structure of the wholesale lending mechanisms used to fund mortgage origination. 5 These contractual funding structures assign the cash securities offerings that will be conducted in the future through the shelf registration. The rules governing shelf issuance are part of the Secondary Mortgage Market Enhancement Act (SMMEA) (see Simplification of Registration Procedures for Primary Securities Offerings, Release No. 33-6964, Oct. 22, 1992, and SEC Staff Report: Enhancing Disclosure in the Mortgage-Backed Securities Markets, January, 2003, http://www. sec.gov/news/studies/mortgagebacked.htm#secii). Abstract 3 For visual clarity, we do not show sales between entities within the investment bank or independent mortgage holding company (the green entity on the right-hand side of Figure 1 ) to the bank and thrift entities, but these sales would also exist. There also would be sales between bank/thrift entities and investment bank/mortgage company entities. 4 Technically, a network is a general graph of nodes and links, with no restriction with respect to the existence of cycles or connectivity, whereas a tree is a connected graph with no cycle. 5 The two most important of these funding mechanisms are (1) Examples of network loan sales for a sample of seven loans originated and securitized in 2006. The geographic location of the loans varied, as did the lender of record, the shelf registration of the loan, and the holding company that owned the shelf. Abstract flows of the originated mortgages forward to each purchaser. However, the lender of record, or in some cases the aggregator, retains a contractual put-back option on the loan, which makes the risk structure of the loan flows bidirectional. Abstract In line with this observation, Stanton, Walden, and Wallace (2014) find that the mortgage market is well represented by a bidirectional network, and that the performance of an individual node is closely related to the performance of the node's neighbors (i.e., the nodes with which it shares a link) in the network. We therefore follow Stanton, Walden, and Wallace (2014) and use a bidirectional network representation. Table 1 shows an example of actual loan flows for a sample of seven loans originated and securitized in 2006. Each of the seven loans was aggregated by the same subsidiary of Bank of America. As shown in the table, Bank of America (BofA) aggregated loans from independent mortgage companies (Accubanc, Ameriquest, GMAC, Taylor, and Bean & Whittaker Mortgage (TB&W Mtg)), from a S&L (World Savings), from a Bank of America branch, and from the subsidiary of another bank depository (Wells Fargo Bank). Bank of America then sold the mortgages to REMICs created within five different shelf-registration facilities. Three of these shelves were owned by Lehman Brothers and two by Bear Stearns. Thus, this Bank of America aggregator had a one-to-many relation both with lenders (the bottom level in Figure 1 ) and with holding companies (the top level in Figure 1 ), in line with the network description in Figure 1 . We stress that since links in the mortgage network represent loan flows, a neighboring relationship between two nodes has no geographical interpretation. Figure 2 shows the network structure for a small subset of the market containing 21 lenders, eight aggregators and four holding companies, which are connected via loans originated and securitized in 2006. The network has 61 links, compared with 28 links in a tree representation, with 4 trees "rooted" at the holding company level. Thus, in a tree representation, more than half of the links would be unaccounted for. InAppendixA, a so-called "minimum spanning tree" (MST) representation of the subset is presented, which, by including the links with the highest loan flow volumes, provides the most complete tree representation of the market. For the full market of intermediaries, consisting in 2006 of 11,095 lenders, 2,030 aggregators, and 56 holding companies, the MST representation only accounts for about 20% of the links. The fraction of loans accounted for in the MST is higher-about 50%-but still a significant fraction of the market is excluded when using a tree representation rather than a network representation of the market. Abstract Stanton, Walden, and Wallace (2014) find a positive relation between loan performance and the intermediary's network position. For example, they document a correlation of 0.23 between the average default rates of loans handled by an aggregator and those of other aggregators indirectly connected to that aggregator via a common node. 6 Why is this network effect present? One potential reason is that a shock that affects an intermediary spills over to its neighbors through contractual and business interactions. This effect, which plays out once a shock occurs and which we therefore call an ex post effect, is in line with the propagation mechanism described, for example, in Elliott, Golub, and Jackson (2014). Another reason is that the very presence of ex post effects influences the behavior of intermediaries ex ante, before shocks occur, in their decisions regarding whom to interact with and which standards to choose. Indeed, a 6 We verify and extend these results in Section 4.2. common explanation for the observed heterogeneous performance of banks and other financial institutions is that they vary in their standards, through their ability to monitor and evaluate the projects they undertake (see Berger and Humphrey 1997; Billett, Flannery, and Garfinkel 1995, and references therein). Heterogeneous and decreasing lending standards were documented in the mortgage market in the years before the crisis (see Demyanyk and Van Hemert 2011; MacKenzie 2011; Poon 2008) . In what follows, we develop a model in which both ex ante and ex post network effects are important for explaining default rates in the U.S. mortgage market. Abstract We introduce the model in several steps. There are N intermediaries with limited liability, each owned by a different risk-neutral agent. Each intermediary initially has full ownership of a project that generates risky cash flows at t = 1, P n , and may moreover incur some costs at t = 0. The 1-period discount rate is normalized to 0. The intermediary's cash flow at t = 1 is denoted byF n , which may differ fromP n , because of insolvency costs and because intermediaries enter into risk-sharing agreements with each other. Agent n's objective is to maximize expected cash flows, net of any costs incurred at time 0, Abstract The risky project has scale s n > 0, with two possible returns represented by the Bernoulli-distributed random variables ξ n , so that R n = R H if ξ n = 1, and R n = R L if ξ n = 0. The probability, p, that ξ n = 0 is exogenous, with 0 <p 1. We assume complete symmetry of risks in that the probability is the same for each of the N projects. 7 Realized cash flows to all agents are summarized by the random vectorF = F 1 ,...,F N , and the realized project cash-flows are summarized by the vectorP = P 1 ,...,P N . Each agent has the option to invest a fixed amount, C n 0 = cs n at t = 0, where c >0, to increase the quality of the project. This cost is raised externally at t = 0. If the agent invests, then in case of the low realization, ξ n = 0, the return on the project is increased by R > c, to R L + R. This investment cost could, for example, represent an investment in a screening procedure that allows the agent to filter out the parts of the project that are most vulnerable to shocks. Abstract We represent the quality investment choice by the variable q n ∈{0,1}, where q n = 1 denotes that the intermediary invests in quality improvement. Intermediaries who choose q = 1 are said to be high quality, whereas those who choose q = 0 are said to be low quality. For the time being, we assume that c 7 Note that each project may be viewed as a representative project for a portfolio of a large number of small projects with idiosyncratic risks that cancel out, and an aggregate risk component measured by ξ n . is the same for all intermediaries. We will subsequently allow c to vary across intermediaries, representing exogenous variation in costs. 8 There is a threshold, d >0, such that if the return on the investment for an intermediary falls below d, additional costs are imposed, and no cash flows can be recovered by the agent. 9 For simplicity, we call these costs "insolvency costs," in line with Nier et al. (2008) , who note that systemic events typically originate from insolvency shocks, although they are often also associated with liquidity constraints. We stress, however, that d would not necessarily represent the point at which a firm becomes insolvent, but more broadly a region below which additional costs are incurred. Also, although only important from a policy viewpoint and not for the actual predictions of the model, we take the view that these additional costs are wasteful in that they impose real costs on society rather than representing transfers. Abstract It will be convenient to define the functions Abstract We also make the following parameter restrictions: Abstract The first restriction implies that there will be insolvency costs for a low-quality intermediary after a low realization. The second restriction states that the outcome in the high realization is always higher than in the low realization, even for a high-quality intermediary. Abstract We first focus on the setting in which intermediaries do not interact and study the choice of whether to be high or low quality. The cash flows generated by project n are thenP Abstract the total cash flows generated to the owner after insolvency costs are accounted for areF Abstract 8 Several variations of the model are possible, for example, assuming that screening costs, c, are part of the t = 1 cash flows; fixing the scale of all intermediaries to s = 1; and imposing a cost function concave in the size of the node, c = c(s n ). All lead to qualitatively similar results. The version presented here was chosen for its tractability in combination with empirical relevance. Abstract 9 This assumption, similar to assumptions made, for example, in Elliott, Golub, and Jackson (2014) and Acemoglu, Ozdaglar, and Tahbaz-Salehi (2015), is a stylized way of modeling the additional costs related to risk for insolvency, for example, direct costs of bankruptcy, costs of fire sales, loss of human capital, and customer and supplier relationship capital. It could also more generally represent other types of convex costs of capital faced by a firm with low capitalization, along the lines described in Froot, Scharfstein, and Stein (1993). Abstract Downloaded from https://academic.oup.com/rfs/advance-article-abstract/doi/10.1093/rfs/hhx097/4095670 by University of California, Berkeley/LBL user on 08 June 2018 Abstract The Review of Financial Studies / v 0 n 0 2017 and the t = 0 value of the intermediary is Abstract Given the parameter restrictions (1), we have V n (0) = s n (1−p)R H . We make the technical assumption that if an intermediary is indifferent between being high and low quality, it chooses to become low quality. Therefore, q = 1 if and only if V n (1) >s n (1−p)R H , immediately leading to the following result: Proposition 1. An isolated intermediary chooses to be high quality, q = 1, if and only if Abstract Proposition 1 is very intuitive, implying that increases in the probability of a high outcome, the insolvency threshold, or the costs of quality investments, make it less attractive for an intermediary to be high quality. The first argument in the maximum function on the RHS ensures that a high-quality firm avoids insolvency in the low state. If the condition is not satisfied, there is no benefit to being high quality even in the low state. The second argument ensures that the expected increase of cash flows in the low state outweighs the cost of investing in quality. The value of the isolated intermediary when following the rule (6) is then V n I = s n V I , where Abstract Note that the intermediary's optimal choice in (6) is decreasing in the solvency threshold, d, that is, for low thresholds it is potentially optimal to invest in quality, whereas for high thresholds it is not. Also note that the objective functions of the agents coincide with that of society in this case with isolated intermediaries. Specifically, given that society has the social welfare function, V = n V n , under the constraint that intermediaries must act in isolation, the efficient outcome is realized by the intermediaries' joint actions. We obviously do not expect this to be the case in general, when agents interact. Abstract Intermediaries may enter into bilateral contracts that transfer risk, and we represent such relations with links in a market network. Associated with the market network is the N ×N sharing matrix , where nn represents the fraction of risk that intermediary n transfers to n. Abstract The model's key ingredients are intuitive: The network allows intermediaries to diversify risks and thereby avoid insolvency in some states. However, the network also creates incentive problems when intermediaries pay the full cost of quality investments that they then share as benefits from with 10 Downloaded from https://academic.oup.com/rfs/advance-article-abstract/doi/10.1093/rfs/hhx097/4095670 by University of California, Berkeley/LBL user on 08 June 2018 Abstract other intermediaries, and it also exposes intermediaries to systemic risk. Intermediaries are free to add or sever links if it makes them better off. An equilibrium network must be robust against such strategic changes in network structure, which significantly restricts the possible equilibrium outcomes. 10 The market's network is represented by the graph G = (N ,E), N = {1,...,N}. The relation E ⊂ N ×N describes which intermediaries (nodes) are connected. Specifically, the edge e = (n,n ) ∈ E, if and only if there is a connection (edge, link) between intermediary n and n . No intermediary is connected to itself, (n,n) / ∈ E for all n, that is, E is irreflexive. The transpose of the link (n,n ) is (n,n ) T = (n ,n). Connections are bidirectional, e ∈ E ⇔ e T ∈ E. The operation E +e = E ∪{e,e T }, augments the link e (and its transpose) to the network, whereas E −e = E\{e,e T } severs the link if it exists. The number of neighbors of node n is Z n (E)= |{(n,n ) ∈ E}|. Abstract Because of the high dimensionality of the problem when agents act strategically, we necessarily need a limited contract space. Specifically, we assume that the contracts available are such that intermediaries swap claims on the aggregate cash flows generated by their projects in a one-to-one fashion, similar to what is assumed in Allen, Babus, and Carletti (2012). Although obviously a simplification, this assumption qualitatively captures the bidirectional risk structure between intermediaries, discussed in the previous section. The contracts are settled according to a market-clearing system along the lines of that in Eisenberg and Noe (2001). Abstract The risk-sharing rule is represented by the sharing matrix ∈ R N ×N + , where 0 ≤ nn ≤ min{s n ,s n } is the amount of project risk that intermediary n receives from (and in turn gives to) intermediary n . The residual risk intermediary keeps is nn , leading to the summing up constraint, 1 = s, where s = (s 1 ,...,s N ) , and 1 = (1,1,...,1) is a vector of N ones. For a general vector, v ∈ R N , we define the diagonal matrix v = diag(v) ∈ R N ×N . It will be convenient to characterize the fraction of the risk that intermediary n provides to agent n, which is represented by element nn of the matrix = −1 s , implying that s = s, and also the fraction of intermediary n's risk that it receives from n , represented by nn of the normalized sharing matrix Abstract which, in turn, satisfies 1 = 1. The network represents a restriction on which sharing rules are feasible. This restriction may be self-imposed by intermediaries in equilibrium, who could choose not to interact even if they may, or it could be exogenous. Specifically, for a sharing rule to be feasible it must be that every off-diagonal element in the sharing matrix that is strictly positive is associated with a pair of agents who are linked, nn > 0 ⇒ (n,n ) ∈ E. 10 The reader who wishes to skip the formal details of the model may, with this intuition, directly move to Section 3. We focus on a simple class of sharing rules that ensure that all weights are nonnegative and that each intermediary keeps some of its own project risk, namely Abstract and Abstract We write (E) when stressing the underlying network from which the sharing rules is constructed. The joint quality decision of all agents is represented by the vector q = (q 1 ,...,q N ) ∈{0,1} N . In the general case, the cost of investing in quality may vary across intermediaries, represented by the vector c = (c 1 ,...,c N ) ∈ R N ++ . In our analysis, however, we focus on the case in which c n = c 0 /N is the same for all intermediaries. The state realization is represented by the vector ξ = (ξ 1 ,...,ξ N ) ∈{0,1} N . We will work with a limited state space, assuming Abstract Here, δ n represents a vector of zeros, except for the nth element which is 1. Thus, either zero or one low realization occurs, and the probability for a low realization is the same for all intermediaries. Abstract The clearing mechanism for contract settlements is similar to that of Eisenberg and Noe (2001) (see alsoAcemoglu, Ozdaglar, and Tahbaz-Salehi 2015; Elliott, Golub, and Jackson 2014), providing a mapping from project cash flows,P , to realized net settlement cash flows,F = CM [P ]. The outcome is chosen so that it minimizes the number of defaults (which all agents agree are costly), by solvingF = fG , where (10) Abstract Here, f , represents the solvency vector f ∈{0,1} N , with f n = 1 if intermediary n is solvent in equilibrium and f n = 0 if intermediary n is insolvent. Moreover, G represents the cash flows generated by intermediaries, taking into account the default of all other intermediaries but not the intermediaries' own defaults, whereasF represents the cash flows to the owners (which will be zero below the insolvency threshold), taking into account the intermediaries' own defaults. Condition (11) ensures that the number of solvent intermediaries is maximized, whereas condition (12) Abstract the input vector-is a constraint that ensures that only intermediaries above the solvency threshold remain solvent. Abstract As discussed in the appendix, (10)- (12) can be solved by initially assuming that all intermediaries remain solvent, and then iteratively updating those that violate (12) until no further insolvencies occur. This leads to a dynamic interpretation of how defaults propagate: after m steps of the iteration,F m and G m represent the cash flows, given the insolvencies that have occurred so far. Abstract The net cash flows to the intermediaries are given by the vector w(ξ |q,E)=F (ξ,q)− c s q, (13) and the t = 0 value-vector of intermediaries, given quality investments, q, and network E is then given by Abstract We build upon the pairwise stability concept of Jackson and Wolinsky (1996) , in addition requiring equilibrium in the multistage game to be subgame perfect. Abstract Starting with a proposed equilibrium network, E, each agent may unilaterally decide to sever a link to another agent or to sever links with all other agents. Bilaterally two agents can decide to add a link between themselves. In equilibrium we require agents to have correct beliefs about the quality decisions made by their counterparties. Appendix C provides an extended treatment. Let E * denote the complete network in which all nodes are connected and E 0 = ∅ the empty network in which all nodes are isolated. There is a maximum possible network,Ē ⊂ E * , such that only links that belong toĒ may exist in the equilibrium network. This restriction on feasible networks could, for example, represent environments in which it is impossible for some agents to credibly commit to deliver on a contract written with some other agents, because of low relationship capital or limited contract enforcement across jurisdictions. A network, E, is feasible if E ⊂Ē. If all agents who may be linked actually choose to be linked in equilibrium, that is, if E =Ē, we say that the equilibrium network is maximal. It also may be the case that E is a strict subnetwork ofĒ. The primitives of the economy are then summarized in the tuple Abstract The sequence of events in the game is described in Figure 3 . At t = −2, each agent may unilaterally decide to sever a link to another agent, or to all other agents. Each agent can also propose to add a link, in which case the other agent has the option to accept or decline at t = −1. Then, after the resultant network is determined, agents choose quality and outcomes are realized. Note that we implicitly assume that the actual quality decision is not contractible. 11 Abstract 11 In our stylized model, the quality decision can be inferred from the realization of project cash flows. This issue would be avoided by assuming a small positive probability for R = 0 in case of a low realization with quality investments. Abstract Downloaded from https://academic.oup.com/rfs/advance-article-abstract/doi/10.1093/rfs/hhx097/4095670 by University of California, Berkeley/LBL user on 08 June 2018 Consider a candidate equilibrium, represented by a network E and quality choices q. Each agent, n, has the opportunity to accept the sharing rule,ˆ (E), as is, by neither severing nor proposing new links at t = −2. But, in line with the pairwise stability concept, any agent n can also unilaterally decide to sever a link with one neighbor, n , leading to the sharing network E = E −(n,n ), and corresponding sharing ruleˆ (E ).Also, any agent can propose an augmentation of another link (n,n ) ∈Ē\E, which if agent n accepts leads to the sharing network E = E +(n,n ) with sharing ruleˆ (E ). Finally, we assume that each agent can unilaterally choose the isolated outcome, V n I , by severing its links to all other agents. Abstract The possibility to unilaterally sever all links in a sharing network-although not technically part of the standard definition of pairwise stability-is natural, in line with there being a participation constraint that no intermediary can be forced to violate. It provides a minor extension of the strategy space. Abstract The severance, proposal, and acceptance/rejection of links occur at t = −2 and t = −1. The agents then decide whether to invest in quality or not at t = 0, each agent choosing q n ∈{0,1}. A pair (q,E), where E ⊂Ē, is defined to be an equilibrium, if agents given network structure E choose investment strategy q, if no agent given beliefs about other agent's actions-under the current network structure as well as under all other feasible network structures inĒ-has an incentive to either propose new links or sever links, and if every agent's beliefs about other agents actions under network E as well as under all feasible alternative network structures are correct. Abstract We first analyze some specific types of equilibrium networks, shown in Figure 4 , then use simulations to study the relationship between quality choice and network position, and finally provide a partial characterization of node behavior in general networks. The key takeaways from our analysis, relating local network position, global network structure, and quality, is that heterogeneous financial norms tend to be clustered in the network, that the equilibrium quality decision of a node is related to the size and connectedness of that nodes' neighbors, and that the quality decisions of a systemically pivotal subset of nodes are disproportionately important for the systemic vulnerability of the market. Abstract Consider the case with two intermediaries in the network with risk sharing shown in Figure 4A , with scales s 1 = s 2 = 1. The risk-sharing contract is such that intermediary 1 agrees to deliverP 1 /2 to intermediary 2 at t = 1, and, in turn, receiveP 2 /2 from intermediary 2. The sharing matrix in such a risk-sharing equilibrium is There is also another possible equilibrium in this case, the isolated one E 0 , with sharing matrix Abstract For the action q ∈{0,1}, we let ¬q denote the complementary action (¬q = 1−q). The conditions for risk sharing to be an equilibrium are then the following Abstract Condition (15) ensures that it is incentive compatible for both agents to choose the suggested investment strategies given that they share risks, while condition (16) presents participation constraints that state that risk sharing dominates acting in isolation for both agents. (1,0|E*) Abstract Equilibrium: There are four different regions with qualitatively different equilibrium behavior. In the first (leftmost) region, where 0.6= R L + R > d, the unique equilibrium is the one where both agents invest in quality (q = (1,1)) and there is no risk-sharing (network E 0 ), leading to values V I for both intermediaries. No intermediary ever becomes insolvent in this region (since d <R L + R). The outcome where both agents invest and share risk would lead to the same values, but cannot be an equilibrium because each agent would deviate and choose to avoid investments in this case, given that the other agent invests. This can be seen by observing that the red line with stars corresponding to V 1 (0,1|E * ), that is, risk sharing with low quality for agent 1 and high quality for agent 2, is above the magenta line with squares, which corresponds to V 1 (1,1|E * ), that is, risk sharing and high quality for both agents. The deviation strategy is profitable because the deviating agent shares the benefits of quality investments, and therefore the benefit of investing is only p × R/2= 0.15×0.4/2= 0.03 at t = 1, but he incurs the whole investment cost of c = 0.05 at t = 0. The agents therefore cannot coordinate on the high-quality outcome. Abstract In the second region, where 0. Abstract , the equilibrium changes so that both agents choose low quality, q = (0,0) and share risks, that is, the equilibrium network is E * . The outcome corresponds to the green line with crosses, and default never occurs. The reason why isolation 16 Downloaded from https://academic.oup.com/rfs/advance-article-abstract/doi/10.1093/rfs/hhx097/4095670 by University of California, Berkeley/LBL user on 08 June 2018 Abstract is no longer an equilibrium is that quality investments in isolation are no longer sufficient to avoid default after a low shock realization (R L + R ≤ d). Therefore, V I drops substantially. A risk-sharing outcome with quality investments would increase the value to the magenta line with squares, but coordination on this outcome is not possible for the same reason in the first region. Abstract In the third region, where 0.7= ( Abstract , the equilibrium is one of risk sharing, E * , with quality investments q = (1,1) (magenta line with squares). The reason why it is possible to coordinate on quality investments in this region is that without quality investments, default occurs after a bad realization ((R L +R H )/2 ≤ d), so the expected benefit for an agent of investing in quality rather than deviating is p((R L + R +R H )/2) = 0.15×0.9= 0.135, which readily outweighs the cost of 0.05. Abstract Interestingly, although insolvency costs are higher in the third region than in the second region, so is equilibrium welfare. This suggests that if the insolvency cost friction can be affected, for example, by a regulator, the policy implications of decreasing d may be nontrivial: decreasing the friction may actually decrease welfare. Abstract Finally, in the fourth (rightmost) region, where 0.9= (R L + R +R H )/2 ≤ d, default always occurs after a bad realization regardless of the risk-sharing agreement and quality investments. Investment in quality is therefore useless and the agents also choose to be isolated since defaults will propagate if they share risk ( increasing the individual probability of default from p to 2p). Thus, q = (0,0), and the network is E 0 in this region. Abstract We note that q 1 = q 2 for all equilibrium outcomes. This suggests that the "financial norm" of an intermediary-defined as its quality-depends on the financial norm of the intermediary with which it interacts, in line with the intuition that norms are jointly determined among interacting agents. In the two-agent case, it is straightforward to show that this property is generic: Proposition 2. In any equilibrium of the network model with two agents, both agents make the same quality choice, that is, q 1 = q 2 . No insolvencies occur in equilibria with risk sharing. Abstract In our terminology, intermediaries share financial norms in equilibrium. 12 The possibility for agents to cut links is crucial for the result. As shown in the proof 12 Note that our notion of financial norms follows from game theoretic principles. Each intermediary maximizes its own "utility" (defined as its total expected payoff), and the common quality is an equilibrium outcome. Our approach is in line with much of the economics literature on networks, but has been criticized in the sociology and organizations literature as being too narrow to capture the richness of network interactions in a business environment. Granovetter (1985) and Uzzi (1997) , for example, suggest that economic actions are embedded in structures of social interaction, and therefore must be understood within such a context. Such considerations would likely amplify the importance of financial norms if incorporated into our model. of Proposition 2, if the risk-sharing network was exogenously given, it would be possible to get a risk-sharing outcome with heterogeneous financial norms. In other words, common equilibrium financial norms are a consequence of the possibility for agents to affect network structure. Abstract The complete network E * is shown in Figure 4B with N = 4 intermediaries. For large N, we can completely characterize when a complete network is an equilibrium, as shown in the following proposition: Proposition 3. Consider the economy E with maximal networkĒ = E * . For large N: Abstract , then the complete network, E * , with no quality investments, q = 0, is an equilibrium. No intermediary ever becomes insolvent in this equilibrium, and there is no other complete-network equilibrium. (b) If both conditions in (a) fail, then there is no complete-network equilibrium. Abstract The result suggests that the complete network efficiently facilitates complete risk sharing-no insolvencies occur-but may not achieve efficient quality investments. Indeed, intermediaries may well be better off if they could coordinate to invest in quality, but the free-rider problem becomes more severe the larger the complete network, since each intermediary shares less of the benefits of quality investments the larger the network. Therefore, only lowquality equilibria may survive in large complete networks. When the conditions in (a) fail, it is more efficient for an intermediary to isolate and invest in quality, and the low-quality complete network no longer constitutes an equilibrium. Also note that, like in the two-node network (which is a special case of a complete network), all agents share the same (low) financial norms in large complete network equilibria. Abstract The star network E S is shown with N = 5 intermediaries in Figure 4C . Note that the network is asymmetric in that the central "hub" has 4 neighbors whereas the peripheral nodes, n = 2,...,5 have one neighbor each. We first study the special case where the hub is exactly as large as all the other nodes together, s 1 = N −1, s 2 ,...,s N = 1, so that each peripheral node shares exactly half of its risk with the hub, which, in turn, shares half of its risk with the other nodes altogether. In this case, we have Thus, for large star network equilibria, the financial norms are again homogeneous in this case. Like in previous cases, high-quality nodes will not keep connections with low-quality nodes, either preferring to isolate or to switch quality. If we allow other size relations between the hub and peripheral nodes, then there exist equilibria for which the financial norms of the nodes differ. We have: and all the peripheral nodes are high quality, whereas if α ≥ 1, there are no such star network equilibria. (c) For no α is there a star network equilibrium for which the hub is high quality and all the peripheral nodes are low quality. Abstract The result provides further intuition about the relationship between size, number of connections, and quality choice. Specifically, within the class of star networks, all else equal, it is more likely for a node to be high quality if it is larger and if it has fewer connections. In both cases the node keeps a larger fraction of its own project, and therefore has a higher incentive to invest in quality. Abstract Note that there is an asymmetry in Proposition 5 in that it is possible to have a hub with low norm and peripheral nodes with high norms, whereas the reverse equilibrium outcome is not possible. The reason is that in a hypothetical equilibrium in which the hub is high quality, and the peripheral nodes are low quality, the hub can always increase its value by severing one link. Indeed, such a move is preferred by the hub, since it does not change the states in which insolvency occurs because each peripheral node has a very marginal impact on the hub, while allowing it to keep more of its high-quality project. The situation is quite different in an equilibrium with a low-quality hub and high-quality peripheral nodes. In this case, the deviation strategy is for two peripheral nodes to form a link, but because of the more severe incentive problems they face when they share more risk, the outcome may be that the peripheral nodes switch to low quality in this case, making the outcome worse. Therefore, the star network with a low-quality hub and high-quality peripheral nodes survives as an equilibrium. We stress that the aforementioned argument is only valid for large networks. after controlling for other observable characteristics like type and geographical position of the lender. We also find a positive relationship between predicted and actual out-of-sample default rates of the firms in the market. Finally, we compare estimated firm quality with labor intensity, which we argue is a proxy for how much firms invested in monitoring of loans, and again find an economically and statistically significant positive relationship. The U.S. Residential Mortgage Market The precrisis residential mortgage origination market comprised thousands of firms and subsidiaries, including commercial banks, savings banks, investment banks, savings and loan institutions (S&Ls), mortgage companies, real estate investment trusts (REITs), mortgage brokers, and credit unions. These had various roles in handling the loan flows from origination to ultimate securitization. Except for the closure of the Office of Thrift Supervision in 2011, the types of firms in the market are largely the same today. The U.S. Residential Mortgage Market A major driver of the subprime mortgage crisis was increased credit supply, as shown by Mian and Sufi (2009 , who study heterogeneous loan performance at the ZIP-code level and show that performance was closely related to credit availability. Other authors (see, e.g., Bernanke 2007; Di Maggio and Kermani 2014; Kermani 2014; Rajan 2010) have argued that the cumulative effect of low interest rates over the decade leading up to the financial crisis lowered user costs and increased the demand for credit to purchase housing services. Others have argued that the rapid expansions in the precrisis mortgage market arose due to widely held beliefs concerning continued house price growth (see, e.g., Cheng, Raina, and Xiong 2014; Glaeser and Nathanson 2017; Shiller 2014) Alternative explanations have focused on how mortgage securitization led to the expansion of mortgage credit to risky or marginal borrowers (see, e.g., Demyanyk and Van Hemert 2011; Loutskina and Strahan 2009; Nadauld and Sherlund 2013) . Palmer (2015) suggests that vintage effects were important in explaining heterogeneous loan performance: mortgages originated earlier had more time for house price appreciation in the booming market, which created a cushion against default. Our focus complements this literature, since as we shall see, precrisis network effects were also important in explaining heterogeneous loan performance in the securitized residential mortgage market. Figure 1 presents the market structure for loan sales, decomposed into three levels. Loans flow from the mortgage originator of record to the aggregator of the loans, and then to the securitization shelf and to the holding company that owns it. 2 Figure 1 portrays two possible holding-company types. The lefthand side of the schematic, shown in yellow, represents bank or thrift holding Figure 1 The residential mortgage market structure Loan sales within affiliated firms (gray arrows) versus loan sales between unaffiliated firms (blue arrows). Figure 1 company operations, while the right-hand side of the schematic, shown in green, represents investment bank or large independent mortgage company operations in the precrisis period. Figure 1 The gray arrows represent loan sales between entities that are subsidiaries (they may or may not be fully consolidated) of the same holding company and the blue arrows represent loan sales between two unaffiliated firms and holding companies. 3 The graph of the gray arrows represents
{'paper_id': '37109826', 'title': 'Mortgage Loan Flow Networks and Financial Norms', 's2_url': 'https://api.semanticscholar.org/CorpusID:37109826', 'source': 'S2ORC'}