Collateral and Asymmetric Information in Lending Markets

We study the benefits and costs of collateral requirements in bank lending markets with asymmetric information. We estimate a structural model of firms&apos; credit demand for secured and unsecured loans, banks&apos; contract offering and pricing, and firm default using credit registry data in a setting where asymmetric information problems are pervasive. We provide evidence that collateral mitigates adverse selection and moral hazard. With counterfactual experiments, we quantify how an adverse shock to collateral values propagates to credit supply, credit allocation, interest rates, default, bank profits, and document the relative importance of banks&apos; pricing and rationing in response to this shock.


Introduction
A vast theoretical literature studies the benefits and costs of collateral in debt contracts. On the positive side, collateral is argued to increase borrowers' debt capacity and access to credit, by mitigating both ex ante and ex post agency problems arising from asymmetric information in credit markets. Since Stiglitz and Weiss (1981), the theoretical literature motivated collateral as a screening device to attenuate adverse selection (Bester 1985, Besanko andThakor 1987a), and as a way of reducing various ex post frictions such as moral hazard (Boot and Thakor 1994), costly state verification (Gale and Hellwig 1985), and imperfect contract enforcement (Albuquerque and Hopenhayn 2004). 1 On the negative side, apart from limiting borrowers' use of the pledged assets, collateral is often blamed for amplifying the business cycle, through the so called "collateral channel" (Bernanke andGertler 1989, Kiyotaki andMoore 1997). Appreciating collateral values during the expansionary phase of the business cycle fuels a credit boom, while their subsequent depreciation weakens both the demand and supply of credit, leading to a deeper recession. The collateral channel is viewed as one of main drives of the Great Depression (Bernanke 1983), and as an important factor behind the 2007-2009 financial crisis in the United States Sufi 2011, 2014).
The extant empirical literature provides sharp micro-evidence on the impact of collateral on the demand and supply of credit, analyzing each individually by holding the other constant. Several studies show that increases in exogenous collateral values give firms access to more and cheaper credit for longer maturities (Benmelech, Garmaise andMoskowitz 2005, Benmelech andBergman 2009), while exogenous drops in collateral values lead to higher loan rates, tighter credit limits and lower monitoring intensity (Cerqueiro, Ongena and Roszbach 2016). The associated changes in credit supply are found to have a significant impact on firm outcomes, such as investment (Chaney, Sraer andThesmar 2012, Gan 2007) and entrepreneurship (Schmalz, Sraer and Thesmar 2017). Changes in collateral values are also shown to induce similar and contemporaneous changes in households' consumption, which further undermine firms' profits, and hence demand and access to credit Sufi 2011, 2014). While these results provide evidence consistent with the expected role of collateral in credit markets with information frictions, they do not fully shed light on the underlying mechanisms and interactions, as they do not separately identify the role of demand and supply channels.
We contribute to the empirical literature on collateral by bringing the costs and benefits of collateral into a unified micro-founded structural framework. This approach allows us to test key assumptions and predictions of the theoretical literature that underlie the benefits of collateral, and to study how a shock to collateral values affects both the demand and supply of credit in the presence of asymmetric information frictions. We contribute to the literature on three key dimensions. First, by modeling firms' demand for secured and unsecured credit and subsequent loan repayment, we provide micro-founded evidence of the benefits of collateral under both the ex ante and ex post theories, estimating structural parameters that mea-1 There are many other important theoretical contributions on the role of collateral at mitigating information frictions, including Barro (1976) and Hart and Moore (1994). More specifically, Besanko and Thakor (1987b) and Chan and Kanatas (1985) consider ex ante frictions, whereas papers on ex post frictions focus on moral hazard (Boot, Thakor and Udell 1991, Aghion and Bolton 1997, Holmstrom and Tirole 1997, imperfect contract enforcement (Banerjee andNewman 1993, Cooley, Marimon andQuadrini 2004), and costly state verification (Townsend 1979, Williamson 1986, Boyd and Smith 1994 sure the effectiveness of collateral in mitigating both sets of frictions. Second, by modeling banks' loan supply of both collateralized and uncollateralized loans, we are able to separately quantify the role of credit demand and credit supply within the collateral channel, accounting for their interaction. We do so by simulating a counterfactual scenario where the value of the pledged assets deteriorates, and measure the effect of this shock on banks' expected profits, their offering and pricing of secured and unsecured loans, and borrowers' loan demand and default. Third, by estimating a micro-founded model with both adverse selection and moral hazard, we can study how the effectiveness of collateral as a screening and monitoring device and the propagation of collateral shocks are influenced by the severity of adverse selection. We estimate our empirical framework using the detailed credit registry data of Bolivia for the period between March 1999 andDecember 2003. Besides extensive data availability through a comprehensive credit registry, Bolivia provides a good setting for analysis for two main reasons. First, the Bolivian credit market is characterized by deep informational asymmetries between borrowers and lenders, where the informational inefficiencies highlighted by the extant literature are likely to be important. In fact, even for our sample of mostly large and less risky firms, there is very little reliable information other than what is available through the credit registry. This happens because during the sample period there was no private credit bureau and the vast majority of Bolivian firms do not have audited financial statements (Sirtaine, Skamnelos and Frank 2004). This aspect is particularly useful in the context of our model, as it minimizes differences in the available information between the bank and the econometrician. Second, during the period of analysis the Bolivian credit market did not undergo any deregulation wave or phenomena such as loan sales and securitization. Banks in the sample are operating in steady-state under the traditional "originate and hold" model, allowing us to more closely approximate the bank and borrower incentives modeled in the related literature.
On the demand side, we estimate a structural model of borrowers' demand for credit where firms choose their preferred bank, and conditional on this choice they select a secured or unsecured loan and how much to borrow. We model imperfect competition among lenders allowing banks to be differentiated products and borrowers to have preferences for bank characteristics other than the contract terms offered. We also model borrowers' default on these loans. We let borrowers have heterogeneous preferences for loan interest rates and collateral requirements, and we allow their unobserved heterogeneity in price and collateral sensitivity to be jointly distributed with unobservable borrower characteristics that determine whether they default on their loans. This follows the approach of the empirical literature on testing for asymmetric information (Chiappori andSalanié 2000, Einav, Jenkins andLevin 2012), allowing us to test for the empirical relevance of both the ex ante and ex post channels of collateral, and to separately quantify adverse selection and moral hazard. The first channel predicts a negative correlation between borrowers' sensitivity to collateral and their default unobservables, which implies that riskier firms have greater disutility from pledging collateral than safer ones, and hence determines the extent to which collateral can mitigate adverse selection. The second channel predicts a negative effect of collateral on default risk, which implies that when firms pledge collateral their incentives to default on a loan are reduced, consistent with collateral mitigating moral hazard. Similar to Crawford, Pavanini and Schivardi (2018), we interpret a positive correlation between borrowers' price sensitivity and their default unobservables as evidence of adverse selection, since riskier borrowers are less price sensitive and thus more likely to take credit. Finally, we interpret a positive causal effect of loan interest rate on default as additional evidence of moral hazard.
On the supply side, we allow banks to offer borrower-specific contracts, in the form of secured and unsecured loans, and compete Bertrand-Nash on interest rates to attract borrowers. We let borrowers have private information about their unobservable (to both the lender and the econometrician) default risk, which implies that each bank offers the same interest rate to observationally equivalent borrowers. Specifying banks' borrower-specific profit functions we derive the equilibrium pricing equations for both secured and unsecured loans for each lender, and use these to back out their marginal costs.
We then use the combination of demand, default, and supply models to conduct counterfactual policy experiments, where we simulate how shocks to collateral values or the severity of adverse selection influence the demand and supply of credit and banks' expected profits. This allows us to study the propagation of the collateral channel in the presence of asymmetric information, and to investigate how this propagation varies with the severity of the information frictions.
As mentioned above, we estimate our models using loan-level data from the Bolivian credit register. The credit registry includes detailed contract and repayment information on all loans originated in Bolivia. We have data for the period 1999-2003 and focus on commercial loans granted by commercial banks as in Berger, Frame and Ioannidou (2011). This allows us to keep the set of lenders and borrowers homogenous and focus on a class of loans where collateral is (only) sometimes pledged, as predicted by the theoretical literature. The sample includes installment loans and single payment loans, which account for 91% (85%) of the total value (number) of commercial loans to firms in the registry. 2 We avoid modeling the evolution of borrower-lender relationships over time, to minimize the asymmetry of information about borrowers' quality between the econometrician and banks, and therefore focus on firms that take a loan for the first time within our sample period. Crucially, these are the borrowers for which information frictions might be most severe, and collateral requirements might be most effective. One challenge we face is that we only observe the loan a borrower finally chooses, but not the whole set of offers available to the borrower. We therefore need to predict the set of contracts that are available to each borrower as well as the interest rate offered. Exploiting multiple lending relationships that each borrower has, we use fixed effects models and a propensity score matching method to predict the available contracts and the missing interest rates. The advantage of using borrower fixed effects is that it controls for borrowers' information that is observable to banks but not to the econometrician. In the estimation of the structural model, we provide an identification strategy to address potential price endogeneity concerns in both our borrowers' demand and default models.
We find evidence consistent with both the ex ante and ex post theories of collateral, and quantify their empirical relevance. Consistent with the presence of adverse selection, we find a positive and significant correlation of 0.47 between borrowers' price sensitivity and their default unobservables, implying that riskier borrowers are indeed less price sensitive and hence more likely to demand a loan than safer borrowers. In accordance with the ex ante theories that collateral mitigates adverse selection, we find a negative and significant correlation of -0.81 between borrowers' sensitivity to collateral and their default unobservables, which suggests that riskier borrowers tend to have a higher disutility from pledging collateral, and are therefore less likely to demand a secured loan compared to safe borrowers, allowing collateral to serve as a screening device. Furthermore, we find that riskier borrowers have a higher marginal rate of substitution of collateral for price -a key assumption in the ex ante theories, which to the best of our knowledge has never been verified before. Consistent with the presence of moral hazard, we also find a positive and significant causal effect of loan interest rates on default. Our estimates indicate that a 10% increase in loan interest rates raises the average default probability of a loan by 17.5%. Finally, in accordance with the ex post theories that pledging collateral mitigates moral hazard, we find a strong negative and significant causal effect of collateral on default, indicating that on average posting collateral decreases the probability of default by 88.7%.
We use the estimates of our structural model, together with our supply side framework, for counterfactual policy experiments. We simulate the effects of a 40% drop in collateral values on credit supply, credit allocation, interest rates, and banks ' expected profits. 3 This exercise allows us to study the propagation of the collateral channel across various credit, borrower, and bank outcomes. We find that almost 25% of loans become unprofitable under this scenario, which could imply that those loan applications would now be rejected, while the remaining ones experience a 12% increase on average in interest rates, which in turn leads to a 16% average reduction in credit demand, and a 22% decrease in banks' expected profits. We further investigate the role of adverse selection and how its severity influences the propagation of collateral shocks. We find that when adverse selection is more severe, it is easier for lenders to achieve separation of safe and risky borrowers using collateral (i.e., collateral becomes a more effective screening device). As a result, stronger adverse selection mitigates the propagation of the collateral channel, making the increases in interest rates and default in response to a 40% drop in collateral value less pronounced. We also find, however, that when adverse selection is higher, banks suffer larger drops in expected profits as the use of collateral for screening reduces their profit margins ex ante.
We contribute mostly to three broad strands of literature. First, we provide new supportive evidence of the ex ante and ex post theories of collateral. Existing work provides reduced form evidence consistent with theoretical predictions of both sets of theories. Consistent with the ex post theories that banks require collateral from observably riskier borrowers, several studies document that the incidence of collateral is positively related to observable borrower risk. 4 Evidence for the ex ante theories is instead scarce, as borrowers' unobservable risk is typically not observable to the econometrician and difficult to disentangle from ex post frictions. A rare exception is Berger, Frame and Ioannidou (2011), who exploit an information sharing feature of the Bolivian credit registry, using borrowers' historical performance that is unobservable to lenders but observable to the econometricians as a proxy of borrowers' private information. Their findings support both sets of theories and indicate that ex post frictions are empirically dominant. The structural approach 3 A 40% drop in collateral values is similar in magnitude to drops in collateral values documented in the literature during economic downturns, such as the burst of the Japanese assets price bubble that caused land prices in Japan to drop by 50% between 1991 and 1993 (Gan 2007), the early 30% drop of the Case-Shiller 20-City Composite Home Price Index in the U.S. during the 2007-2009 financial crisis, and the increase in average repo haircut on seven categories of structured debt from zero to 45% between August 2007 and December 2008 (Gorton 2010). 4 See, among others, Berger and Udell (1990), Blackwell and Winters (1997), Machauer andWeber (1998), John, Lynch andPuri (2003), Jiménez and Saurina (2004), Brick and Palia (2007), Berger, Frame and Ioannidou (2011), and Godlewski and Weill (2011). in this paper allows us to go beyond testing the two sets of motives for pledging collateral to additionally assessing whether collateral is effective in mitigating the associated frictions.
Some papers use borrower-lender relationships to proxy for ex ante asymmetric information, assuming that the length of a credit relationship implies less asymmetric information and hence less need for collateral (Petersen and Rajan 1994, Berger and Udell 1995, Degryse and Van Cayseele 2000. However, a strong borrower-lender relationship could also reduce the cost of monitoring and state verification problems, accordingly resulting in less ex post asymmetric information. This approach cannot thus disentangle whether less observed collateral in longer borrower-lender relationships is the result of reduced ex ante or ex post asymmetric information. Other studies have used different ways to identify unobserved risk. For example, Gonas, Highfield and Mullineaux (2004) argue that for large, rated, and exchange listed firms asymmetric information is less severe, and show that those firms are less likely to have secured loans. In Berger, Espinosa-Vega, Frame and Miller (2011), the authors take advantage of the adoption of an information-enhancing loan underwriting technology, after which lower collateral incidence is consistent with the ex ante channel. We contribute to the literature by proposing a micro-founded mechanism to incorporate and test for both the ex ante and ex post theories, and by estimating a structural model that allows us to simultaneously quantify the magnitude of adverse selection and moral hazard, and their effects on credit supply.
Second, we contribute to the empirical literature on the collateral channel. One line of papers in this area focusses on how exogenous variation in collateral values influences credit supply by exploiting exogenous variation in commercial zoning regulations (Benmelech, Garmaise and Moskowitz 2005), asset redeployability of airline fleets Bergman 2008, 2009), and regulatory changes affecting creditor seniority Roszbach 2016, 2019). A related line of papers in this area traces the effects of exogenous shocks to collateral values on firms' investment (Chaney, Sraer andThesmar 2012, Gan 2007), employment (Ersahin and Irani 2018), and entrepreneurship (Adelino, Schoar and Severino 2015, Corradin and Popov 2015, Kerr, Kerr and Nanda 2015, Schmalz, Sraer and Thesmar 2017. A smaller set of papers studies the broader effects of collateral shocks. For example, Benmelech and Bergman (2011) study how drops in collateral values, arising from negative externalities of bankrupt firms on their non-bankrupt competitors, amplify industry downturns. A more recent line of papers in this area also studies the amplifying role of the housing net worth channel during the recent financial crisis. House price appreciation prior to the financial crisis triggered significant increases in existing homeowners' consumer demand and leverage (Mian and Sufi 2011), while the subsequent collapse in house prices during the financial crisis led to decreases in consumer demand, which in turn weakened further the real economy, especially in the non-tradeable sectors (Mian and Sufi 2014). We are closer to the first line of papers in this area, as we focus on the effect of the collateral channel on firms' debt capacity and access to credit. Our structural approach allows us to trace the impact of shock to collateral values, accounting for feedback effects between banks' and borrowers' behavior. Differently from the papers listed above -that exploit identification strategies holding either credit demand or supply constant -our structural framework can decompose the collateral channel into its demand and supply effects. Moreover, our approach also allows us to capture spillover effects of a shock to collateral values from secured to unsecured loan rates and demand, a channel previously unexplored by the extant literature. We find that spillover effects on unsecured loan rates are of similar magnitude to direct effects on loan rates of secured loans.
Last, we also contribute to the recent strand of literature on empirical models of asymmetric information using both reduced form and structural methods (Karlan and Zinman 2009, Adams, Einav and Levin 2009, Einav, Jenkins and Levin 2012. Our modeling approach is closest to Crawford, Pavanini and Schivardi (2018), who focus on the interaction between asymmetric information and imperfect competition in the context of Italian unsecured credit lines. We share a similar identification method by combining credit demand for differentiated products and ex post debt performance. We generalize their approach by considering both secured and unsecured loans, allowing for multi-dimensional bank screening through both interest rates and collateral requirements. More generally, we contribute to the growing literature using structural methods from empirical industrial organization to model financial markets, with applications to deposits (Ho and Ishii 2011, Egan, Hortaçsu and Matvos 2017, Honka, Hortaçsu and Vitorino 2017, corporate loans (Crawford, Pavanini and Schivardi 2018), mortgages (Benetton 2018, Robles-Garcia 2019, insurance (Koijen and Yogo 2016), and investors' demand for assets (Koijen and Yogo 2019).
The paper is organized as follows. Section 2 provides a data description and institutional details. Section 3 presents the structural model. Section 4 describes the econometric framework, including price prediction and identification strategies. The estimation results are presented in Section 5. Section 6 presents the counterfactuals, and Section 7 concludes.

Data and Descriptive Evidence
We make use of the data from Central de Informatión de Riesgos Crediticios (CIRC), the public credit registry of Bolivia, provided by the Bolivia Superintendent of Banks and Financial Entities (SBFE) between January 1998 and December 2003. The SBFE requires all formal (licensed and regulated) financial institutions operating in Bolivia to record and share information on their loans. 5 This aims to facilitate the supervision of the financial sector and reduce the otherwise pervasive information asymmetries in the Bolivian credit markets. Besides the information shared through the registry, banks have very limited reliable information about potential borrowers. For example, during the sample period there was no other comprehensive private credit bureau operating in the country (De Janvry, Sadoulet, McIntosh, Wydick, Luoto, Gordillo and Schuetz 2003) and the vast majority of firms in the registry did not have audited financial statements (Sirtaine, Skamnelos and Frank 2004).
For each loan, we observe the identity of the bank originating the loan, the date of loan origination, the maturity date, the loan amount, the loan interest rate, the type and estimated value of collateral securing a loan as well as ex-post loan performance information (i.e., overdue payments or defaults). Information on type of credit is only available as of March 1999. We thus begin our sample in March 1999 and use the earlier information from January 1998 to identify pre-existing bank-borrower lending relationships. Borrowers information includes a unique identification number that allows us to track borrowers across banks and time, an industry classification code, the region where the loan was originated, the borrowing firms' legal structure, current and past bank lending relationships, the borrowers' internal credit rating with each bank, and current and past credit history (i.e., overdue payments or default with any bank in the registry).
The credit registry includes loans from commercial banks as well as other non-bank financial institutions (e.g., microfinance institutions, credit unions, mutual societies, and general deposit warehouses). To keep the set of lenders and borrowers homogenous in terms of financial structure, regulation and lending technologies, we focus exclusively on commercial loans granted by commercial banks. Typically only the larger and better firms in Bolivia have access to the commercial banks. A large number of micro firms have access only to the informal sector and microfinance institutions. During the sample period, there are 12 commercial banks operating in Bolivian, half of which are foreign owned. 6 There are several types of commercial credit contracts in the data, including credit cards, overdrafts, installment loans, single-payment loans (i.e., entire loan amount and interest due at maturity), and credit lines. As in Berger, Frame and Ioannidou (2011) in order to give a meaningful role to the ex ante and ex post theories of collateral we focus on installment loans and single-payment loans, for which collateral is (only) sometimes pledged. 7 Installment loans and singlepayment loans account for about 92% (85%) of the total value (number) of commercial loans to firms. This yields a sample of 32,274 loan originations to 2,676 different firms, including new loans to new or existing customers and renegotiations of previous loans.
In order to minimize the information asymmetry on borrowers' private information between the econometrician and banks, we follow the literature on testing for asymmetric information (Chiappori and Salanié 2000) and focus only on the firms that enter the formal credit market for the first time, for which banks have no previous credit records. This yields a sample of 561 loan originations to 561 new borrowers, which we use for the estimation of the structural model. For some analyses we also employ a slightly larger sample.
As we explain in more detail in Section 4, we need to predict interest rates for loan contracts not chosen by borrowers. For this exercise, we increase slightly the sample size to achieve higher statistical power for prediction by expanding the sample to loans originated within 6 months from each borrower's first loan origination. This larger sample consists of 2,877 loan originations to 1,421 borrowers among which are the 561 borrowers in our restricted sample that enter the credit registry for the first time. Foreign-owned banks operating in Bolivia have similar rights and responsibilities as domestically-owned institutions. 7 We exclude, for example, mortgage loans since collateral is always pledged or overdrafts and credit lines, which are almost always unsecured. 8 Small interest rate discounts between secured and unsecured loans are driven by borrower heterogeneity as riskier borrowers which pay higher premiums are also more likely to be asked to pledge collateral. Interest rate comparisons between secured and unsecured loans in the literature yield mixed results with many studies finding no discounts or even higher interest rate on secured loans, even in regression analyses with borrower controls, due to inability to fully account for unobserved borrower heterogene- and 46% of collateralized loans are secured with real estate ("Immovable"), 28% to 30% are secured with liquid movable assets such as bonds, securities, and deposits ("Liquid Movable"), and about 26% to 27% are secured with more firm-specific movable assets that are less liquid such as inventories, equipment, vehicles, account receivable ("Illiquid Movable"). The average collateral value to the loan amount is 2.8 in both samples. The average loan amount is between USD 140,000 to USD 156,000 and the average loan maturity is between 16 and 20 months. Between 53% to 62% of loans are installment loans, while the rest are singlepayment loans. About 2% of first loans and 6% of all loans are classified as having potential problems or as being unsatisfactory or doubtful ("Bad Credit Rating"). For both samples, about 60% of borrowers are corporations, while the rest are mainly sole proprietorships or partnerships. Between 13% to 28% of loans are granted to "Defaulting Borrowers" with ex post repayment problems, i.e., borrowers who had at least one non-performing loan during the sample period after receiving their first loan. This is also our definition of a "Defaulting Borrower" throughout the paper, which is as in Crawford, Pavanini and Schivardi (2018).
In Panel B of Table 1 we summarize monthly bank balance sheet information on household deposits -an important piece of data that we will use in our identification strategy later on. Deposits from households are distinguished into savings and demand deposits with a mean of 62 and 60 million USD, respectively. On average, banks pay 1.26 million USD as interest on deposits, and the average annualized interest rate on savings deposits is 7 percentage points.
As illustrated in Figure 1, the number of banks that are lending to new borrowers varies significantly across regions, with more banks present in urban areas. For example, in La Paz, the country's capital, all 12 banks originated loans to new borrowers, while in more rural areas such as Potosi, only 3 banks originated loans to new borrowers. Each bank is active across different regions. For example, during the sample period, Banco Nacional De Bolivia and Banco De Credito De Bolivia established new lending relationships in almost all regions, while Banco Do Brasil only granted loans to new borrowers in La Paz. This gives us heterogeneity in borrowers' choice sets of banks depending on their location. In particular, we define a lending market as the region-quarter combination where and when each borrower is making its choice of preferred lender and loan, and all banks actively lending in each market as each borrower's potential choice set. In total, we have 105 region-quarter markets in the sample.
Among the loans granted to new borrowers within the first 6 months, nearly one-third of loans (213) are secured. Borrowers compare potential loan offers not only with respect to the bank, but also with respect to whether they have to pledge collateral or not. The data suggest that a certain level of discretion exists. For example, Figure 2 reports the distributions of the propensity score for taking a secured loan for borrowers that take up a secured or an unsecured loan. 9 The two distributions' overlap in the middle, which indicates that a wide range of borrowers with similar characteristics are almost equally likely to choose secured or unsecured contracts.
ity (see related discussions and literature review in Benmelech and Bergman 2009 and Berger, Frame and Ioannidou 2016, for example). 9 The propensity score is estimated using the bank identity, the loan amount and maturity categories, the borrower's legal structure, and whether the loan is the borrower's first loan in the registry. In Section 4.1.2 we discuss the propensity score matching in detail. Value-to-loan ratios vary significantly with the type of collateral pledged. As can be observed in Figure 3, collateral values for loans secured with immovable assets are often three to four times larger than the loan amount, possibly reflecting the indivisible nature of such assets. Consistent with the more divisible nature of movable assets, a larger number of loans secured with movable assets have value-to-loan ratios equal to one, particularly when secured with movable assets that are more "generic" and liquid in nature. For example, value-to-loan ratios for loans secured with deposits and other financial securities (liquid movable collateral) are clustered around one. Loans secured with other movable assets such inventories, equipment, vehicles, and accounts receivable (illiquid movable collateral) have instead somewhat higher value-to-loan ratios, consistent with lower expected recovery rates on such assets. Such assets are typically more firmspecific with smaller and less liquid secondary markets (Williamson 1988, Shleifer andVishny 1992) and are more susceptible to managerial tunnelling (Aghion and Bolton 1992, Hart and Moore 1994  Note: This figure shows the distributions of the propensity score of choosing a secured loan as opposed to an unsecured loan for borrowers that accepted a secured loan (secured borrower) or an unsecured loan (unsecured borrower). The solid line represents unsecured borrowers, and the dashed line represents secured borrowers. There is a wide range over which the two distributions overlap: A borrower with a propensity score in the overlapping region can become either a secured or an unsecured borrower. Note: This figure illustrates the distribution of collateral to loan value for immovable collateral, liquid movable collateral, and illiquid movable collateral. The collateral to loan ratio is truncated at 5, which means the collateral value is 5 times of the loan amount. For liquid movable, illiquid movable, and immovable collateral type, there are 3.8%, 3.9%, 14.5% of loans with Value-to-Loan ratio above 5 respectively. a 30% discount relative their estimated market values (i.e., the bank expects that on average 30% of these assets will be lost in liquidation), in sharp contrast to immovable assets which are found to carry almost no discounts.
In the empirical analysis, we account for this collateral "pecking order" by assigning a 100% expected recovery rate on defaulting loans secured with immovable collateral, a 90% expected recovery rate on loans secured with liquid movable collateral, and a 70% recovery rate on loans secured with illiquid movable collateral. We thus effectively assume that immovable collateral is fully pledgeable (as in Moore 1994, 1998), while movable collateral is only partially pledgeable. 10 We approximate banks' expected recovery rates on defaulted unsecured loans using the average recovery rates on defaulted unsecured loans to similar borrowers in the registry (i.e., borrowers in the same industry and with the same credit rating). 11 To avoid right censoring, we focus exclusively on loans that reach maturity before the end of our sample, and estimate the recovery rate on defaulted unsecured loans as 1 minus the write-off amount at maturity divided by the contractual loan amount. For these calculations, we only focus on loans that have been persistently classified as non-performing or in default for at least 6 months.
As shown in Table 1 Panel C, the average loss given default rate is 0.35 and therefore the average recovery rate in default is 0.65, in line with estimates in the literature. 12 Similarly, we define the loss rate of defaulting borrowers (i.e., those having at least one non-performing loan within the sample period) as the borrower's total amount of write-offs divided by the borrower's total amount of loans granted. This variable is mechanically smaller than the loss rate given default, as we are simply increasing the size of the denominator from the previous formula by taking into account the borrower's total amount of loans granted. As can be observed in Table 1, the average loss rate of an unsecured loan granted to a defaulting borrower is 0.05. We need this variable to match our definition of defaulting borrower in the structural model where the unit of observation is at the firm-bank level. Accordingly, if on the one hand our defaulting borrower variable is on average actually higher than the default probability over an individual loan, on the other hand this is balanced by the loss rate from defaulting borrower that is on average lower than the loss given default over an individual loan. 10 In robustness checks we also assign 100% recovery rates on loans secured with deposits. Results (available upon request) are both qualitatively and quantitatively similar to those presented in the paper. 11 Note that we cannot rely on the same data to derive banks' average recovery rates on secured loans, as recovery time for collateralized loans is considerably longer. For this reason we rely on literature evidence for recover rates on secured loans, and on our own data for unsecured loans. 12 The literature suggests that bank loan recovery rates range from 60% to 90%. Several factors such as loan and borrower characteristics as well as macroeconomic conditions affect the recovery rates. Asarnow and Edwards (1995) use 831 commercial and industrial loans and 89 structured loans made by Citibank over 24 years and find an average recovery of 65% for commercial and industrial loans and 87% for heavily collateralized structured loans. Acharya, Bharath and Srinivasan (2007) report recovery rates of 81.12% for bank loans in the United States for the period from 1982 to 1999. Khieu, Mullineaux and Yi (2012) find the average recovery rate is 84.14% for North American loans in default in the period 1987 to 2007. Davydenko and Franks (2008) provide information on small firms that defaulted on their bank debt in France, Germany, and the United Kingdom in the years 1996 to 2003. The bank recovery rates are sharply different with median recovery rates of 92% in the United Kingdom, 67% in Germany, and 56% in France.
It remains an open question whether borrowers in our sample use all of their pledgeable assets for the secured loans they take or whether they have any remaining assets that could be pledged if they wanted to take any extra collateralized credit. This is an important piece of information for our counterfactual analyses because when we simulate a drop in collateral value we do not give borrowers the option of pledging additional assets to increase their debt capacity. We justify this assumption with descriptive evidence consistent with borrowers being "collateral constrained". We find that 31% of borrowers whose first loan is unsecured, obtain a new unsecured loan within 3 months. We find instead that just 19% of borrowers whose first loan is secured obtain a new secured loan within 3 months. Among this 19%, only 4% use a different collateral type compared to the one used for the first loan, while the remaining 96% use the same collateral type.
(We focus on a 3-months horizon as firms might be acquiring new assets over time, eventually expanding their potential set of pledgeable assets.) We interpret this as suggestive evidence that firms are collateral constrained, hence almost always using the maximum value of their pledgeable assets to take credit. This allows us to rule out the option of firms to pledge new assets when their pleaded assets drop in value.
3 The Model

Demand and Default Model
Our modeling approach generalizes that of Crawford, Pavanini and Schivardi (2018). We assume that new borrowers seek credit for an exogenously given amount and maturity combination, 13 and shop around banks that actively lend in their region-quarter looking for the most profitable option. We allow firms to choose not only their preferred bank, but also whether they want to pledge collateral or not, conditional on a bank offering them the option of both a secured and an unsecured loan. Unfortunately, we do not observe firms not taking loans, so we are unable to model borrowers' choice of an outside option. Specifically, we let borrower i = 1, .., I in market m = 1, .., M , defined as a region-quarter combination, take a loan of type k = S, U, where S stands for secured and U for unsecured, from bank j = 1, .., J m based on the following indirect utility function, which determines the borrower's loan demand (D): where P ijkm is the interest rate offered by bank j to borrower i, C ijkm is a dummy indicating whether the loan is secured S or unsecured U, X jm are bank-market characteristics, and ν D ijkm are Type 1 Extreme 13 We will allow firms to choose their preferred loan amount in the counterfactual exercises, as discussed in Section 4.3. However, allowing for endogenous firms' choice of amount and maturity at this stage would substantially complicate the model, as it would require us to assume a set of potential amount and maturity options available to the borrower that we do not observe in the data. Moreover, it would imply that banks could use amount and maturity as additional screening and competitive devices, on top of interest rates and collateral requirements. However, given the non-exclusive nature of these loan contracts, it is less likely that banks would use the loan amount as a screening device, as borrowers can linearize the price schedule by taking multiple loans from various banks. Modeling these margins is challenging and we leave it for future research.
Value distributed shocks. We let α D Pi , α D Ci be borrowers' normally distributed heterogeneous preferences for interest rate and collateral, which will depend on borrowers' private information ε D Pi , ε D Ci (unobserved by banks and the econometrician) as follows: Following the descriptive evidence reported in Section 2, we assume that when choosing a secured loan a firm has no discretion over the type and amount of collateral to pledge, as this is entirely determined by the lender. We model a situation in which the firm presents its pledgeable assets to the lender and requires the maximum amount of credit that the lender is willing to grant using those assets as collateral. Hence, we rule out any signaling that the firm might engage in by choosing a specific type and amount of collateral to pledge. We do so to keep the model tractable, and because we do not have data on other potential pledgeable assets that each firm might have.
Similarly to loan demand, we model borrowers' default (F ) as being determined by the following indirect utility function: where ε F i represents the borrower's private information component, unobserved by banks and the econometrician, that affects their likelihood of repayment. Y i are instead borrowers' observed characteristics. In the spirit of the empirical literature on testing for the presence of asymmetric information (Chiappori and Salanié 2000, Einav, Jenkins and Levin 2012), we let ε D Pi , ε D Ci , ε F i be distributed according to the following multivariate normal distribution: The demand and default model allows us to disentangle the adverse selection and moral hazard channels. The adverse selection channel is identified through the covariance matrix of unobservables, which captures the relations of unobserved default risk and firms' unobservable preference for interest rate and collateral in loan demand. The moral hazard channel is identified through the direct impact of interest rate and collateral on default, given that the selection channel has been accounted through unobservables.
We interpret a positive correlation between unobservables determining price sensitivity and default ρ PF > 0 as evidence of adverse selection, as riskier borrowers have lower price sensitivity (as α D P < 0) and therefore are more likely to take credit. We interpret a negative correlation between unobservables determining collateral sensitivity and default ρ CF < 0 as evidence that collateral mitigates adverse selection by inducing separation of borrowers of different risk, as riskier borrowers have higher disutility from pledging collateral. Moreover, we would expect ρ PC < 0, which implies that borrowers with higher disutility from price (i.e., safe borrowers if ρ PF > 0) are also those with lower disutility from pledging collateral (i.e., safe borrowers if ρ CF < 0). Finding that ρ PC < 0 is also evidence that collateral combined with interest rate can serve as a signaling or screening device, because it implies that a price sensitive borrower is more likely to be collateral tolerant. Consequently, safer firms find it more favorable than risky ones to pledge collateral for lower interest rate, and banks can offer a lower interest rate for collateralized loans as the pool of borrowers that self selects into those will be more creditworthy. This would be evidence consistent with the ex ante private information hypothesis that motivates collateral as a signaling device to mitigate adverse selection.
Our model captures moral hazard through two distinct channels. The first is through α F P . Finding that α F P > 0 implies that, conditional on selection, a higher interest rate increases the likelihood that a borrower will default, which provides evidence of moral hazard. The coefficient α F P can identify the moral hazard channel distinctly from the adverse selection channel, which is captured by the correlations between unobservables, leaving the remaining relationship between loan interest rates and default to capture the ex post moral hazard channel. The second is through α F C . Finding that α F C < 0 implies that, after controlling for selection, borrowers pledging collateral are less likely to default, as they have more at stake. This coefficient allows to evaluate whether collateral is effective in mitigating ex post incentive problems.
In our demand and default frameworks we decided to include collateral as a binary variable C ijkm , instead of having a continuous variable measuring collateral value, for the following two reasons related to model tractability. First, a continuous collateral value in the demand model would have a constant value across lenders' alternatives for secured loans within a borrower's choice set, which would not provide extra identifying variation to estimate α D Ci . Second, the unobserved heterogeneity of the demand random coefficient for collateral α D Ci is already capturing the heterogeneous valuation for collateral across borrowers. However, one limitation of this approach is that in our counterfactual simulations a drop in collateral value will not have a direct effect on borrowers' default rate, but will be instead affected indirectly through a change in the equilibrium interest rate.

Supply
We let banks use the interest rate on secured S and unsecured U loans both as a competitive and as a screening device. In particular, we assume that banks compete Bertrand-Nash on interest rates for each individual borrower. We do not model banks' decision to offer either both secured and unsecured loans or one of the two types to each borrower, mostly to keep the model tractable. We do, however, observe in the data heterogeneity across borrowers in terms of types of loans offered, mostly varying across banks and firms' industries. As discussed in more detail in Section 4, we rely on propensity score matching to determine whether each borrower is offered both types of loans or only one type by each bank. 14 To be more specific, we allow each bank j to set its interest rates on secured S and unsecured U loans to maximize its expected profit from a relationship with borrower i as follows: where 1 ijkm indicates the availability of type k loan. Banks can offer both loans, one of them or neither to any borrower. The bank's expected profit from secured and unsecured loans is defined as: where T ijm is the term of the loan (in years) determined by the firm demand, P ijkm is the interest rate offered by bank j to borrower i for loan type k, and F ijkm is the expected default probability of the borrower under each loan type. M C ijkm is the marginal cost of the lending relationship with firm i, including cost of capital as well as administrative and screening costs, which can vary across bank, market and loan type. Q ijkm is the expected demand defined as the probability of demand times the size of the loan: where Pr D ijkm is the probability of demand and LS ijkm is the loan size. 15 R ijkm is the bank's expected loan recovery rate in default. We assume that: where CV ijm is the collateral value to loan amount ratio if the firm would post collateral, and ω ijSm is the expected recovery rate for defaulting borrowers on secured loans, with ω ijSm = 1 for immovable assets, ω ijSm = .9 for liquid movable assets, and ω ijSm = .7 for illiquid movable assets. The expected recovery rate for secured loans depends on the collateral value, but cannot exceed each borrower's total repayment obligation. The expected recovery rate for unsecured loans ω ijU m is calculated using the loss rate reported in Table 1, by taking 1 minus the average loss rate of unsecured loans to defaulting borrowers in the same industry and with the same credit rating. If a bank offers both a secured and an unsecured loan to a borrower, taking the first order conditions of the bank's profit with respect to each interest rate delivers the following equilibrium pricing equations: 15 These two variables are defined in more detail in Section 4.2 and Section 4.3, respectively.
There are two types of loans, secured and unsecured, i.e., k ∈ {S, U} and −k is the other loan type. Q ijkm,P S and Q ijkm,P U are the derivatives of demand with respect to secured and unsecured interest rates, F ijkm,P S , F ijkm,P U are the derivatives of default with respect to secured and unsecured interest rates, and − Q ijkm Q ijkm,P k is bank j's markup on a loan of type k to firm i. The first term on the right hand side of the equation shows how the effective marginal costs influence interest rates, whereas the second term describes the effect of the effective markup. We refer to Crawford, Pavanini and Schivardi (2018) for a detailed discussion on how these two terms, and in particular their denominator, capture the interaction of adverse selection and imperfect competition in their effect on loan pricing. We focus instead on two main novel aspects of our pricing first order condition.
The first novelty is that, in the second term on the right hand side of the pricing equation, the value of the collateral directly affects the recovery rate, and hence the interest rate offered. Intuitively, this implies that the higher is the collateral value (and the bank's expected recovery rate), the lower will be the interest rate, due to the negative sign in front of the second term on the right hand side of the equation. This makes economic sense, as more collateral (or better expected recovery rate) implies less risk and more profit for the lender in case of default. This effect, however, depends on the sign and magnitude of the term in the parenthesis that R ijkm multiplies, which can be interpreted as follows. The more likely is the firm to default (larger F ijkm ), the larger is going to be the price reduction driven by the recovery rate, as the bank now gives more importance to the value of the collateral pledged. However, the stronger is the bank's markup , which is negative, the smaller is going to be the price reduction driven by the recovery rate, as the bank exercises its market power.
The second new point is that the two interest rates on secured and unsecured loans in each bank-borrower combination are jointly determined and affect each other, as the two types of loans are in direct competition for the same borrowers. This competition effect is captured by the last term on the right hand side of equation (10). It shows that a higher profit for a secured (unsecured) loan is positively associated with the interest rate for the unsecured (secured) loan offered by the same bank to the same borrower. In other words, banks are multi-product firms and internalize their profits from the secured (unsecured) loans when setting the interest rate for the unsecured (secured) loan to borrower i.
Our counterfactual on the collateral channel, where we shock the value of the collateral and hence the value of the recovery rate R ijkm , will therefore rely on the mechanisms highlighted by this first order condition to propagate to the supply response of banks, and consequently to their expected profits, and to borrowers' demand and default.

Price Prediction
In order to construct the full choice set of each borrower we need to predict all loan contracts available to a borrower and their corresponding interest rates. We make a set of assumptions to determine borrowers' contract availability. First, we include a bank in a borrower's choice set if that bank granted at least one loan in the region-quarter combination where-when the borrower is taking her loan. Second, if a bank has never granted a loan with a similar amount, duration, or type (secured or unsecured) to a similar borrower, we assume that the bank and/or contract type is not part of the borrower's choice set. This means that we do not assume that all firms are offered both secured and unsecured loans by all banks, but we allow instead banks to screen borrowers also by offering them only one contract type or neither. Once we determine each borrower's available choice set, we predict the interest rates of contracts not observed in the data following a three steps procedure.
First, we use an OLS regression model with a large set of fixed effects to predict the average interest rate across all loans that each borrower is offered by all banks it borrowed from in each market. Crucially, using multiple loans for each borrower, we are able to recover borrower-specific fixed effects that capture both hard and soft information common to all banks that is used for pricing. Second, as the first step doesn't give us a separate prediction for secured and unsecured loans' interest rates, we use propensity score matching to pair borrowers that are equally likely to take a secured loan from a given bank, and then assign the secured rate of a firm that took a collateralized loan in the data to its matched counterpart that took instead an uncollateralized loan, and vice-versa. A drawback of our data is that we do not observe what assets could be pledged as collateral for borrowers that only take unsecured loans. For this reason, we use this same propensity score matching to assign the collateral value and type of collateral of secured borrowers to their matched unsecured ones. Last, we combine these two methods to give the most credible prediction of loan interest rates for secured and unsecured loans for each borrower-bank combination. In what follows, we describe these steps in detail and assess the prediction accuracy of our approach. Note that we only need to predict interest rates to estimate our demand model, whereas we will use actual interest rates to estimate our default model.

Fixed Effects Model
In the first step we predict the average interest rate I ijm across secured and unsecured loans of firm i from bank j in market m as follow: where A i indicates borrower i's loan amount category, and M i indicates i's maturity category. Both variables are categorized by quantiles. 16 γ jm are bank-market fixed effects, λ i are borrower fixed effects, and ijm are prediction errors. By including multiple loans granted to the same borrower within the first six months from its first loan origination, we gain the possibility of identifying borrowers' fixed effects, which are likely to capture, at least to some extent, how the soft and hard information that banks acquire at origination (unobserved by the econometrician) maps into interest rates. Using the estimated coefficients β, γ jm , λ i we can predict I ijm for all banks j that are available in market m. 16 The four loan amount categories are 600$ to 15,000$, 15,001$ to 30,000$, 30,001$ to 90,000$, and 90,009$ to 12,000,000$.
The four maturity categories are 1 to 2.9 months, 3 to 5.9 months, 6 to 18 months, 18.1 to 180 months. Table 2 shows the results for predicting the average interest rate. In the first column, we report the estimation results for equation (11). The model's adjusted R-square is 0.914, indicating that the explanatory variables explain a large fraction of the variation of the average loan interest rate in the data. To evaluate the accuracy of this model, in the second column of Table 2 we report estimation results of a default model where the residuals from equation (11) along with all other explanatory variables, except for the borrower fixed effects, are included as explanatory variables, and the dependent variable is a dummy equal to one if a borrower has any non-performing loans within our sample period. 17 Crucially, we find that residuals are not statistically nor economically significant, which suggests that our prediction error is not related to borrowers' default and hence represents noise in banks' pricing strategy. We interpret this as a sign of the accuracy of our price prediction method.
This approach doesn't yet take into account the different interest rates that a bank offers to the same borrower for a secured or an unsecured loan, mostly for reasons of statistical power, as we do not have enough observations to identify firm-secured loan and firm-unsecured loan fixed effects. The predicted average interest rate can thus be thought as the weighted average of interest rate between secured and unsecured loans that bank j has granted to borrower i, where the weight is given by the likelihood that i will take a secured or an unsecured loan. Hence, we rely on propensity score matching to separately predict interest rates for collateralized and uncollateralized loans for each borrower-bank combinations, as described in the next section.

Propensity Score Matching
In the second step we use propensity score matching (PSM) to determine for each firm-bank relationship in each market the probability that the firm will select a secured loan. This probability will be then used to derive from the predicted average interest rate I ijm the predicted loan interest rates for secured and unsecured loans P ijSm , P ijU m . The matching process works as follows. First, following the criteria suggested by Caliendo and Kopeinig (2008), we select as variables for the PSM the bank identity, the loan amount category, the loan maturity category, a first loan dummy (i.e., whether the loan is the first loan of a new borrower), and the borrower's legal structure (i.e., a dummy variable indicating whether the borrower is a corporation). Second, based on these variables, we use a logistic model to determine the propensity score P SC ijm of borrower i in market m taking a secured loan from bank j. Third, we match each firm i that took a secured (unsecured) loan from bank j with another firm with the same propensity score P SC ijm that has instead taken an unsecured (secured) loan from bank j, and assign to each other the secured (unsecured) interest rate τ ijSm (τ ijU m ) for the loan we do not observe in the data. When there are more than one match for the same combination of P SC ijm we use random assignment. As a result, for each firm we obtain the interest rate for secured and unsecured loans offered by all banks that are actively lending in the market. Appendix A.1 provides detailed information on the optimal matching algorithm and the selection of the variables. We restrict the potential matches to be loan contracts provided by the same bank with the same matching variables, which implies that for some borrower type-bank combinations we may not find any secured or unsecured match, and hence assume that either the secured or the unsecured loan is not offered to that borrower. This implies that we are allowing banks to use also this margin of contract availability, on top of interest rates, to screen borrowers and manage credit risk. Therefore, the predicted loan contracts are those provided by banks that are actively lending in a region-quarter combination, and those that are offered to borrowers with similar characteristics in the sample.
When both secured and unsecured loans are available and the matching is done, we define the interest rate difference D ijm as the difference between the matched unsecured interest rate τ ijU m and the matched secured interest rate τ ijSm : In the next step, we use both this interest rate difference D ijm and the propensity score P SC ijm to derive the predicted interest rates P ijSm , P ijU m . The reason why we do not use the matched τ ijU m , τ ijSm as predicted interest rates is that I ijm captures much more heterogeneity across borrowers because of the firm-specific fixed effects, and as a result a combination of the two steps is what provides an accurate prediction as shown in Section 4.1.4.

Price of Secured and Unsecured Loans
In the last step we predict the interest rate of secured and unsecured loans by adjusting the predicted average interest rate I ijm depending on the propensity score. Intuitively, if most of the loans used to predict I ijm are secured, then I ijm will be a good predictor for P ijSm , but a bad predictor for P ijU m . The opposite occurs if most of the loans used to predict I ijm are unsecured. The propensity score, which determines the probability that the borrower receives a secured loan offer, can similarly be interpreted as the probability that the loans used to predict I ijm are secured. Therefore, for a given average interest rate I ijm and price difference D ijm , the interest rates for secured and unsecured loans are defined as follows: Taking a secured loan as an example, this means that if a borrower is very likely to choose a secured loan (P SC ijm ≈ 1), then also most of the loans used to predict I ijm should be secured ones, and therefore it is reasonable to have that P ijSm ≈ I ijm . If on the other hand a borrower is very unlikely to choose a secured loan (P SC ijm ≈ 0), then most of the loans used to predict I ijm should be unsecured ones, which implies that I ijm ≈ τ ijU m , and therefore it is reasonable to have that P ijSm ≈ I ijm − τ ijU m + τ ijSm ≈ τ ijSm . A similar argument applies for the case of the unsecured loan interest rate.
If bank j only provides one contract to borrower i, then the average interest rate is just the price of the available contract, and the other contract is not available. Hence: P ijSm = I ijm if only secured loan is available; P ijU m = I ijm if only unsecured loan is available.
If bank j provides neither contract to borrower i, then no contract is available to that firm.

Price Prediction Results
Based on our choice set assumptions and matching procedure, we predict the set of available contracts for each borrower at the time of her first loan's origination. From the benchmark case in which all banks were to offer both types of loans to each borrower, our assumptions and matching end up keeping 42.6% of those contracts as actually available to the borrowers. Among the unavailable contracts, in 83.9% of the cases they are not available because the bank is not actively lending in the borrower's market, and in 14.1% of the cases because the bank does not offer the amount and maturity combination required by the borrower. The median secured borrower (i.e., a borrower that chose a secured loan in the data) has 5 secured and 6 unsecured loans available, while the median unsecured borrower (i.e., a borrower that chose an unsecured loan in the data) has 4 secured and 7 unsecured loans available. Among the available contracts, in 11% of the cases the bank only provides a secured loan to a borrower, in 39% of the cases only an unsecured one, and in 50% of the cases it offers both types of loans. Our propensity score matching allows for different contract availability between secured and unsecured borrowers, which implies that banks can screen borrowers both with contract terms and contract availability. More detailed information on the contract availability is presented in Appendix A.2.
In order to assess the accuracy of our price prediction, we compare the actual and predicted interest rates for the contracts that we observe in the data. Figure 4 (a) shows the distribution of the prediction bias, measured as the difference between predicted and observed interest rates. The prediction biases are concentrated around zero with mild deviations. Similarly, Figure 4 (b) shows the distribution of observed and predicted interest rates. Although the predicted prices have a higher standard deviation, the two distributions have a very large overlap.
We also assess the accuracy of our price prediction by investigating whether the predicted contract assignment reasonably matches various key features of the data. In Table A.6, reported in the Appendix, we summarize how the average loan and borrower characteristics vary depending on whether the borrower has been offered both types of contracts, or only secured or unsecured loans. In Panel A we provide these descriptives for all borrower-bank pairs, whereas in Panel B we show the same descriptives only for the bank eventually chosen by each borrower. Differently from Panel A, in Panel B we can distinguish between the case in which a borrower was offered both types of contracts and chose an unsecured one ("Both/Unsecured"), and the case in which it was offered both types of contracts and chose a secured one ("Both/Secured"). The evidence in Panel A suggests that larger firms (proxied by the loan amount and the corporation dummy) and firms without a bad credit score are more likely to be offered both types of contracts. Borrowers with a bad credit score are instead more likely to be offered only a secured loan. Borrowers demanding loans with the longer maturities are also more likely to be offered only a secured contract, while those demanding the shorter maturities are more likely to be offered only an unsecured loan. There does not seem to be a significant difference in the type of contracts offered across borrowers' operating in different sectors.
Panel B reports similar results as those of Panel A, with the addition of the variable "Defaulting Borrower", which identifies whether borrowers ended up defaulting on the chosen loan. The means of this variable present a coherent ranking across different contract availabilities, which we interpret as further evidence of the appropriateness of our contract availability prediction. In particular, borrowers that were offered both contracts and choose an unsecured contract are the ones with the highest incidence of default, whereas those that were offered both contracts and choose a secured contract have the lowest likelihood of default, and those offered only one type are somewhere in between. This can be interpreted as preliminary evidence consistent with both the ex-ante and ex-post theories of collateral. Our structural model will allow us to separately quantify the effect of both of these theories. Table A.7, also in the Appendix, provides some additional evidence of this ranking of default rates across contract availabilities, confirming with a regression model that borrowers that were offered both contracts and chose secured have a significantly lower default rate than those that were offered both contracts and chose unsecured, even conditioning on borrower characteristics and bank fixed effects. 18

Demand and Default
We estimate the model by simulated maximum likelihood, using a mixed logit for the demand model and a probit for the default model. Starting from the former, we define the probability that borrower i = 1, .., I in market m = 1, .., M takes a type k = S, U loan from bank j = 1, .., J m as follows: where we approximate the integral in the first row using Monte Carlo simulations with S = 100 Halton draws, and index each draw by s. The simulation draws enter the random coefficients on interest rate and collateral as in equation (2): where, following the conditional distribution of the multivariate normal: with ζ D Pis , ζ D Cis ∼ N (0, 1). Conditional on taking a specific loan from the most preferred bank, which is determined by ε D Pi and ε D Ci , we model each borrower's default probability, that is the probability that the utility from defaulting is positive, as: Following the conditional distribution of the multivariate normal, we have that: with: Solving the matrix multiplication we get: We use these probabilities to estimate all the parameters θ = {α D , α F , Σ} jointly by maximum simulated likelihood, where α We use the following log likelihood function: where d ijkm takes the value of one if the borrower chooses a bank-loan combination j with loan type k, and zero otherwise, and f ijkm takes the value of one if the borrower defaults, and zero otherwise.

Loan Amount
In the demand model we assume that loan amount and maturity are exogenously determined, depending on firms' financing needs. If the exogenous amount assumption can be justified for the demand estimation, it can become problematic when simulating counterfactual scenarios, especially because we do not allow borrowers to choose the outside option of not taking a loan, which would make aggregate credit demand invariant across scenarios. To overcome this limitation, we model separately the loan size LS ijkm (i.e., total amount granted) that firm i borrows from bank j in market m when choosing contract k as follow: where P ijkm is the interest rate, C ijkm is the collateral dummy, and X jm and Y i include the same variables as in demand and default utility except for the loan amount categories. v ijkm is an IID normally distributed error term. This model will allow us to have variation in credit demand in the counterfactual scenarios, as it will enter banks' profit functions.

Identification
Since we do not know the precise actuarial model that banks use to determine the interest rate for each borrower, a natural concern is that the loan interest rate, both predicted (used in the demand model) and observed (used in the default model), may be endogenously related to unobservables that influence borrowers' demand and default. If this is the case, our estimates of the price sensitivity in both the demand and the default models are likely to be biased. To address this potential endogeneity concern, we use the control function approach suggested by Train (2009), motivated by the fact that both demand and default are nonlinear models. 19 This method consists of two steps. In the first stage, we regress the predicted and actual interest rates on the same set of observables that we use in the demand and default models, plus a set of instrumental variables. In the second stage, we include the residuals from each pricing regression as control variables in the demand and default models to control for any unobserved factors correlated with prices, thus allowing the identifying variation left over in prices to be orthogonal to demand and default unobservables.
In line with Crawford, Pavanini and Schivardi (2018), we use two partially overlapping sets of instruments for demand and default, as they need to satisfy different exclusion restrictions. For both the demand and the default models we include proxies for banks' funding sources and costs from household deposits data, such as banks' deposit interest expense, the total amount of savings deposits, the ratio of savings to demand deposits, and the savings deposits interest rates. Columns (1) and (2) in Table 3 present the first-stage results for predicted and observed loan interest rates, showing that these instruments are relevant for both measures of loan interest rates, with positive coefficients as expected. We believe this set of instruments fulfills the exclusion restriction, as household deposit markets represent a different segment of banking activity compared to corporate loans, therefore any change in its conditions is likely to be correlated with loan rates, but uncorrelated with unobserved determinants of firms' choice of bank and of their likelihood of default.
A potential violation of this exclusion restriction could occur based on the following argument. On the one hand, the market discipline literature in banking argues that banks' funding costs reflect their riskiness, as subordinated debt holders (i.e., large depositors and other subordinated bond holders) demand a premium for lending to riskier banks (Flannery andSorescu 1996, Martinez Peria andSchmukler 2001). On the other hand, there is a literature on the credit side which argues that bank-firm matching is not random, as firms tend to select healthier banks and multiple banks to avoid shocks in credit supply (Detragiache, Garella andGuiso 2000, Ippolito, Peydró, Polo andSette 2016). This evidence suggests that bank risk jointly determines banks' funding sources and costs, as well as firms' choice of banks, which would invalidate the exogeneity of our instrumental variables. We address this concern by focussing only on small household deposits, which are covered by deposit insurance and implicit government guarantees, and are therefore not sensitive to banks' level of risk (Egan, Hortaçsu and Matvos 2017).
Additionally, for the default model's first-stage, we include loan interest rates charged by the same bank in the same quarter in other regions. This instrument, in the spirit of Hausman and Taylor (1981), can violate the exclusion restriction in the demand model, but is unlikely to violate it for the default model, as the loan interest rates in other markets are unlikely to affect borrowers' ex post behavior.
The use of predicted prices in the demand model can also give rise to measurement error. On the one hand, we believe our instruments serve the purpose of addressing this potential source of bias. On the other hand, as borrowers are also likely to be predicting some of the prices that banks in their choice sets might be offering them, our prediction is likely to provide a good approximation of the potential prices that firms actually consider in their borrowing decision.

Estimates
We use data on each borrower's choice of her first loan to estimate the demand, default, and loan amount models. Table 4 presents the estimation results of our structural model. The first two columns refer to the demand equation, with the first and second columns reporting respectively the estimates of the mean component of the random coefficient on price and collateral. The third column refers to the default equation. The bottom panel shows the covariance matrix of the unobservables. Both the demand and the default equations are estimated using maximum simulated likelihood. The fourth column reports regression results for the loan amount model, which are mainly used in the counterfactual analyses for the supply-side model.
In the demand equation, we control for bank-fixed effects, and allow the random coefficients (RC) on prices and collateral to depend on unobserved heterogeneity. Since we have no information on borrowers that do not demand a bank loan, we cannot control for loan and borrower characteristics, as these are constant across borrowers' options in their choice set and their effect on demand would therefore not be identified. We have experimented interacting price and collateral with the borrowers' variables we have (legal status and rating), but found no statistically significant effect. The mean utilities from interest rate and collateral in the demand model are reported in the "Constant" row of Table 4, in the first two columns. We find that on average borrowers get disutility from higher interest rates and from pledging collateral. The mean own price and collateral elasticities suggest that a 10% increase in interest rate reduces the own probability of demand by 1.7%, and requiring collateral reduces the own probability of demand by 15.8%. The last column shows that the interest rate has a negative impact on the loan amount: a 1 percentage point increase in interest rate decreases the loan amount by 21.7%. Therefore, in our counterfactuals we allow demand to adjust to price changes through both an extensive margin (demand probability) and an intensive margin (loan amount).
In the default equation, we include fixed effects for bank, loan amount, maturity, region, and the borrower's industry. We find that the loan interest rate has a positive and significant effect on default, while collateral has a negative and significant effect. The results suggest that on average a 10% increase in the interest rate increases the probability of default by 17.5%, while posting collateral decreases the probability of default by Note: This table shows the first stage results for prices using the first 6 months loans sample. In the first column, the dependent variable is predicted price. In the second column, the dependent variable is the price we observe in the sample. The instrumental variables are banks' deposits interest expense, the total amount of saving deposits, the ratio of saving to demand deposits, interest rate of saving deposits, interest rates in other markets. Loan Controls include dummy variables for Collateral, Instalment, Corporation, Bad Credit Rating. The number of observation is less than the total number of predicted prices and observed prices due to some missing values of the instrumental variables in the first 6 months loans sample. There is no missing value in the first loan sample used for estimation. * p<0.1; * * p<0.05; * * * p<0.01.
Note: This table presents the estimates of the structural model. The first two columns are for demand and the third column is for default, all of which are estimated using maximum simulated likelihood. The last column is for loan amount estimated using a two-step regression with the control function approach, where the dependent variable of the second step is the logarithm of loan amount. There are two random coefficients (RC) in demand: price (1st column) and collateral (2nd column), which contain constant and a normally distributed random terms. In the demand part, the variable Price stands for predicted price, while in the default part, Price stands for observed price. Price and Price residual are normalized at the 95 th percentile of predicted price (i.e., 18 percentage points per year) in the demand and default models. * p<0.1; * * p<0.05; * * * p<0.01. Stiglitz and Weiss (1981), the price effect implies that, conditional on selection, a higher interest rates makes borrowers less likely to repay their loan. The collateral result instead is consistent with collateral mitigating the ex post incentive problem. When borrowers pledge collateral they are more likely to repay, given that they have more at stake in the loan. Consistent with the ex post theories of collateral, this result indicates that collateral is a very effective tool in mitigating moral hazard and other ex post frictions that facilitate or encourage defaults.

88.7%. Consistent with
The bottom panel of Table 4 shows the covariance matrix for unobservable shocks. The positive and significant correlation between price sensitivity and borrowers' unobserved riskiness ρ PF suggests that firms with high unobservable default risk are less price sensitive and more likely to take credit, which we interpret as evidence of adverse selection. On the other hand, the negative and significant correlation between collateral sensitivity and borrowers' unobserved riskiness ρ CF suggests that riskier firms are less likely to demand credit if collateral is required, which we interpret as evidence that collateral can mitigate adverse selection and induce separation of borrowers of different risk. Moreover, the negative correlation between price and collateral sensitivities ρ PC implies that firms with higher disutility from interest rate have instead lower disutility from collateral, as illustrated by the red linear model smoothed line in Figure 5 (a). This implies that borrowers with higher unobservable risk are more price tolerant as well as collateral sensitive, suggesting that safe borrowers prefer a secured loan with low interest rate, while risky borrowers prefer an unsecured loan with high interest rate. Figure 5 gives a graphical interpretation of these results. Figure 5a reports the joint distribution of the price and collateral coefficients, where the center corresponds to two mean utilities, and the two random coefficients are negatively correlated as indicated by the red dashed line. Figure 5b shows the relationship between borrowers' preferences for price and collateral and their unobserved riskiness levels. As conditional on taking a specific loan the unobserved risk ε F i is normally distributed with idiosyncratic meanμ F i , we use as measure of unobserved risk the estimate of this mean as of equation (20), which is distributed with mean 0.00 and standard deviation 0.01. A standard deviation increase in our measure of unobserved risk µ F i increases the probability of default by 3.4% on average.
In Figure 5b risky borrowers are in red while safe borrowers are in green. The riskier a borrower is, the further away it locates from the center towards the top-left corner. That is, riskier borrowers have lower price disutility and higher collateral disutility. The opposite holds for safe borrowers, they are closer to the bottom-right corner, as they have lower collateral disutility and higher price disutility. Hence, this figure demonstrates that it is possible for banks to screen borrowers using collateral. Notice that the collateral coefficient to price coefficient ratio corresponds to the borrower's marginal rate of substitution of collateral for price M RS C,P . As illustrated in the figure, riskier borrowers have higher M RS C,P , as assumed by the theoretical literature that motivates collateral as a screening device of unobserved borrower risk. Therefore, by setting the interest rates on secured and unsecured contracts, banks can make the interest rate benefit of choosing a secured loan compared to choosing an unsecured loan high enough for safe borrowers but too low for risky borrowers, inducing a separating equilibrium. Hence, safe borrowers will be more likely to choose a secured loan with low interest rate, while risky borrowers will be more likely to choose an unsecured loan with a high interest rate, just as what Figure 5b shows. These results confirm the existence of both ex ante and ex post asymmetric information frictions and show that collateral can reduce both kinds of frictions. Furthermore, it provides empirical evidence that risky borrowers have a higher marginal rate of substitution of collateral for price, a fundamental assumption in the ex ante theories of collateral (Bester 1985, Chan andThakor 1987), which to the best of our knowledge has never been verified before. Exploiting the variation in borrowers' preferences, lenders can use interest rate and collateral to affect borrowers' choices, implement screening, reduce credit rationing, and increase social welfare.

Model Fit
We use the estimates of the demand and default models to calculate predicted credit demand Q ijSm , Q ijU m , default probabilities F ijSm , F ijU m , and their derivatives with respect to interest rates. Credit demand is defined as demand probability times the loan amount. Based on equation (10), we solve the first order conditions to back out the marginal costs for secured and unsecured loans: where: If only one type k ∈ {S, U} is offered, then the marginal costs implied by our model estimates are: where the recovery rates R ijSm and R ijU m are defined in equations (8) and (9). Note that these depend on the collateral value CV ijm , which is observable for secured borrowers, but not for unsecured borrowers. Hence, for each unsecured borrower, we take the collateral value of their respective matched secured borrower found using propensity score matching.  Note: This figure shows the distribution of interest rate, demand, default, and profit for not rejected contracts. Expected demand is trimmed at 30,000$, which represents 94% of all contracts. Expected profit is trimmed at 500$, which represents 70% of all contracts. Table 5 reports the descriptive statistics in terms of prices, default, demand and profits for our baseline model. The first row of each section ("Actual") reports the interest rates, demand, default, and profits observed in the data. The second row ("Baseline") shows the same equilibrium outcomes as predicted by our model in the baseline scenario. For each of these rows, we report the mean, median and standard deviations of the loan contracts that have non-negative profits. In fact, given that our model doesn't allow for borrower rejection, in a few cases of unprofitable borrowers, the equilibrium price is pushed to a very high level in order to minimize the borrower's demand probability and loan amount. Hence, we do not report the descriptive statistics for those cases and just summarize the share of contracts that have negative profits in the last column, under each scenario. In general, the model predicted equilibrium is very close to the actual observed outcomes, which is illustrated in the distribution of actual and model fit outcomes in Figure  6.
The last two rows of Table 5 report banks' marginal costs and profit margins, variables usually unobserved in the data, backed out from our model's first-order conditions. These model-implied marginal costs capture the overall cost of lending an extra dollar, including among other things funding, screening, and monitoring costs. We can then calculate how profitable an extra dollar lent is by looking at the ratio of marginal cost to the repayment obligation 1+T ijkm P ijkm , as a low ratio suggests that the bank can extract high margins from lending. We relate the model-implied marginal costs to observed banks' financing costs to demonstrate that the estimated marginal costs capture the decreasing interest rates in Bolivia over the sample period. We show this in Figure 7, where the grey box-plots show marginal costs' 25th percentile, median, 75th percentile, and 95% confidence interval in each year-quarter combination of the sample period, and the red ones illustrate the distribution of the originating banks' funding costs, defined by the ratio of interest expenses on deposits to the total amount of deposits in that quarter. The estimated marginal costs decrease over time, in line with the steady drop in banks' funding costs as reported in their balance sheets, confirming the reliability of our marginal costs' estimates.
We analyze banks' marginal costs and profit margins in Table 6, which presents regression results of model implied marginal costs on loan and borrower characteristics. The dependent variable in the first three columns are the model implied-marginal costs, M C ijkm , while in the last three columns are the marginal costs divided by the repayment amount 1 + T ijkm P ijkm . As shown in Columns (3) and (6), secured loans have higher marginal costs in absolute and relative terms. From Column (1), the marginal cost of lending one dollar with collateral is 0.06 dollar higher than that of unsecured loans, equivalent to 5.0% of the average marginal cost. From Column (4), on average, the marginal cost represents 94% of loan prices. For low quality firms, whose probability of default based on observed risk is above the median, banks have higher marginal costs to lend. However, the marginal costs to total repayment obligation is lower, meaning that banks can charge higher interest rates for borrowers with a high probability of default, and hence the bank's profit margin is higher. In Columns (3) and (6), we add another variable that indicates whether banks provide both secured and unsecured contracts to a firm (Both). That is, banks are using collateral for screening. We find that screening is costly, as providing both types of contracts implies higher marginal costs for banks, but yields higher profit margins. This result highlights the information rent banks obtain by screening, captured by the last term of equation (10). year-quarter combination of the sample period, while the red boxplots illustrate that of bank's funding costs in that quarter defined by the ratio of interest expense on deposits in that quarter to the total amount of deposits (in percentage points).  (4) to (6) are the marginal costs to the repayment obligation M C ijkm /(1 + T ijkm P ijkm ). Collateral is an indicator which equals one for a secured loan and zero for an unsecured one. Low Quality indicates firms with probability of default based on observed characteristics above the median. Both equals one if a loan belongs to a pair of secured and unsecured loans that are offered by one bank to the same borrower. * p<0.1; * * p<0.05; * * * p<0.01.

Counterfactuals
We conduct three counterfactual policy experiments to quantify the credit demand and supply responses to a shock to collateral value, and understand the role of asymmetric information within the collateral channel. First, we simulate a 40% drop in collateral value and quantify the changes in lenders' expected profits and interest rates, and in borrowers' demand and default. Second, we increase the extent of adverse selection and document how the effectiveness of collateral changes. Last, we introduce simultaneously both a shock to collateral value and an increase in adverse selection, to show how the extent of the agency problem can mitigate the collateral channel.

The Collateral Channel
We use the estimates of our demand and default models, together with our supply-side framework, to understand how a shock to collateral values propagates to credit supply, credit allocation, interest rates, and banks' expected profits. Through this exercise we aim to separately identify credit demand and supply responses within the collateral channel. We first simulate a scenario where the collateral value CV ijm drops by 40%. This is similar to the magnitude of various collateral value shocks documented in the literature, such as the burst of the Japanese assets price bubble that caused a 50% drop in land prices in Japan between 1991 and 1993 (Gan 2007), the nearly 30% drop of the Case-Shiller 20-City Composite Home Price Index in the U.S. during the 2007-2009 financial crisis, and the rise in average repo haircut on seven categories of structured debt from zero in August 2007 to 45% in December 2008 (Gorton 2010). This gives rise to various effects through our model. First, it affects directly banks' expected profits from secured loans through the level of collateral, implying that banks will change their equilibrium interest rate, which will in turn affect demand and default. Also banks' expected profits from unsecured loans are affected, as some borrowers might now change their choice between a secured and an unsecured loan, which will in turn imply a change in equilibrium interest rates also for uncollateralized loans. This highlights how our model is able to capture spillover effects of the collateral channel from secured to unsecured loans, a novel result compared to the existing literature.
Assuming that banks' marginal costs of lending to each firm remain constant in the counterfactual scenario, we simulate a 40% drop in collateral value and find the new equilibrium in terms of interest rate P ijkm , probability of default F ijkm , expected demand Q ijkm , and banks' expected profit Π ijkm . Table 7 summarizes the new equilibrium after the collateral value shock compared with the baseline model. We find that a 40% decrease in collateral value generates on average a 13.1% and 11.0% increase in the interest rates of secured and unsecured loans that have non-negative profits, respectively. Overall, the interest rate increases by 12.0%, namely 1.8 percentage points. The probability of default increases by 8.0% on average. The expected demand and profit drop significantly, especially for secured loans, with a 17.9% and a 24.4% decrease, respectively. Crucially, we find that the share of non-profitable offered loans goes from around 5% (3% for secured and 6% for unsecured loans) in the baseline case to 25% (18% for secured and 30% for unsecured loans). Although we observe a large increase in interest rate and a drop in demand and expected profit for secured loans, a larger portion of unsecured loans become unprofitable when the collateral value drops. Credit supply shrinks as borrowers face higher financing costs and less loan offers. The distributions of the percentage changes in the new equilibrium are depicted in Figure 8. These results are qualitatively in line with the findings in Cerqueiro, Ongena and Roszbach (2016), who investigate how a legal change in Sweden reduces the collateral value by 13% for outstanding loans, generating a 0.2 percentage points decrease in interest rate, an 11% decrease in internal credit limit, and 12 percentage points more delinquent borrowers. These results quantify the relevance of various components of the mechanism at play in our model, following up on the discussion at the end of Section 3.2. A shock to collateral value directly impacts lenders' profits through the recovery rate term. Banks respond to this shock increasing the interest rate on both secured and unsecured loans, as they can use both margins to make up for this potential profit loss. The heterogeneity in these price responses is driven by both the average borrowers' default rate (F ijkm ) and banks' markup terms, as can be seen in equation (10). As expected, borrowers respond to this by reducing their credit demand and increasing their likelihood of default, through the moral hazard channel α F 1 . Another driver of the larger increase in interest rates for secured loans compared to unsecured ones is adverse selection, because safe borrowers are the most price sensitive ones, and the larger price increase might induce them to switch to unsecured loans, worsening the pool of borrowers choosing collateralized loans. In other words, the increase in interest rates for unsecured loans is also determined by the riskiness of the marginal borrowers who switch away from secured loans.
An interesting implication of this shock to collateral value is that the difference in interest rates between secured and unsecured loans is now reduced. In the baseline case, the average interest rate of unsecured loans is 0.9 percentage points higher than the secured loans, with a 95 confidence interval between 0.6 and 1.1 percentage points, while in the collateral value shock scenario, the average interest rate difference drops to 0.6 percentage points with a 95 confidence interval between 0.3 and 0.9 percentage points. This implies that one of the consequences of the collateral channel is making it less profitable to induce separation between secured and unsecured loans, which can potentially increase the extent of agency costs.

High Adverse Selection
The second counterfactual exercise investigates how the extent of adverse selection affects the effectiveness of collateral as a screening mechanism. In our model, the existence of adverse selection is captured by the positive correlation between unobserved borrowers' riskiness and their price random coefficients (ρ PF ). However, if we want to make adverse selection more severe while keeping borrowers' unobserved risk constant, we can only do it by increasing the standard deviation of borrowers' preferences for interest rates (σ P ). In fact, as shown in equation (20), changing ρ PF would also affect µ F i . Hence, we increase five times the standard deviations of the price random coefficient σ P . 20 Figure 9 gives a graphical intuition for this counterfactual, showing how the change in σ P from the baseline (left figure) to the counterfactual (right figure) leads to a more dispersed distribution of borrowers in their preference space, while holding unobserved risk fixed. This can be interpreted as an increase in adverse selection, as riskier borrowers are now even more likely to take credit (less price sensitive), hence moving further towards the top of the figure, while the opposite happens for safe borrowers. The new equilibrium after the adverse selection shock is summarized in Table 8 and Figure 10. We find that all outcomes for secured and unsecured loans change in opposite directions. When adverse selection increases, the interest rate of secured loans decreases by 0.65%, while it increases by 0.12% for unsecured loans. On average, higher adverse selection lowers the overall interest rate by 0.23%. The probability of default changes accordingly in the same direction as their respective interest rate change. In the new equilibrium, the pool of borrowers attracted by secured loans are less risky than before with a 0.43% decrease 20 We arbitrarily chose a fivefold increase as we do not have a benchmark for what a reasonable increase in adverse selection could be. Note that smaller or larger increases in this parameter would just lead to smaller or larger changes in the relevant outcomes of our model.  This counterfactual shows that when adverse selection becomes more severe it is easier for lenders to achieve separation of safe and risky borrowers in secured and unsecured loans, because of the larger polarization in their M RS C,P . This implies that the average risk of borrowers choosing unsecured loans increases, whereas that of borrowers choosing secured loans decreases, as reflected by the rise in interest rates for the former and the drop for the latter ones. The decline in default rates for secured loans is caused both by this selection effect and by a reduction in moral hazard through the direct effect of a lower price on default. The opposite happens for default rates of unsecured loans. This simulation exercise shows how collateral becomes a more effective instrument the larger is the extent of adverse selection. It causes an increase in borrowers' surplus, through lower interest rates, but a decrease in lenders' expected profits.

The Collateral Channel with High Adverse Selection
In the last counterfactual we investigate whether the extent of adverse selection can mitigate the propagation of a shock to collateral value. Therefore, we combine the two previous simulation exercises into one, by simultaneously dropping the collateral value by 40% and raising adverse selection with a fivefold increase in σ P . We summarize in Table 9 and Figure 11 the new equilibrium results compared with the baseline case (i.e. no collateral value nor adverse selection shock) across the four relevant outcomes: interest rates, default, demand, and banks' expected profits.
When the collateral value shock occurs in a market with high adverse selection, we observe that interest rates increase on average, but less relative to the case of baseline adverse selection. In particular, the largest reduction in interest rate increase happens for secured loans (11.9% vs. 13.1%). Similarly, on average the probability of default increases less when adverse selection is more severe. 21 This implies that if a shock to collateral value hurts the effectiveness of collateral screening, higher adverse selection works in the opposite direction, making the propagation of the collateral channel less pronounced than in the baseline case, in terms of interest rates and default. This however is mostly driven by the lower price and default increase for secured loans, while instead the larger demand drop for unsecured loans reduces overall demand and banks' profits by more than in the baseline case.

Effectiveness of Collateral as Screening Device
We provide additional evidence of the main mechanisms driving the results in our counterfactuals, further investigating how collateral values and the level of adverse selection affect the effectiveness of collateral as a screening device. We estimate a simple regression model using our baseline and counterfactual results  to understand the relationship between borrowers' likelihood of choosing a secured loan, given by the corresponding estimated demand probabilities, and their unobserved riskiness, defined as our estimate of µ F i from equation (20). We take as unit of observation each bank-firm combination for which a lender offers both a secured and an unsecured loan, and use as dependent variable in an OLS regression the probability of choosing a secured loan from each bank, conditional on having chosen that specific bank. We estimate this model for our baseline case and for the three counterfactuals we run, and summarize the results in Table 10. We include the interest rate of secured loans, as well as fixed effects for bank, loan amount, loan maturity, industry, and quarter. The benefits of this exercises are twofold. First, we can summarize within a single regression model an important takeaway of our counterfactuals, that is how the effectiveness of collateral as a screening device changes across different scenarios. Second, we make direct use of our model-implied borrowers' unobserved riskiness, not explicitly employed in our previous policy experiments.
In the baseline model, that is the first column on Table 10, we find that the probability of choosing a secured loan is negatively related to borrowers' unobserved risk, which implies that safe borrowers are more likely to choose a secured loan. In particular, one standard deviation increase in a borrower's unobserved risk leads to a 0.2 percentage points decrease in her probability of choosing a secured loan. This is consistent with collateral mitigating adverse selection problems by inducing separation of borrowers of different risk. However, once we shock the collateral value, the screening effect of collateral loses explanatory power, as can be seen from the coefficient of unobserved risk in the second column of Table 10. This reinforces the conclusion stated at the end of Section 6.1, as the drop in collateral value decreases lenders' profits from secured loans, which in turn decreases their incentive to differentiate between safe and risky borrowers using collateral. Moreover, from the borrowers' perspective, the collateral value shock increases significantly the interest rate on secured loans, which decreases safe borrowers' demand for secured loans.
On the contrary, an increase in adverse selection leaves the screening effect of collateral roughly unchanged, as reflected by the negative coefficient on unobserved risk in the third column of Table 10 compared to the baseline case. If anything, the adverse selection shock actually makes the screening effect even stronger. This is in line with the findings in Section 6.2, as higher adverse selection makes it easier for banks to separate borrowers of different risk using collateral, which results in lower average risk of borrowers choosing secured loans and therefore lower prices, and the other way around for borrowers choosing unsecured loans. The last column in Table 10 refers to the third counterfactual, the collateral value shock with high adverse selection. Differently from the results in the second column, under this scenario the higher level of adverse selection counterbalances the collateral channel, allowing collateral to still be an effective screening device. We find in fact a negative relationship between borrowers' unobserved riskiness and likelihood to choose a secured loan, larger in magnitude than the other columns but with weaker statistical significance. This suggests that higher adverse selection mitigates the drop in screening effectiveness of collateral caused by a negative shock to collateral value. However, the cost for banks to maintain screening is higher, as shown by the larger drop in profits in Table 9. This implies that drops in collateral values are more destabilizing to banks profitability in markets with high adverse selection.

Conclusions
In this paper we study the benefits and costs of collateral requirements in bank lending markets with asymmetric information. We develop a structural model of firms' credit demand for secured and unsecured loans, banks' contract offering and pricing, and firm default using detailed credit registry data on corporate loans and borrowers' performance from Bolivia, a country where asymmetric information problems in credit markets are pervasive. We make three important contributions to the literature.
First, by modeling borrowers' demand for secured and unsecured credit, we provide micro-founded evidence of the benefits of collateral pledging, estimating structural parameters that measure both the ex ante and ex post reduction in agency costs that collateral determines. We provide evidence supporting both the ex ante and ex post theories of collateral. Consistent with the ex ante theories, we find a negative and significant correlation of -0.81 between borrowers' sensitivity to collateral and their default unobservables, which suggests that borrowers with high default risk tend to have high disutility from pledging collateral, and are therefore less likely to demand a secured loan compared to safe borrowers. Furthermore, we provide empirical evidence that riskier borrowers have a higher marginal rate of substitution of collateral for price, a key assumption in the ex ante theories which, to the best of our knowledge, has never been verified before. Consistent with the ex post theories, we find a negative and significant causal effect of collateral on default, suggesting that on average posting collateral decreases the probability of default by 88.7%.
Second, by modeling also lenders' supply of both collateralized and uncollateralized loans, we are able to separately quantify the role of credit demand and supply within the collateral channel, accounting for their interaction. We simulate the effects of a 40% drop in collateral value on credit supply, credit allocation, interest rates, and banks' expected profits. We find that almost 25% of loans would become unprofitable under this scenario, while the remaining ones would experience a 12% increase on average in interest rates, a 16% reduction in average demand, and a 22% decrease in banks' expected profits.
Third, we can study how the use of collateral and the propagation of collateral shocks is influenced by asymmetric information frictions. We find that when adverse selection becomes more severe it is easier for lenders to achieve separation of safe and risky borrowers in secured and unsecured loans. As a result, stronger adverse selection mitigates the propagation of the collateral channel, making the increases in loan interest rates and default in response to a shock to collateral value less pronounced. We also find, however, that when adverse selection is high, banks suffer larger drops in expected profits as the use of collateral for screening reduces their profit margins ex ante.
Overall, our results indicate that collateral has a large impact on firms' access and terms of credit. Swings in collateral values have a large effect on the fraction of borrowers that are able to obtain credit, as well as on the amount and terms of credit, by altering banks' expected profitability and equilibrium loan interest rates. Our work opens the floor for various other potential directions of research. First, our approach could be extended to quantify not only how the severity of adverse selection, but also how the severity of moral hazard can influence the propagation of shocks to collateral values. This would have important implications for policymakers, who could then prioritize their interventions on the key friction. Second, the current analysis holds banks' marginal cost of funds constant. Additional counterfactual experiments could allow this to change, providing insights on the role monetary policy in the transmission of shocks to collateral values. Third, our model could be extended by allowing loan maturity to be another screening and monitoring dimension, substituting or complementing the use of collateral. Last, this framework could be used to investigate how policy interventions aimed at improving lenders' recovery rates could mitigate the negative effects of a shock to collateral value. We regard all of these as promising directions of future research.

A.1 The Matching Algorithm
This section explains the process of determining the optimal matching algorithm. We first provide a simple example of matching, and then show how to determine the optimal matching algorithm, based on the performance of matching observed unsecured loans (untreated) to observed secured loans (treated).
A simple example for matching: Take the case in which we only observe four firms obtaining a loan of the same amount and maturity in the same region and quarter from two banks, Bank A and Bank B. Table A.1 summarizes the interest rates observed in the data (in bold) and those predicted by our matching exercise (in italics). Following the table, we observe Firm 1 taking a secured loan from Bank A at a rate of 14 p.p., Firms 2 and 3 taking an unsecured loan from Bank A at respectively 16 p.p. and 15p.p., and Firm 4 obtaining an unsecured loan from Bank B at a rate of 18 p.p.. If Firm 3 is the best match for Firm 1, then we can assign Firm 3's rate on the unsecured loan form Bank A to Firm 1's unobserved unsecured loan from Bank A. Similarly, if Firm 2 is the best match for Firm 4, then we can assign Firm 2's rate on the unsecured loan form Bank A to Firm 4's unobserved unsecured loan from Bank A. Given that Firm 1 is the only firm that received a secured loan from Bank A, its interest rate will be the best predictor for what the other three firms would have been offered for a secured loan from Bank A. Similarly, given that Firm 4 is the only firm that received an unsecured loan from Bank B, its interest rate will be the best predictor for what the other three firms would have been offered for an unsecured loan from Bank B. Last, given that no firm has been given a secured loan from Bank B, we assume that no firm has been offered a secured loan from Bank B. Selecting the variables for propensity score: Following Caliendo and Kopeinig (2008), we use two criteria to select the variables for our propensity score matching exercise. First, the variables must be statistically significant at predicting the propensity score. Second, the variables are chosen to maximize the rate of correct prediction. We start including only banks' identifiers, and progressively add variables only if they are statistically significant and can improve the number of correct predictions. We end up with the following set of variables: banks' identifiers, amount category, maturity category, first loan dummy, corporation dummy. The propensity score generated by these variables delivers 580 correct predictions out of 842 secured loans.
Choosing the algorithm: To ensure that after matching the covariates are as close as possible between matched secured and unsecured loans, we set the radius very close to zero such that the matched loans must share the same characteristics as the loan to be matched (i.e., exact matching). If there are more than one loan that have the same characteristics, we randomly choose one loan as the match. This gives us balanced covariates after the matching. There are 168 secured loan could not be matched. Table A.2 summarizes the statistics before and after matching. Table A.3 presents the matching covariates before and after matching. Through matching, the differences between the covariates of secured and unsecured loans are completely removed, as the percentage of bias is zero for all covariates. This is also illustrated in Figure A.1 (a). Figure  A.1 (b) shows the propensity score distribution of secured loans (Treated) and unsecured loans (Untreated). "Treated: Off Support" indicates the unmatched secured loans.

A.2 Price Prediction Results
Contract Availability: Table A.4 shows the number of secured and unsecured loan contracts that are predicted to be available to secured and unsecured borrowers, where secured borrowers are those that chose a collateralized loan in the data, and unsecured borrowers are those who chose an unsecured loan. Our sample includes 2,871 loan contracts (842 secured and 2,029 unsecured), 561 new borrowers, and 12 banks. The maximum number of potential contracts is therefore 2, 871 × 2 × 12 = 68, 904. For secured and unsecured contracts, the first column shows the total number of contracts to be predicted, the second column the number of contracts predicted to be available, and the last column the share of contracts predicted to be available contracts among all potential contracts. Our matching exercises predicts that secured borrowers are more likely to be offered a secured loan than unsecured borrowers (38% vs 34%), while unsecured borrowers are more likely to be offered an unsecured loan (52% vs 45%). Note: This table summarizes the number of secured and unsecured loans that are available for borrowers. The first column is the total number of potential contracts to be predicted (Total), the second column is the number of contracts predicted to be available (Available), and the last column is the percentage of contracts predicted to be available (% Available). Table A.5 shows the availability of the pair of contracts offered by banks to firms. Our matching method allows for the possibility that a bank provides only secured or only unsecured loans to each firm. It also allows banks not to offer any contract to some borrowers, either because the bank is not active in the borrower's market (in 83.9% of the cases), or because the bank does not offer the type of loan required by the borrower in terms of amount and maturity (in 14.1% of the cases). Our propensity score matching allows for different contract availability between secured and unsecured borrowers, which means that banks can screen differently secured and unsecured borrowers not only with contract terms, but also with contract availability.  Note: Panel A summarizes average characteristics of borrowers and of loans that were offered by all available banks. A bank may offer both secured and unsecured contracts to a borrower (Both), only an unsecured loan (Only/Unsecured), or only a secured loan (Only/Secured). Amount is the loan amount in 1,000 USD. Maturity is in months. Corporation is a dummy variable taking the value of one if the borrower is a corporation and zero if it is a sole proprietorship or partnership. Bad Credit Rating is a dummy variable taking the value of one if the loan has any overdue payments or is in default and zero otherwise. Interest Rate is the annual percentage rate. Defaulting Borrower is a dummy variable indicating that loans are granted to borrowers who had at least one non-performing loan in the sample. Manufacturing, Construction, Wholesale and Retail Trade, Real Estate Activities, Social Services, Other Activities are dummy variables indicating borrowers' industry. Panel B presents average characteristics of borrowers and of loans that were eventually chosen. Both/Unsecured (Both/Secured) are borrowers that were offered both secured and unsecured contracts by the bank and chose an unsecured (secured) loan. Only/Unsecured (Only/Secured) are borrowers that were only offered an unsecured (a secured) contract. Both/Secured is a dummy variable taking the value of one if the borrower was offered both contracts and chose the secured one and zero otherwise. Only/Unsecured is a dummy variable taking the value of one if the borrower was only offered an unsecured contract from the bank that was finally chosen and zero otherwise. Only/Secured indicates the borrower who was only offered a secured contract. * p<0.1; * * p<0.05; * * * p<0.01.