The Working Paper Series seeks to disseminate original research in economics and fi nance. All papers have been anonymously refereed. By publishing these papers, the Banco de España aims to contribute to economic analysis and, in particular, to knowledge of the Spanish economy and its international environment. The opinions and analyses in the Working Paper Series are the responsibility of the authors and, therefore, do not necessarily coincide with those of the Banco de España or the Eurosystem. The Banco de España disseminates its main reports and most of its publications via the INTERNET at the following website: http://www.bde.es. Introduction Every state in the United States has experienced a sharp increase in mortgage foreclosures since the beginning of the housing market crisis. As the economic recession deepened and home price depreciation mounted, many households were heading for default and foreclosure on their properties. And this epidemic has proved to be persistent. According to Corelogic (2012) , the percentage of homeowners nationally who were more than 90 days late on their mortgage payments, including homes in foreclosure and real estate owned (REO) properties, mariaward@example.com percent in February 2012. Furthermore, 11.1 million, or 22.8 percent, of all residential properties with a mortgage were in negative equity at the end of the fourth quarter of 2011, putting more upward pressure on foreclosure trends. Introduction Taking into consideration the negative externalities of foreclosure on individuals, lenders and communities, it is not surprising that "foreclosure" has emerged as one of the most debated topics among government officials, professionals and scholars since 2006. Introduction While the Federal Government tried to conceive of measures to curb foreclosure, states put their own solutions on the table, basically enacting laws to protect homeowners and make the foreclosure process more costly for lenders. For example, in April, 2008, officials from Introduction Maryland signed an emergency package to fight foreclosures. One important aspect of this legislation was to lengthen the foreclosure process from 15 to 150 days. Some states followed the same philosophy, such as Georgia, Massachusetts and Illinois, while others strengthened protection by imposing mediation programmes before foreclosure (e.g. Introduction Washington and South Carolina), among other measures. Introduction As states worked on new rules, doubts began to be raised about the effectiveness of such measures. The most common criticism is that tighter rules may make mortgages more expensive, especially in cases where foreclosure time periods are extended and more judicial procedures are required. In this paper, we go a step further and directly address the question of whether state borrower-protective laws ultimately achieve their intended goals, i.e. if they are successful in protecting homeownership and reducing the number of foreclosures. Introduction Interestingly, after six years of crisis in the mortgage market, this analysis is still controversial. Many US states are debating or have recently passed modifications to their state foreclosure laws. At the same time, a debate on the convenience of unifying foreclosure regulation at federal level is growing among lenders, lawyers and politicians. Furthermore, although the focus of our analysis is state regulation in the United States, the conclusions could be of interest to the policy-makers of any country suffering the effects of a housing market collapse. Specifically, some countries are questioning their mortgage laws, with the focus on protecting mortgagors, encouraging deed-in-lieu practices or promoting loan modification and refinancing programmes, which according to the IMF (2012) may help avert self-reinforcing cycles of household defaults, further house price declines and additional contractions in output. Introduction We study the effects of state laws on foreclosures using a two-stage approach. Introduction Firstly, we consider how laws affect rates of default (defined as 60-day delinquency), which are a consequence of decisions made by the debtor and creditor at loan origination and by the borrower at the time of default; secondly, we look at how laws affect the pass-through from delinquency to foreclosure, i.e. the negotiation process between borrower and lender once default has occurred. As far as we know, this is the first attempt to estimate the different effects of regulation on each stage of the foreclosure process in an integrated framework. Introduction This distinction is useful to help achieve an optimal design of effective foreclosure laws, ensuring that such effects are as intended. Introduction In order to estimate those effects, we make use of a panel data model of mortgage default at state level. We look at differences in delinquency and foreclosure rates between states, in the light of the degree of protection provided to borrowers by state laws. The sample covers a complete credit cycle (2000) (2001) (2002) (2003) (2004) (2005) (2006) (2007) (2008) (2009) (2010) , which allows us also to analyse whether protective regulation has been effective during the current crisis. As a proxy of the level of protection, three state-level dummy variables are included in the model. A state is classified as borrower-protective if its laws require court intervention in the foreclosure process (judicial foreclosure), grants a redemption right to the borrower (redemption period after the foreclosure sale) or bans a deficiency judgment for the lender (right to go after other assets if the sale price is not enough to recover the whole of the unpaid debt). These dummies change by state (between dimension) but do not change over time (within dimension) in the sample, which means that the traditional endogeneity problem of regulation due to inverse causation is avoided. In order to deal with the estimation of parameters associated with time-invariant variables in panel data models, which are deleted in the within transformation of the traditional fixed-effects estimator, we make use of an extension of the Random Effects Mundlak transformation model proposed by Krishnakumar (2004) . This model expands the original panel regression with an auxiliary equation that takes into account the relationship between the explanatory variables and the individual effects. Once we combine the two regressions, the parameters of time-invariant variables, along with those of time-variant variables, can be consistently estimated with the GLS estimator. Introduction The empirical findings contradict officials and legislators who argue that stricter regulation reduces foreclosure rates. After controlling for a set of economic and sociodemographic variables that are classic in the default literature, we find that, in the United Introduction States, a higher degree of protection does not lead to lower foreclosure rates at state level, although the transmission channels are not straightforward. Firstly, protective regulation reduces delinquency rates. As protection is costly for lenders, it encourages borrower discrimination through the underwriting process, which ultimately reduces delinquency rates, ceteris paribus. 1 Those rates are 16% lower in states with redemption periods and 24% lower in states that prohibit a deficiency judgment. Surprisingly, we do not find any statistically significant difference in delinquency rates between judicial and non-judicial states. But, once a borrower has defaulted, the pass-through from delinquency to foreclosure is higher in borrower-friendly states, where borrowers have incentives to seek protection and lenders have less bargaining power to avoid a costly and lengthy foreclosure process. The passthrough may be as much as 5% higher in judicial states and 4% higher in states where redemption periods are granted or deficiency judgments are prohibited. Given the opposite impact of regulation on the two different stages of the foreclosure process, the final effect on foreclosure starts will depend on the magnitude of these two impacts. We find that this final effect is positive but weak. In particular, foreclosure rates are 9% higher in judicial states, though the difference is negligible for the other protective elements. Introduction 1. We do not address the welfare effects of protective regulation in this paper, but only its final effect on foreclosure rates. At first glance, protective regulation may be socially beneficial since it reduces the overall risk of the economy through borrower discrimination. Nevertheless, it also introduces mortgage market distortions and credit restrictions, through more restrictive covenants and more expensive loans. Furthermore, although more protection may initially reduce delinquencies at the expense of tighter credit, the final effect on foreclosures may be not be as desired. Introduction Furthermore, we propose a difference in difference regression model to analyse whether protective regulation has been effective during the current crisis. We find that the crisis has exacerbated the reaction to protective laws of both lenders and borrowers and that, finally, protective regulation has not actually protected borrowers, since the difference in foreclosure rates between protective and non-protective states has not decreased -and in some cases has even increased -since the crisis. Introduction Several studies show that the core element of protection is the length of the foreclosure process. On this basis, many modifications to state laws have focused on lengthening the foreclosure process, which was expected to work as an incentive for lenders to renegotiate with borrowers, since going through the foreclosure process would be more costly, while also giving borrowers more time to recover from financial distress. We analyse the empirical evidence and conclude that lengthening the foreclosure process is not the answer. A 100-day increase in the duration of the foreclosure process produces a 7% increase in the foreclosure rate. Introduction All these results suggest that new foreclosure legislation needs to be reconsidered, and that the current debate should look at new solutions, while acknowledging the adverse effect of regulation on every part of the foreclosure process. When analysing the effects of borrower-protective laws our ultimate aim is to give useful insights for devising more effective regulatory frameworks. Introduction The paper is organised as follows. Section 2 reviews the literature. Section 3 presents the legal framework that regulates foreclosures at state level and the different stages of the foreclosure process. Section 4 discusses the theoretical approach of our working hypothesis. Section 5 describes the data sources and variables used in the model. Section 6 explains the empirical approach used to test our hypothesis. Section 7 reports the main findings. And Section 8 concludes. Review of the literature Economic literature has documented the negative impact of foreclosure on borrowers and lenders -it is a time-consuming and costly process for all parties -and its spillover effects on neighbourhoods, such as increases in crime rates and depreciation of house prices [see, for instance, Moreno (1995) , Apgar et al (2005) , Immergluck and Smith (2006) , Lin et al (2007) and Campbell, et al. (2011) ]. Some politicians, trying to remedy the negative effects of foreclosure, have enacted legislation that protects homeowners from this undesirable event. Introduction The proponents of such legislation argue that protective regulation makes the foreclosure process fairer and delays foreclosure, so that borrowers have a chance to overcome bad times and lenders are more willing to renegotiate with borrowers. Unfortunately, such legislation does not always contribute to social welfare. Introduction Part of the credit market literature has focused on the study of how regulatory frameworks affect market conditions and the behaviour of economic agents. Alston (1984) looks back at the 1930s and examines the negative impact that legislation had on farm foreclosures. He argues that while legislation was implemented to protect farmers, it actually led to fewer farm loans and higher mortgage rates. Meador (1982) and Jaffe (1985) find that mortgage rates are higher in states where foreclosure takes longer. Barth et al (1986) argue that restrictions on the use of default remedies do not confer net benefits on the typical borrower but rather impose net costs. Clauretie and Herzog (1990) demonstrate that loan losses for lenders are greatly affected by foreclosure laws and affirm that lenders protect themselves with higher interest rates and more restrictive covenants. Lawrence (1993) notes that in a period of sizable house-price declines, the prohibition of deficiency judgments can increase the incidence of default by two or three times over a period of several years. Khan and Yavas (1994) analyse renegotiation in foreclosure processes and argue that it can change the effective interest rate that the lender receives; reforms that favour defaulting debtors will raise interest rates on mortgages to compensate for that change. More recent studies reassert these findings. For example, Pence (2003) estimates that loans are 7% smaller in defaulter-friendly states; her results also suggest that defaulter-friendly laws impose material costs on borrowers at the time of loan origination. Cutts and Merrill (2008) show that foreclosure costs increase significantly with the length of the foreclosure timeline and that the likelihood a borrower will cure the loan falls as that length increases. Introduction Nevertheless, the literature has paid less attention to the direct effect of state foreclosure laws on delinquency and foreclosure rates themselves. Furthermore, the results are not conclusive and sometimes contradictory. For example, in a pioneering empirical study, Clauretie (1987) found that foreclosure is more likely in states where the legal costs for lenders are lower (for instance, due to the existence of non-judicial proceedings), since lenders appear less willing to work with delinquent borrowers. But, at the same time, as Cutts and Merrill (2008) point out, lengthy foreclosure processes provide an incentive for borrowers to forego reinstatement of the loan even if they have the necessary means. In this sense, Goodman and Smith (2010) use a hierarchical regression model to examine the effects on foreclosure of laws regarding predatory lending and foreclosure proceedings. They affirm that laws that are costly for lenders impose credit discrimination at origination and, therefore, should reduce default rates. They conclude from their estimation that foreclosure rates are lower in states where foreclosure processes are longer and redemption periods are granted. Introduction Nevertheless, other authors have found that the effect of borrower protection goes in the opposite direction. For example, Jones (1993) , by analysing data from Alberta (Canada), Introduction found that the prohibition of deficiency judgments increases default rates during times of house price decline. More recently, Ghent and Kudlyak (2011) In summary, the question of whether foreclosure regulation to protect borrowers achieves the intended goals of curbing foreclosures and preserving homeownership is still unresolved. The aim of this paper is to shed some light on that issue. State regulation of foreclosure and the foreclosure process Basic elements of state foreclosure laws Foreclosure laws are unique to each state and represent an often perplexing amalgam of English legal history, common law, and legislation [Nelson (2010) ]. Although terms, procedures and timeframes differ from one state to another, most foreclosure regulation can be fitted into one of two frameworks: borrower protective and non-protective laws, 2 referring to the level of protection provided by the law to borrowers in default. The main difference between them relates to whether legislation requires court intervention for foreclosure, whether borrowers have redemption rights and whether deficiency judgments are available to lenders. 3 According to Nelson et al (2007) , a judicial foreclosure involves a court procedure and is characterised by the sale of a property in a court action in equity. When a borrower defaults, the lender must file a complaint specifying the amount of the debt and the due date. 3 She also needs to notify other parties, such as tenants and second or junior mortgagees, and file a public notice of action called a "lis pendens" (pending legal action). The borrower simultaneously has an opportunity to defend herself. If the court finds that the lender has the right to foreclose, it will issue a judgment against the borrower. After foreclosure the property will be sold through a sheriff´s sale or public auction. At the end of the auction, the highest bidder will be the owner of the property. 3 A non-judicial foreclosure, on the other hand, requires no court ruling. This speeds up the process, which is frequently completed within four to eight months (half the length of a judicial foreclosure). Such foreclosures are based on the "power of sale" of the mortgagee, which allows it (or the trustee) to sell the property, without court intervention, to satisfy the outstanding debt. Once the sale has taken place, the buyer has full title to the property. A notice of default is first sent to the borrower. If the borrower does not respond to the notice, or does not cover the amount and expense of the default during the legally required time, the lender can initiate the foreclosure and the auction sale. 3 Legal theory has traditionally distinguished between "title states", where the lending institution holds title to the property in the name of the borrower through a deed of trust; 4 and "lien states", where the deed remains with the borrower and the lender places a lien on the property using the mortgage instrument. Generally, foreclosure in title states occurs through a non-judicial procedure, while in lien states it is conducted via a judicial process. Nevertheless, this distinction is not that clear, since the laws of many states allow both methods of foreclosure, although usually one of these methods is more commonly used in practice. 3 2. Other authors have used the term defaulter-friendly laws (Pence 2003) . We prefer the term protective, to emphasise the intention of law promoters. 3 3. There are other protection provisions in state laws (such as prompt return of surplus, accounting for sale proceeds, etc.) but the literature assigns them a minimal role in characterising the level of protection or the behaviour of homeowners. 4. A deed of trust is a type of secured real-estate transaction that is used in some states instead of a mortgage. It involves three parties: a lender, a borrower, and a trustee. The borrower gives the lender a promissory note in exchange for the borrowed money. As security for the promissory note, the borrower transfers a real property interest to a thirdparty trustee (in many cases, the borrower actually transfers legal title to the trustee, who holds the property in trust for the use and benefit of the borrower). A deed of trust always includes a power-of-sale clause: if the borrower defaults on the terms of her loan, the trustee may exercise the power of sale, take full control of the property and sell it to compensate for the borrower's default. 3 There are two additional elements that protect borrowers by imposing restrictions on lenders in the foreclosure process. A common mechanism is the provision for a statutory right of redemption, which provides the borrower with a longer period of time after the foreclosure sale to redeem the property if she is able to pay back the sale price at auction plus foreclosure expenses and fees [Singer (2002) ]. During the redemption period (usually from 75 days to 18 months), the borrower continues living in the property and the lender receives no income from the owner. Proponents claim that statutory redemption encourages those who bid at the sale to bid a fair price. Nevertheless, redemption periods extend the foreclosure process and, in practice, depress bids at the foreclosure sale since the buyer cannot occupy the property until the redemption period has expired [Clauretie and Herzog (1990) ]. Statutory redemption may be available in both judicial and power-of-sale states. 3 To complicate the foreclosure process further, there exists a third mechanism in state laws, known as a "deficiency judgment", which is the right of the lender to go after the borrower's remaining assets when the proceeds of the collateral sale do not suffice to cover the debt. In states where deficiency judgments are forbidden the lender's recourse is restricted to the value of the mortgaged property; the borrower has a put option on the property and is more likely to default. 3 The absence of a deficiency-judgment option reduces the lender's expected return from a foreclosure action. Although most states allow lenders to appeal in court for deficiency judgments, they are rarely observed and certain mechanisms can mitigate their impact [Ghent and Kudlyak (2011) ]. For example, in some states judgments are costly to obtain, or their value is limited to the difference between the unpaid debt and the fair market value of the property, which could be higher than the sale mariaward@example.com. Nevertheless, recourse involves a threat that may affect borrower behaviour and result in mitigation of lender losses through renegotiation [Ghent and Kudlyak (2008) , Clauretie and Herzog (1990) , and Kennedy (2004) ]. 3 New foreclosure laws are intended to prevent foreclosures from spiking and to protect borrowers when they face financial difficulties. However, judicial procedures and redemption rights lengthen the foreclosure process, thereby increasing costs for lenders and borrowers [Cutts and Merrill (2008) ]. Higher costs and delays have encouraged alternative legislative approaches (such as power-of-sale clauses) to speed up the foreclosure process and protect the value of properties from excessive depreciation. As Nelson (2010) should be handled by a real estate broker and not by a court. Non-judicial foreclosure is seen in this Act as mutually beneficial, because it protects the borrower and is efficient for the lender, since it preserves the value of the property and ensures that the sale proceeds are as high as possible. 3 However, other experts advocate more borrower-protective regulation on the basis that borrowers should be provided with a secure and fair process that protects their rights [Rao and Walsh (2009)] . The UNFA has not been adopted by many states, but it is at the centre of debate. The steps to foreclosure As shown in Graph 1, the path to foreclosure starts when the borrower technically defaults on her loan, i.e. when the borrower stops making the scheduled loan payments [Giliberto and Houston (1989) ]. As Quercia and Stegman (1992) highlight, when payments are first missed it is not possible to know whether the borrower has defaulted or is just temporarily delinquent. To avoid this problem, we assume in this paper that the borrower has decided to stop payment completely (i.e. is in default) if payments are not met for two consecutive months (60-day delinquent). The steps to foreclosure Graph 1. The foreclosure process SOURCE: Own elaboration After default, the parties are likely to engage in some kind of negotiation and a set of bargaining tools (or "threats") are available to them in order to protect and pursue their interests in the negotiation [Kennedy (2004) ]. The parties will choose to renegotiate the loan terms or to start the foreclosure process on the basis of the expected losses associated with these actions [Foote et al. (2008) and Quercia and Stegman (1992) ]. Lenders are usually willing to work out with borrowers since they maximise their profit by taking payments from the debtor and not by managing foreclosed properties, which usually involves large costs. SOURCE: Own elaboration Nevertheless, the key element of renegotiation is that it can benefit the lender, i.e. if the reduction in the value of the loan is lower than the loss the lender would sustain in a foreclosure. Therefore, not all loans in default will end up in foreclosure; some of them will be cured, while others will be definitively in default and will enter into foreclosure. This passthrough from delinquency to foreclosure will be a key variable in our study. There are many ways to avoid foreclosure and the loss of the property (see Graph 2) once a loan is in arrears. When a borrower misses some payments, the lender will send a notice to accelerate the due date of the loan and typically the borrower and the lender will initiate conversations to explore the options available. At this point, the borrower can reinstate the loan, sell the property and cancel the loan, or refinance the outstanding debt before the foreclosure process starts. Furthermore, the lender and the borrower have the option to agree a loss mitigation scheme, which could include a loan modification, forbearance, repayment plan, or loss of the property via short sale, deed in lieu or loan assumption. All of those cases will avoid foreclosure and not dramatically harm the borrower's credit rating. If the borrower ignores the acceleration and demand letters and does not agree a solution with the lender, the latter will file a formal foreclosure notice with the court (in a judicial state) or will send a notice of sale (if a power-of-sale clause is included in the contract). Once foreclosure is started, the procedure will depend on the state laws relating to judicial involvement, the existence of a right of redemption for the borrower and whether the lender has the right to seek a deficiency judgment against the borrower. SOURCE: Own elaboration 4 Theoretical approach The effect of state laws on default State foreclosure laws affect the way lenders and borrowers behave. Following Pence (2003) , in the mortgage market lenders aim to maximise their profits on the basis of their cost structure, which is partially dictated by the risk of not getting repaid. In other words, lenders adjust the supply of credit according to the expected value of their loans, which is determined by: (i) the present value of future payments; (ii) the probability of obtaining those future payments; and (iii) the costs of enforcing payment when necessary, combined with the portions that may be impossible to recover. In a competitive market, those profits will be zero in equilibrium: The effect of state laws on default where M is the outstanding mortgage loan balance, DP is the down-payment, r is the interest rate, z is the stochastic change in house value, and k is the foreclosure cost for the lender. It is clear that foreclosure laws have a direct impact on lender costs through the third determinant mentioned above. In states that require judicial foreclosure it is more expensive for lenders to enforce repayment. Additionally, states with long redemption periods impose additional costs on the lender, who has to wait longer for payments, probably without compensation in the form of additional interest or rent. Finally, when the law bans the possibility of a deficiency judgment, lenders may never recover part of the loan, since the market value of the property is all they can obtain from the borrower. Moreover, foreclosure laws may indirectly affect lender costs through the riskiness of loans. If borrowers are aware of the protection provided by laws they will find it safer to default in more protective states. The effect of state laws on default Lenders are certainly aware of those risks and of the differences in state laws so they adjust in various ways [see Jones (1993) , Wood (1997) and Pence (2003) ]. By requiring borrowers to meet stricter conditions of financial stability, decreasing loan-to-value ratios or lowering the supply of credit, lenders can reduce a priori the probability of default. The effect of state laws on default However, default is ultimately a borrower's decision. Once the loan has been granted, homeowners who face a change in their financial conditions may default on their mortgage. From the borrower's perspective, we follow a "double trigger" model for default [see, for example, Aron and Muellbauer (2010) or Jackson and Kassrman (1987) ]. Borrowers default if they cannot afford to continue making payments (cash-flow problems) and if they owe more than the property is worth (excessive debt relative to equity). The model is a combination of two approaches. On the one hand, the equity model, or option pricing approach, which states that a household will default once housing equity falls below the mortgage debt level by a certain percentage (the borrower's tolerance to negative equity on her house): P[D(t)] = P[equity(t )/ mortgage(t) < C t ] , C t < 0 This behaviour is associated with a strategic default, which occurs when the negative equity level hits a trigger threshold. That level of tolerance to negative equity will increase with the expected growth rate of house prices, with removal costs and with the expected interest rate movements. P[D(t)] = P[equity(t )/ mortgage(t) < C t ] , C t < 0 On the other hand, the ability-to-pay model states that a household will default if its current income net of essential expenses is not enough to cover the periodic mortgage payments: P[D(t)] = P[income(t) < P] Bajari et al (2009) introduce a more accurate approach based on cash-flow problems and argue that borrowers default when a function of the debt service ratio (dsr) exceeds a certain threshold. This default trigger function also depends on employment status (ur), creditworthiness (cs) and the expected growth rate of household income (ye): P[D(t)] = P[income(t) < P] Both circumstances (negative equity and cash-flow problems) are to some extent necessary for default since: (i) if there is equity remaining the borrower has incentives to refinance the mortgage or sell the house, pay off the debt and keep the difference; and (ii) if the borrower can afford the payments but there is negative equity she will generally keep servicing the debt (unless that negative equity is excessive) because renting is costly, her credit rating could be seriously damaged after default, while keeping the house preserves the option of future gains in the property's value and moving costs are substantial [Cutts and Merrill (2008)]. Furthermore, Guiso et al. (2009) consider that the most important variables in predicting strategic default are moral and social considerations. They find that no household would default if the equity shortfall is less than 10% of the value of the house. Yet, 17% of households would default, even if they can afford to pay their mortgage, when the equity shortfall reaches 50% of the value of their house. P[D(t)] = P[income(t) < P] In principle, state foreclosure laws can be introduced in both models. According to Ambrose et al. (1997) , defaulter-friendly regulation makes default less costly for borrowers. P[D(t)] = P[income(t) < P] Therefore, it increases the probability of strategic default -reducing the tolerance to negative equity -or lowers the threshold in the default trigger function. P[D(t)] = P[income(t) < P] To sum up, at the time of loan origination, lenders are aware of the costs associated with protective regulation and tighten credit and grant less risky mortgages, thereby reducing the probability of borrower default. But, once the property has been purchased, borrowers who suffer cash-flow problems and negative equity are more likely to default in states where they feel protected by the law, simply because, ceteris paribus, the cost of defaulting is lower. P[D(t)] = P[income(t) < P] The final effect on default rates is ambiguous. Nevertheless, as Pence (2003) points out, it is unlikely that debtors are aware of and consider foreclosure laws at the time of debt origination. Furthermore, Cutts and Merryl (2008) show that generally borrowers are unaware of work-out options when they stop making payments and, by the same token, it seems implausible that they will simultaneously be aware of foreclosure regulation. If that is the case, the theory predicts that borrower-protective regulation will induce lower default rates. The effect of state laws on the pass-through from delinquency to foreclosure Once the borrower defaults (i.e. stops making regular mortgage payments) the borrower and lender initiate a negotiation process. Again, state foreclosure laws may affect the way borrowers and lenders behave during that negotiation process. Borrowers will usually contact a counselling service or an attorney to advise them of the best options to avoid foreclosure and the loss of the property. Protective regulation favours the debtor in the post-default negotiations and reduces the bargaining power of the creditor by reducing its ability to make credible threats to injure the debtor. To the extent that debtors are aware of the state statute regime, and depending on their susceptibility to "moral hazard" in relation to their obligation to the creditor, borrower-protective laws ought to increase the foreclosure rate, other things being equal [Kennedy (2004) ]. The same idea exists in Cutts and Merryl (2008) , who suggest that excessive protection gives borrowers incentives to "go for foreclosure", since they may feel protected by the court, get extra time to negotiate, can rule out a deficiency judgment or enjoy a free rent during the lengthy foreclosure process. On the other hand, if foreclosure resolution is fast and the borrower can lose her home quickly, the borrower has incentives to reinstate the loan or negotiate with the lender. In this context, Ghent and Kudlyak (2011) show that in protective states borrowers are less likely to resume payments following the delinquency that precedes the foreclosure and lenders have less power to negotiate a quick resolution of the default. In contrast, lenders in non-protective states have better bargaining positions and foreclosure is more likely to occur through a lender-friendly procedure, such as a short sale, with a lower cost to lenders. Hence, our theory predicts that in borrowerprotective states the pass-through from default to foreclosure is likely to be higher than in non-protective states. The effect of state laws on the pass-through from delinquency to foreclosure In short, according to our theoretical approach, there is a two level implication of state laws. On the one hand, lenders impose tighter credit standards at time of loan origination and give less risky mortgages in order to compensate for the higher costs associated with borrower-friendly regulation. Therefore, the theoretical implication is that default rates are lower in protective states. Then, once the borrower defaults, protection implies a higher pass-through from delinquency to foreclosure. The final result on the foreclosure rate is uncertain. Data sources and variables We use a panel data set that includes 50 states plus Washington D.C. and a time-span of 11 years, dating from 2000 to 2010. We analyse mortgage default and foreclosure rates at state level. Default rate is defined as the ratio of the number of loans 60 days past due to the total number of outstanding mortgages. Foreclosure rate is defined as the ratio of the amount of loans entering the foreclosure process in the period in question (foreclosure starts) to the total amount of outstanding mortgage loans. We also analyse the passthrough from defaulted loans to new foreclosures, measured as the ratio of foreclosure starts to 60-day delinquent loans. Data sources and variables Mortgage loans include all types of loans granted for mortgage purposes, such as fixed-and adjustable-rate mortgages, prime and sub-prime mortgages, etc. Data on delinquency rates and foreclosure rates at state level come from the National Delinquency Survey (NDS), conducted by the Mortgage Bankers Association of America (MBA). The NDS provides two foreclosure measures for each period: foreclosure inventory over total outstanding loans and new foreclosures over total outstanding loans. In this study, we consider the latter measure of foreclosure rate to be more relevant to our needs. Since we want to relate the foreclosure decision to its main determinants, this analysis can only be carried out by taking the new foreclosures initiated in each period and not through the inventory of properties in foreclosure, which may include foreclosures initiated in previous periods. Furthermore, the foreclosure inventory is dependent on the type of foreclosure procedure allowed by state law and therefore the model would suffer from an identification problem, i.e. it will be always higher in judicial states where foreclosure takes longer to conclude, resulting in a higher foreclosure inventory. Data sources and variables The explanatory variable of interest is the level of borrower protection at state level. Data sources and variables To characterise that level of protection, three dummy variables are included: (i) the existence of judicial procedures; (ii) the inclusion of a redemption period in state regulation; and (iii) ban on a deficiency judgment after foreclosure sale. But that simple classification of states between protective and non-protective turned out to be a difficult and challenging task. As mentioned in Section 2, state regulation is complex and heterogeneous. For instance, the statutes of some states allow both judicial and non-judicial methods of foreclosurealthough usually one of them is more commonly used in practice -and no common rules are set to include redemption and deficiency rights in state statutes. Additionally, different databases use different classifications, which makes it necessary to check and filter several sources of information. The only results admitted were those with the highest rate of agreement between several databases (see Table 1 ). Pence (2003) and Corelogic (2012b) are the basic databases used to construct both judicial and redemption period dummy variables. The classification for "recourse states" (those that admit a deficiency judgment) was collected from Ghent and Kudlyak (2011) . In order to filter and clean-up discrepancies between sources, several on-line information service providers were also used, such as foreclosures.com, e-foreclosuresearch.com and the National Mortgage Servicer's Reference Data sources and variables Directory. Finally, we also include the duration of the foreclosure process, from foreclosure referral to termination of the redemption period, as a proxy of the costliness of the laws. The data are gathered from Cutts and Merril (2008) and come from the Freddie Mac Analysis of Expected Optimal Statutory Timeline for Foreclosure. Agency (FHFA). Some sectors of society (lower income families, less educated people, and minorities) show high financial distress and tend to suffer from predatory lending, which increases the probability of default. In order to control for the effect of these groups, we also include the proportion of minority ethnic groups in the population of each state and the level of education at state level (measured as the percentage of population with higher education). Data sources and variables Additionally, we include the divorce rate, which, along with unemployment and unexpected medical expenses, is usually mentioned in national surveys as a key variable explaining default decisions, since all of them approximate the level of a borrower´s financial distress. All those variables were obtained from the U.S. Census Bureau. Data sources and variables Finally, Dagher and Fu (2011) show that lightly regulated non-bank mortgage originators contributed to a large extent to the recent boom-bust housing cycle and their higher market participation in some states is associated with increased foreclosure filing rates. Data sources and variables Consequently, in order to control for excessive risk-taking and the development of housing bubbles in specific states which may increase default and foreclosure rates, we also include as a control the proportion of sub-prime loans, gathered from the MBA. Furthermore, in the sub-prime sector, borrowers are more vulnerable to life events, have lower equity on their homes, and their bargaining power is low. Also, sub-prime lenders are less willing to renegotiate and prefer quick resolution of foreclosure [Kennedy (2004) ]. Methodology and empirical strategy Effect of state laws on the foreclosure process The main aim of this paper is to analyse the effect of state laws on default and foreclosure rates at state level. We make use of a panel data model that takes into account different regulatory characteristics of borrower protection between states. Since foreclosure laws show strong regional variation, such between-state heterogeneity may be a good predictor of the variation of delinquency and foreclosure rates among states. Additionally, a set of explanatory variables considered in the literature as the main drivers of defaults and foreclosures is also included. The panel data model is formulated as the following linear regression equation: .51 states, t = 1...11 years (1) In panel data literature, equation (1) is called a two-way error component regression model [Baltagi (2005) ], and has the advantage of including unobservable time effects (Tt) and unobservable individual effects (αi) responsible for default and foreclosure variations across time and states. Since our purpose is to analyse the whole foreclosure process, we estimate three different equations in which yit is, respectively: (1) the default rate, (2) the pass-through from default to new foreclosures and (3) unemployment is important in explaining a borrower´s probability of default; but it is also key information for lenders if they have to decide whether to modify the loan after default. Or, if .51 states, t = 1...11 years (1) residential property values are in decline, a debtor may opt for strategic default and at the same time be in a good position to obtain concessions, making foreclosure less desirable for the creditor [Kennedy (2004) ]. .51 states, t = 1...11 years (1) The parameters of unemployment rate, mortgage interest rate, proportion of sub-prime mortgages, LTV and proportion of minority population are expected to have a positive sign in the default, pass-through and foreclosure rate equations. By contrast, income level, house price appreciation, FICO score and educational level should have a negative effect. According to the theoretical discussion in Section 3, the variables included in vector Li (judicial, redemption and deficiency) should have a negative effect on default -meaning that borrower-protective states tend to show lower default rates than non-protective states -, but a positive effect on the passthrough to foreclosure, with an ambiguous final effect on foreclosure rates. Base model: estimation and identification issues If it is assumed that equation (1) 6. In our case, for instance, certain characteristics of the states included in α (cultural or economic background, etc.) could lead legislators to choose stricter regulations. Base model: estimation and identification issues In this paper, we apply the MK model, which expands the original regression with an auxiliary equation (2): Base model: estimation and identification issues where ωi is the disturbance and where Xi. is, for each individual i, the average over time of the time-varying variables, such that E (ωi | Xi.) = 0. Combining regressions (1) and (2) yields the MK regression model: Base model: estimation and identification issues Mundlack (1978) and Krishnakumar (2006) prove that when individual effects are correlated with the explanatory variables, the GLS estimator of equation (3) Nevertheless, there is a caveat against this argument. In general, state regulation is not a variable that changes over time. Once a state chooses a type of foreclosure law, it is kept invariant for a long time, and only major events make legislators change the regulatory framework. In our sample (from 2000 to 2010), we have only identified one state that made regulatory changes related to the three dummy variables considered in our study, Nevada, which amended the state law in 2009 through the prohibition to pursue a deficiency judgment in case of first-residence dwellings, the introduction of a compulsory mediation process before foreclosure and an extension of the cure period before foreclosure. Once we exclude Nevada State from our sample, the endogeneity problem does not arise in practice. (2011) remark, the effect of foreclosure on prices is weak and local and "declines in housing prices cause foreclosures much more than foreclosures cause price declines". In any case, we use a traditional lagged value of house price appreciation as a means of mitigating the possible existence of a simultaneity problem. The effectiveness of regulation during the crisis The base model of Section 6.2 above analyses the effect of protective regulation on foreclosure rates. The results will tell us if states with excessive protection show on average a higher or lower foreclosure rate than less strict states. Nevertheless, the model does not tell us about the effectiveness of regulation in protecting borrowers when a crisis event occurs, i.e. if at least protective regulation is effective in crisis times. In order to answer that question we make use of a difference-in-difference (DiD) estimator, which is a powerful and simple tool for estimating treatment effects in econometrics, in our case the effect of borrower-protective regulation ("the treatment"). The logic behind this approach is the following. The sample contains "treated" states (those with protective regulation) and "control" states (those not implementing the "treatment" or protective regulation). We estimate the difference between the outcomes at two points in time (before and after the crisis) for both groups and then compare the difference between the groups. Specifically, we estimate the increase in default and foreclosure rates among borrower-protective states before and after the crisis (years 2006 and 2010) and compare it to the increase in default and foreclosure rates among nonprotective states in the same period. If the DiD effect is statistically significant and negative, then protective regulation is effective. The DiD model relies on the crucial assumption that, in the absence of the crisis, the trend among protective states would have been similar to that of the non-protective states. Tables 3 and 3 (bis) show how regulation (specifically the judicial process requirement) is not correlated with almost any of the observable variables in the model, so states are similar in terms of the other explanatory variables. We can also relax that assumption by incorporating other control variables that influence the delinquency and foreclosure rates at state level. The effectiveness of regulation during the crisis Empirically, the DiD model is formulated as follows: Table 8 . λ is the parameter of interest (DiD estimator) and measures the effect of protective regulation on the variation in the variable y between the two periods (before and after the crisis). If λ is positive it means that the gap between the foreclosure rates of protective and non-protective states has increased after the crisis and, therefore, the protection has been ineffective (i.e. the increase in foreclosure rates in protective states as a consequence of the crisis is higher than the increase observed in non-protective states). Empirical results This section discusses the main empirical results. Firstly, we carry out a descriptive statistical analysis of the variables, and show the main empirical features of the database. Secondly, we present a detailed discussion of the findings following the estimation of the proposed models. Furthermore, regulation is somewhat heterogeneous in terms of mix of borrower-protection elements, since not all states that require judicial procedures include redemption periods or allow for deficiency judgments in their foreclosure laws. Table 2 Aggregating for all states and years in the sample, Table 1 shows that the yearly average rates of delinquency and foreclosure are 3.7% and 2.3%, respectively. Both rates are displayed in Graph 3, which shows a large between-variation among states and within-variation in the time variable. The highest rates are concentrated around 2000-2002 and, more importantly, 2008-09, in line with the two recessions that hit the US economy in the last decade. In 2009, the peak of the foreclosure crisis, the highest delinquency rate was in Mississippi (9.7%), followed by Nevada (9.2%), Georgia (8.8%) and Michigan (8.4%). According to our classification, all of them are characterised as being "very non-protective" or "non-protective" and recourse states. The states with the lowest delinquency rates are North Dakota (2.7%) and South Dakota (3.1%), Montana (3.7%) and Alaska (3.8%), three of them classified as "very protective" states without provision for a deficiency judgment. Regarding foreclosure starts, the states with the highest rates are Nevada (13.8%), Florida (10.6%), Arizona (9.8%) and California (7.6%), all of them, except Florida, classified as "very non-protective" states but without any right of lenders to pursue a deficiency judgment. Descriptive statistics The states with the lowest rates are North Dakota (1.4%), Alaska (1.9%), South Dakota (2%) and Wyoming (2.2%), two of them "protective" states without the right to a deficiency judgment. The rate of pass-through to foreclosure has an average value of 0.59 during the whole sample period, and Indiana (0.7). Finally, the average length of the foreclosure process is 292 days, with a wide range between the minimum of 183 days in Tennessee, a "very non-protective" state, and the maximum of 462 days in Iowa, a "protective" state. 2008, e.g. Nevada (-25.4%), California (-24.2%), Florida (-21.4%) and Arizona (-17.8%). The lowest rates during the boom years are in Michigan (1.6%), Ohio (2.9%), Indiana (3.1%) and Nebraska (3.4%). And states showing mild house price appreciation during the bust are North Dakota (3%), South Dakota (1.7%) and Wyoming (0.9%). Descriptive statistics The unemployment rate averages 5.4% in the whole sample, with a variation from 14.8% to 2.3%. The most important feature is the presence of a large variation over time and across states. The states with the highest unemployment rate during the crisis are Nevada (14.8%), Michigan (13.4%), California (12.3%) and Rhode Island (11.6%). The states with the lowest rates are North Dakota (3.9%), Nebraska (4.6%), South Dakota (4.8%) and Iowa (5.6%). Descriptive statistics Finally, since our main interest is the effect of regulation on foreclosure rates, we report in Table 3 separate statistics for judicial and non-judicial states, in an attempt to capture contrasting behaviours in states with different regulatory frameworks. If, for instance, shocks to house prices or income are more common in judicial states than in non-judicial states, we may observe differences in foreclosure rates that are not due to the regulatory framework. In that case, the effect of regulation on foreclosure would be difficult to isolate and estimate. According to Table 3 , on average, the states look quite similar, independently of the foreclosure regulatory framework. We have run regressions of judicial requirement on all the observable variables of the model. The results are displayed in Table 3 (bis) and show that there are no statistically significant differences in the observable variables between judicial and non-judicial states. In all cases, the coefficients are not statistically different from zero. Results are presented in Table 4 . Firstly, we run several specification tests to decide which of the possible models at hand is the most appropriate to describe the data-generating process (bottom of Table 4 ). The Breush-Pagan test does not reject the existence of random effects (versus no effects) and the Hausman test is not conclusive in rejecting the RE with respect to the FE model. In order to check for the suitability of the MK model, we follow a similar philosophy to that of Chatelain and Ralf (2010) and
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