Consumer risk appetite, the credit cycle and the housing bubble

ABSTRACT

In this paper, we explore the role of consumer risk appetite in the initiation of credit cycles and as an early trigger of the US mortgage crisis. We analyze a panel data set of mortgages originated between 2000 and 2009 and follow their performance up to 2014. After controlling for all of the usual observable effects, we show that a strong residual vintage effect remains. This vintage effect correlates well with consumer mortgage demand, as measured by the Federal Reserve Board’s Senior Loan Officer Opinion Survey, and with changes in mortgage pricing at the time the loan was originated. Our findings are consistent with an economic environment in which the incentives of low-risk consumers to obtain a mortgage decrease when the cost of obtaining a loan rises. As a result, mortgage originators generate mortgages from a pool of consumers with changing risk profiles over the credit cycle. The unobservable component of the shift in credit risk, relative to the usual underwriting criteria, may be thought of as macroeconomic adverse selection.

1 INTRODUCTION

In our experience developing models for forecasting and stress testing portfolio credit risk through the US mortgage crisis, we have often observed the suboptimal perfor- mance of standard underwriting measures, which is insufficient to explain observed variations in credit quality. In this paper, we explore the possible causes of this unex- plained variation and conjecture that consumer risk appetite may be a root cause. We refer to this effect as “macroeconomic adverse selection” to emphasize that loans exhibit anomalous credit risk because of consumers’ perception of macroeconomic conditions.

Changes in default risk that cannot be observed via standard credit scores and are suspected of being caused by consumer behavior are generally referred to as adverse selection. The macroeconomic adverse selection mechanism we consider in this paper relates to anomalous credit risk associated with consumers’ perception of macroeconomic conditions. In this regard, the aim of our paper is similar to that of Breeden et al (2008) and Calem et al (2011), which will be discussed in some detail later in this section.

In contrast, in the standard example, adverse selection can impact a specific lender when it fails to respond to precautionary product or pricing changes made by its peers. Through the lender’s inaction, consumers with lower credit risk are drawn to other lenders, leaving only the riskier borrowers for the unresponsive lender. In this scenario, the credit risk faced by the lender for the originated pool of loans can be much worse than what could be expected using traditional measures of credit quality, such as borrower credit scores. In terms of nomenclature, we have chosen to relabel this standard form of adverse selection “competitive adverse selection” to differentiate it from the macroeconomic adverse selection mechanism that is the subject of analysis in this paper.

The adverse selection just described for retail lending is a specific example of the broader adverse selection problem that arises from asymmetric information (Akerlof 1970). Asymmetric information and the creation of adverse selection have been stud- ied in employment (Bar-Isaac et al 2007) and insurance (Rothschild and Stiglitz 1976). In the context of the competitive adverse selection mentioned above, Stiglitz and Weiss (1981) explored loan pricing versus credit risk. Ausubel (1998) studied credit card default risk and observed that inferior product offers resulted in pools of inferior borrowers.

In general terms, the same result is sought in the current study. Rather than an offer being inferior because of pricing terms relative to other offers in the market, might borrowers view all offers to be inferior during certain economic conditions? The lender cannot know the personal motivations and value assessments of the individual borrowers, which creates an information asymmetry.

When the real estate bubble in the United States and across several European countries burst, it precipitated a deep financial crisis accompanied by an unsettling sovereign crisis in Europe. Understanding the mechanisms that led to the creation of the real estate bubble can prove extremely helpful, particularly for implementing appropriate policies to minimize the risks of asset bubbles in the future. Recognizing this, the analysis of the leading factors contributing to the real estate bubble has generated a growing body of research. In the following, we review some of the most plausible proposed explanations and highlight our contribution to this literature.

Researchers in the empirical macroeconomics field have pointed to the simultaneity of rising asset values and current account deficits in the United States as well as other countries affected by real estate bubbles (see Adam et al 2011; Bergin 2011; Gete 2014; In’t Veld et al 2014). Their analysis suggests that current account deficits need to be accompanied by mispricing risk and falling lending standards to generate bubbles. In a similar vein, some economists have pointed out that the unusually low interest rates in the years before the crisis may have exacerbated the housing boom and bust (Taylor 2014). Other authors, however, are critical of that view. Bernanke (2010) argues that monetary policy during that period was close to his preferred Taylor rule and was appropriate, given deflationary concerns at the time. Further, significant increases in house prices preceded the period of accommodative monetary policy. In addition, cross-country analysis does not support the view that monetary policy played a fundamental role in the housing bubble. MacGee (2010) points out that Canada followed a monetary policy similar to that of the United States but did not suffer from a housing bubble.

Existing empirical microeconomics research points to mispricing risk and falling lending standards as fundamental catalysts of the crisis. In particular, researchers have considered the impact of investors in the mortgage market, either through direct purchases of houses or through the purchase of mortgage-backed securities. Haugh- wout et al (2011) point to the increasing role played by investors during the bubble years. Specifically, they document that investors were responsible for almost half of purchase mortgage originations at the peak of the market bubble. Investors were also associated with higher rates of default after the bubble burst. The Financial Crisis Inquiry Commission (2011) report concluded that irresponsible (and in some cases even egregious and predatory) lending practices and failures of risk management, financial regulation and supervision were the main reasons for a financial crisis that could have been avoided.

Several authors have argued that securitized loans were originated using lower lending standards than loans held in bank portfolios. Elul (2016) calculates that, after controlling for observable risk factors, loans that are privately securitized have a 20% higher rate of becoming delinquent. His finding is consistent with research by Keys et al (2010), who point out that the securitization framework can reduce lenders’ incentives to monitor lending standards (see also Nadauld and Sherlund 2013). Securitization may also have contributed to lower lending standards more broadly through its effects in a competitive market. Levitin et al (2009) argue that private-label securitization was not just a contributor to the crisis, but was, in fact, at the root of it.1 Ruckes (2004) describes theoretically a mechanism for the transmission of low screening activity resulting from intense price competition among lenders.2 Foote et al (2012) take a contrarian view and argue that investment decisions made during the bubble years were rational and logical, given investors’ beliefs about future house prices at the time.

everal authors have focused their attention on the way lending standards were lowered during the years before the bubble burst. Dell’Ariccia et al (2012), using mortgage origination information from the Home Mortgage Disclosure Act (HMDA), document the lowering of lending standards, particularly in areas that experienced faster growth in credit demand. Demyanyk and Hemert (2011) document that the quality of loans deteriorated for six years prior to the crisis. Palmer (2014), using data from privately securitized subprime mortgages, points out that mortgages originated in the two years before the cycle were about three times more likely to default within a three-year period than mortgages that originated around 2003. He argues that one- third of the increase in defaults can be attributed to changing borrower and loan characteristics, while the remaining two-thirds can be attributed to the price cycle.

Previous studies of the US mortgage crisis have suggested that factors beyond those visible to the lenders had a strong impact on credit quality. Breeden (2011) analyzed a fifteen-year data set of mortgage performance by employing a dual-time dynamics approach (Breeden et al 2008) and found that dramatic cycles in credit quality occurred three times during the observation period, even after segmenting by product type, credit score and loan-to-value (LTV). Further, Breeden found that these cycles correlate with macroeconomic factors, such as changes in housing prices and mortgage interest rates. Similarly, Calem et al (2011) used a combination of competing risk models and panel regression to show that riskier households tended to borrow more on their home equity loans when the expected unemployment risk increased.

In this paper, we quantify the impact of macroeconomic adverse selection on a data set of first-lien, installment, fixed-rate, conventional mortgages. We intentionally avoid option adjustable-rate mortgages and negative amortizing products, to focus specifically on the question of the impact of macroeconomic adverse selection effects in this core mortgage product. We create a complete loan-level probability of default model that includes all of the standard predictive factors (loss timing versus age, also known as the life cycle; credit risk scoring attributes, such as FICO score, LTV, etc; and macroeconomic drivers, such as unemployment and house prices) and, using this framework, we demonstrate that a strong vintage-based effect persists beyond these observables. In addition, we demonstrate that this residual credit risk is highly correlated with consumer mortgage demand based on the Federal Reserve Board’s (FRB) Senior Loan Officer Opinion Survey (SLOOS) and changes in mortgage pricing at the time of loan origination. To the best of our knowledge, this is the first paper to affirm the correlation of credit risk with consumer demand and macroeconomic factors for residential mortgages, after controlling for all available scoring attributes.

In the next section, we present the data and provide descriptive statistics for some of the key variables in our sample. Section 3 contains the empirical methodology, and Section 4 presents the empirical model results. Section 5 concludes the paper.

2 DATA AND DESCRIPTIVE ANALYSIS

We analyze mortgage industry data from the McDash Analytics residential mortgage servicing database. This database is mainly composed of the servicing portfolios of the largest residential mortgage servicers in the United States, and covers about two-thirds of installment-type loans in the residential mortgage servicing market. The database includes mortgages from Fannie Mae, Freddie Mac, Ginnie Mae and private securi- tized portfolios, as well as banks’ portfolios. The original data set contains monthly loan performance data from mortgages originating from 1992. The data includes a broad range of loan attributes from the underwriting process (such as product type, documentation type, loan purpose, property type and zip code), borrower character- istics (such as credit score, debt-to-income ratio and owner occupancy) and dynamic loan-level attributes (such as delinquency status, loan balance, current interest rate and investor type).

Our sample of mortgage industry data includes the full performance history of a randomly selected sample of loans in the McDash residential mortgage servicing database. Much has been written about how negative amortizing loans and second liens caused exceptionally high loss rates. To focus our analysis on the question of macroeconomic adverse selection, we restrict our analysis to fixed-term, fixed-rate, first-lien mortgages. We also restrict the analysis sample to loan performance data from 2000–14 on mortgages that originated from 2000 through 2009.

We focus on modeling loan delinquency status to between sixty and eighty-nine days past due (DPD), as the later delinquency data was significantly thinner in the sample. Thus, we consider a loan in default if it reaches or exceeds this delinquency state, including foreclosure or real estate owned. Many lenders will fully or partially charge off a mortgage that reaches this level of delinquency. Further, this delinquency threshold is consistent with other relevant papers in the literature that have adopted this definition of default (see, for example, Gerardi et al 2008).

Table 1 lists the primary risk drivers used in our statistical analysis of credit risk. Relevant variables include loan-specific characteristics such as term, documentation, LTV (defined as the ratio of the loan amount to the appraisal value at origination given as percentage), loan purpose, loan source and occupancy.

Other borrower-specific characteristics include FICO scores at origination and debt- to-income (DTI) ratios at origination. Several variables included in our model specifi- cations are represented as dummy variables, reflecting nonoverlapping ranges across the overall variable range. This approach allows us to estimate the potential nonlin- ear impact of particular variables without having to rely on specific functional form assumptions.

Table 2 presents descriptive statistics across origination vintages for the represen- tative sample used in our analysis.

Observed changes in loan characteristics at origination are consistent with our expectation. We first observe a decrease in origination FICO scores across the years prior to 2007, with the most significant decreases occurring in 2006 and 2007, and a reversal in this trend after that. The percentage of originated loans with full documen- tation increased significantly during the crisis years, although this variable includes a significant proportion of noncategorized loans. As expected, we also observe a decrease in nonowner-occupied loans during the crisis years. Overall, while we observe changes in the average characteristics of loans originated over the years, these changes are by no means dramatic. Thus, loan origination characteristics in the segment of the market composed of the fixed-term, fixed-rate, first-lien mort- gages considered in our study remained relatively stable across the years and across observable risk dimensions.

3 THE MODELING APPROACH

We follow the lives of the loans in our sample from their origination to the time each loan is paid off or defaults. Our primary test for macroeconomic adverse selection is to create a loan-level model that includes all available origination scoring factors, macro- economic factors and vintage fixed effects. The vintage fixed effects are intended to allow us to quantify the magnitude of adverse selection, if any, through time. It will be important to compensate for life cycle, as a function of months on books, and for changes in the macroeconomic environment that can contribute to higher losses across vintages.3 The comparison of estimation results from models with and without vintage effects will assist us in ascertaining the presence and relevance of a residual component that cannot be explained by standard scoring factors.

The default probability is considered monthly, relative to the active accounts in the previous period. This compensates for the competing risk of loan payoff, also known

as loan attrition. This is in the spirit of the popular nonparametric Kaplan–Meier estimator for survival models and compensates for a reduction in active accounts due to causes other than default. Developing a full attrition model was not necessary for our research, since the impact upon default rates was fully compensated in this approach. Instead, we focus on the probability of default, which compensates for early payoff indirectly by having active accounts as the denominator. For the historical data, the equivalent default rate is defined as

where a denotes the age of a loan (or months on book), v denotes the loan’s vintage by origination date, t denotes the calendar date and i denotes a loan-specific identifier. The aim of our research is explanation, not forecasting, so this adjustment in the historical estimator of default rates removes the effects of time-varying payoff rates, thereby avoiding contamination of the results from prepayment.

The monthly odds of a loan defaulting can be represented as a combination of the average population odds of default (ie, the average performance across all loans) and the idiosyncratic odds (ie, divergence of an individual loan from the mean of the population) (Thomas 2009):

Attempting to simultaneously estimate both the population odds and the idiosyncratic odds can lead to instability because of the potential collinearity of macroeconomic and scoring factors when modeled on short timescales relative to the economic cycle. Therefore, we first create a model of the population odds of default as a function of months on books, vintage origination date and calendar date. The population odds are used as a fixed input to a panel data model such that the idiosyncratic odds are measured relative to the calendar date and age-varying population mean.

The two-stage approach of creating the population odds model and then the idiosyn- cratic odds model allows us to make explicit assumptions and tests around the linear trend specification error present in any model that includes age, vintage and time effects. We can solve this in the population odds forecast before computing the idiosyncratic odds, so that the results will be robust. In the following subsections, we describe our approach to modeling population odds and idiosyncratic odds.

3.1 Modeling population odds

When modeling population odds, we are focused on drivers affecting all loans rather than idiosyncratic effects. The most important systematic factors for modeling default rate are the life cycle versus the age of the loan and environmental effects versus calendar date.

Survival models have long been used to capture the risk of a terminal event (such as default) as a function of the age of the account. To add an environment function where the net impact versus calendar is estimated, a Cox proportional hazards model could be used with dummy variables for the observation month. However, since the data being modeled is monthly, the problem simplifies to a discrete time survival model.

In estimating the life cycle and the environment function, the analysis can be improved by including a fixed effect for vintage origination date. Once that is included in the discrete time survival model, it becomes an age–period–cohort (APC) model.

APC models have an extensive literature and publicly available estimation methods. To model the population odds in our research, a Bayesian APC model was used (Schmid and Held 2007). Each rate was decomposed into a life cycle function with age of the account, F .a/; vintage quality, G.v/; and environment function with time, H.t/. Specifically,

where a logistic link function has been chosen because the probability of default follows a binomial distribution. This formulation does not consider any idiosyncratic variation; it just captures the mean of the distribution through age, vintage and time.

A Bayesian APC algorithm was chosen because it creates a nonparametric estimate of the three functions, which provides the greatest possible resolution of changes. Relative to an initial mean-zero prior for each function, the values of the functions are adjusted to optimally predict the in-sample performance. A detailed description of the Bayesian APC algorithm is given in the online appendix.

The life cycle captures the fact that newly underwritten loans have much lower default rates than loans that are a few years old. Further, very old loans will have seasoned and are low risk. The precise shape of this life cycle function will depend on the specific product and is usually measured nonparametrically, as in survival models. The life cycle function is also referred to as a hazard function or loss timing function.

Environmental impacts are traditionally thought of as the macroeconomic environ- ment experienced by all active loans. Changes in unemployment and house prices are the primary drivers of mortgage defaults by calendar date. However, other portfolio management drivers may be present. Because we are conducting an industry-wide study, these drivers would have to be industry-wide portfolio management trends, which may occur. By using the approach in which an environmental function is esti- mated directly from the data, we do not need to explicitly include macroeconomic factors in the model. In this way, we will capture the net effect of both macroeconomic drivers and portfolio management trends.

As an example of this process, a refreshed LTV for a given loan may be esti- mated by comparing the house price index (HPI) for a particular geographic region between the origination date and the observation date. However, rather than updating LTV, the environment function captures the net impact of house prices and any other impacts on that calendar date without introducing any additional estimation error of the approximating refreshed LTV.

Similarly, no economic factors are used in estimating the vintage effects, G.v/. Although G.v/ may be correlated with economics, and that will be part of the later analysis, the initial estimate of the vintage effect is intended to capture the net impact of all possible drivers. Including only macroeconomic or observed factors would risk missing some of the variation in credit quality by vintage. Therefore, the fixed effects approach captures the maximum variability by vintage. At the same time, the use of a vintage function avoids overfitting relative to macroeconomic factors, since the span of the data is only one economic cycle and the risk of spurious correlations is significant.

Any model that includes factors related to the age of the loan, calendar date and vin- tage will have a linear specification error because of the simple relationship, a D t v, where a is age, t is time and v is vintage (Breeden and Thomas 2016). This specifica- tion error is explained well in the APC literature (Mason and Fienberg 1985; Glenn 2005), and no general solution exists. In cases in which some of these dimensions are excluded, as with traditional credit scores that rely solely on information from the origination (vintage) date, a unique solution is obtained, but at the cost of being unable to predict probabilities in future time periods.

In some of the later analyses, the data was segmented so we could study various effects. For segmented data, we can choose to segment any or all of the previously defined functions. For example, segmenting the environment function, H.t/, at the state level allows us to estimate it separately by US state. Using this approach, we are able to include variations caused by the local economic environment in our estimates. Similarly, we will use segmentation to explore differences in the vintage function across segments. Note that, in all the segments tested, the life cycle function was unchanged across the segments.

To test variations in the population odds by segment, we create a set of models, as listed in Table 3.

When the APC algorithm is applied to create the primary model, the algorithm provides point estimates for each value of the life cycle along with 5% and 95% con- fidence intervals (Figure 1). This represents the expected probability of delinquency for the entire sample. By estimating via the APC algorithm, it is normalized for port- folio variations in credit quality and environment, but it is conceptually equivalent to a hazard function.

Figure 2 shows the credit risk function obtained from the APC algorithm. It shows that loans originated in 2002–4 had lower than average log odds of delinquency, whereas loans originated in 2006–8 had significantly higher than average log odds of delinquency. The rest of this paper will focus on testing the possible causes of this credit cycle.

To measure the environment function, we segmented by state. As seen in Figure 3, in a summary across all risk bands, the states were highly correlated through the aftermath of the 2001 and 2009 recessions. In Figure 4, the large outliers in 2005 were Louisiana and Mississippi following Hurricane Katrina. In the final analysis, we segmented the environment function by both state and risk bands.

The environment function shows the change in log odds of delinquency for all loans active on a given calendar date. The life cycle serves as the baseline against which the change is computed, so loans of different ages will be adjusted relative to their life cycle estimates.

The results shown for life cycle, credit quality and environment form a complete portfolio model in themselves but without causal explanation.

No macroeconomic model is needed for the macroeconomic adverse selection study. The environment function from the Bayesian APC algorithm will remove the maximum amount of temporal variability from the signal, most of which should be driven by the economy, but effects such as those from Hurricane Katrina are also obvious in the data. By using the environment function, any deviation as a function of calendar date will be removed, regardless of cause. That said, we created a panel data model of the environment functions measured by state segmentation. We built a single model to simultaneously predict the environment functions for all states, but we included fixed effects for states to allow for level shifts between them. The pur- pose of the panel data modeling of the environment functions with macroeconomic factors was to test for the necessity of a secular trend. If adding a ct term were sta- tistically significant, where ct is an estimated constant for specific calendar date t, this would indicate that the environment functions are nonstationary with respect to macroeconomic effects. We designed the Bayesian APC to produce stationary envi- ronment functions, but the actual constraint we want is that the residuals be stationary

when modeled against macroeconomic data. By showing that no time component is necessary, we can accept the decomposition as stable with respect to our design goals.

3.2 Modeling idiosyncratic odds

The final step in our analysis is to create loan-level models using first origination and then refreshed FICO and LTV attributes. The goal is to model the idiosyncratic odds separately from the population odds estimated via the APC algorithm. To create a score that incorporates the systematic effects (population odds) caused by life cycle and environmental impacts, we include the population odds as fixed offsets to a generalized linear model (GLM).4 This has the effect of adjusting the log odds on the left-hand side by the population odds as reflected by F.a/ and H.t/:

where xij are the values of scoring attribute j for account i, cj are the correspond- ing coefficients and ns is the number of scoring attributes. Again, pi .a; v; t / is the probability of a loan being sixty to eighty-nine days past due.

The vintage function, G.v/, is not included in the offset (population odds) because we want to explicitly test how much of the population odds shift by vintage can be explained by population shifts in the scoring factors. Therefore, rather than include G.v/ for the overall vintage function, we include fixed effects (dummy variables) for the vintages gv to capture the residual vintage performance not explained by the scoring variables.

The method described here is broadly equivalent to a discrete time survival model with the added nuance of carefully controlling for the linear trend ambiguity. With the F.a/ and H.t/ functions as fixed offsets, the linear trend cannot be changed by the inclusion of scoring factors. As soon as one function in a, v or t is held fixed, the other two will be uniquely determined, as explained in the APC literature.

4 AGE–PERIOD–COHORT MODEL RESULTS

To estimate the population odds, we estimated the Bayesian APC algorithm with sixty to eighty-nine days DPD as our proxy for default. The life cycle functions were segmented as subprime, prime and superprime. In general, it also may be advisable to segment the life cycles by loan term. In our data, the loan terms were primarily for ten, fifteen, twenty and thirty years, and, even with our large panel, we could not distinguish differences in the life cycles with this additional level of segmentation.

The y-axis of the life cycle graph (Figure 5) is the expected average monthly delinquency rate averaged across the full time range.

Figure 6 measures credit risk across vintages. Credit risk is measured as a relative scaling of the log odds. The values shown represent the relative risk of a given vintage for the entire life of those loans. The concept of subprime, prime and superprime mortgage loans is broadly utilized in the mortgage industry and the related academic literature, but it is not consistently defined. Chomsisengphet and Pennington-Cross (2006) define subprime lending as a “segment of the mortgage market that expands the pool of credit to borrowers who, for a variety of reasons, would otherwise be denied credit”. For the purposes of this paper, we define subprime as less than 660 FICO, prime as 660–780 and superprime as 780 and above.

We observe that subprime loans have a smaller dynamic range than prime and superprime loans. Thus, subprime loans tend to be less sensitive to the economic cycle in terms of underwriting (credit quality versus vintage) and the environment functions versus calendar date. This is a well-established result. However, in terms of total numbers of delinquent loans, the subprime segment will see the most growth for risky loans.5

The results in Figure 6 disagree somewhat with those obtained by Demyanyk and Hemert (2011), who also attempted to adjust for observed underwriting factors and a set of vintage dummies. Their result showed a monotonic increase in risk from 2001 through 2007. The disagreement between 2001 and 2003 could be due to a lower volume of data in their sample during that time period, but the consequence is that it can change the interpretation of the results. What they saw as a trend due to securitization looks here to be a cycle requiring a broader explanation.

4.1 Idiosyncratic odds results

The estimated credit risk function by vintage date from the APC algorithm captures both the known changes due to observable shifts in underwriting and possible unob- served effects for which we are searching. To distinguish between these two effects, we specify a loan-level probability model where the life cycle versus age by risk band and the environment function versus date by state are used as fixed offsets (see (3.2)). In addition to these inputs, we also include the typical scoring attributes listed in Table 1. In particular, we estimate models with and without quarterly vintage effects and separately for subprime, prime and superprime segments. (Tables of parameter estimates are available from the authors.)

Applying this method to predicting the probability of being sixty to eighty-nine DPD for the first-lien mortgage data provides the scoring results reported in Table 4. The table provides the GLM output for the full sample for all parameters except the vintage effects (graphed later), where the life cycle function and environment function

by state are included in the model as fixed offsets. The coefficients shown are in line with industry intuition.

Since a binary outcome is being modeled, pseudo R-squared was used to measure goodness-of-fit.6

For the regression in Table 4 without vintage fixed effects, pseudo R2 D 0:097.

When vintage fixed effects were included in the model (shown in Figure 8), pseudoR2 D0:114.Includingvintagefixedeffectssignificantlyimprovedthemodel. The overall values of pseudo R-squared are typical when creating monthly panel models of a roughly 1% likely event.

Even though we included all the available scoring factors, the fixed effect in vintage is still significant. When the APC decomposition is compared with having fixed effects in the scores, the major variation is still present (Figure 7). However, by including the scoring factors, the dynamic range for the vintage fixed effects is less pronounced than for the original credit risk function by vintage. In addition, the transition in 2009 is less dramatic. Both measures are normalized for life cycle and environment, which suggests only half of the variation in credit risk observed with APC is explainable by observable underwriting changes.

To test the result seen in Figure 7, the analysis was rerun segmented by score band, with entirely separate models built for each segment. Figure 8 shows the vintage fixed effect functions extracted from these models (see (3.2)). The results are nearly identical, with the exception of the most recent history where the superprime function improves even more than the others.

Compare Figure 8, which resulted from the model with scoring factors, with Fig- ure 6, which resulted purely from the APC analysis. There is a smaller range of variation in Figure 8 than in Figure 6, but the vintage effects are much more aligned after adjustment for scoring factors. Thus, the inclusion of scoring factors does not eliminate the structure observed in Figure 6. Rather, the scoring factors clarify the unobserved vintage effects.

The analysis by risk band in Figures 7 and 8 included loan purpose as a factor in the overall score. Rather than just including a scalar, we also tested to see if each loan-purpose segment exhibited the same dynamism with vintage. Figure 9 shows the separate estimates for the vintage fixed-effect functions when segmented by loan purpose. We observe that “other” as a loan purpose segment is more risky across all vintages relative to purchase or refinance, but it is just a level shift equivalent to the scaling observed in the original model of Table 4. Thus, we conclude that the same credit risk cycle is present across loan purpose segments as well as risk bands.

No matter how we segment the data, we continue to observe that typical scoring factors do not capture all of the variation in credit risk by vintage. Vintage fixed effects (dummies) add significantly to the analysis and show that risk rose steadily from a low in early 2003 to a peak in 2007.

4.2 Comparison with the Senior Loan Officer Opinion Survey

Given the similarity between risk bands in Figure 8, we continue now with a single credit risk function for all mortgages derived the same way as before but without segmentation. When looking for possible ways to explain the variation in credit risk after adjusting for available observed factors, we consider the FRB’s SLOOS (Board of Governors of the Federal Reserve System 2014). This quarterly survey asked questions of senior loan officers of up to eighty large domestic banks and twenty- four US branches and agencies of foreign banks regarding loan origination practices for several loan types.

Before 2007, a single question was asked regarding mortgage underwriting: “Over the past three months, how have your bank’s credit standards for approving applica- tions from individuals for mortgage loans to purchase homes changed?” After 2007, this was separated into three questions for subprime, prime and superprime mortgage origination. To create a continuous history, we computed the survey average after 2007.

Figure 10 shows the history with SLOOS (dashed line) for loosening and tightening of underwriting standards (left y-axis). The solid line is the vintage fixed effect for first-lien, fixed-rate installment loans. These two lines should be anticorrelated. As underwriting standards are tightened, credit risk should decrease. In fact, a small positive correlation of 0:41 ̇ 0:38 is observed between these two measures.

The same survey asks the same senior loan officers a related question about consumer demand for loans:

Figure 11 compares this measure of consumer demand (left y-axis, dashed line) with the same measure of credit risk. Again, we computed the average demand index for data after 2007. Unlike the previous graph, this one shows significant anticorrelation of 0:69 ̇0:30. When consumer demand is high, credit risk is low, or when consumer demand is low, credit risk is high.

In 2006 and 2007, as shown in Figure 7, the separation between the total credit risk assumed by lenders (solid line) and the share of that credit coming from adverse selection (dashed line) was significant. Of the total credit risk, half would have been explainable from the observed underwriting metrics, but half was unobserved.

In 2008, this gap disappeared. Lenders apparently tightened their underwriting standards, reinforced by the SLOOS study (Figure 10). However, this tightening did not affect the share of risk coming from consumer adverse selection. Lenders were being more selective but were still selecting from an inherently risky pool of consumers, ie, risky in ways not observable from the usual loan application and bureau information.

Only in 2009, when lenders dramatically curtailed mortgage lending, did the risk drop dramatically. At the same time, mortgage demand recovered, returning the adverse selection measure to normal levels.

The irony of these graphs is that the same senior loan officers answered both questions, and therefore had all of the information shown here available to them, yet their expectations on credit risk do not align with portfolio realities.

4.3 Comparison with economic drivers

Because consumer demand changes significantly through time, we want to understand what might cause these changes. Figures 12 and 13 compare the SLOOS mortgage demand index with the change in thirty-year mortgage rates and the change in HPI. The interest rate story is clear. We found that the optimal relationship was to the change over a twenty-four-month horizon with a correlation of 0:56. The interpretation is

that consumer demand rises when interest rates have experienced a significant decline over an extended period of time, and conversely for rising rates.

Figure 13 shows the relationship between mortgage demand and changes in the HPI. In a regression including changes in the thirty-year interest rate and in HPI, we find that both are significant, and there is a positive relationship between demand and HPI. However, we really only have a single event in HPI against which to model. The results would be more reliable if we could conduct the analysis by geographic region, but demand is only available as a national measure.

Overall, the relationship between demand and interest rates is stronger and more intuitive. In Figure 14, we compare the vintage fixed effects for sixty to eighty-nine DPD directly with the twenty-four-month change in the thirty-year mortgage interest rate without the intermediate measure of mortgage demand. Again, the relationship is clear.

Our best interpretation of these results is that consumer risk appetite changes with economic conditions. Credit risk for a loan is a function of the economic conditions at the time the loan was originated as well as conditions later on, should they worsen during the life of the loan.

As an industry, we tend to assume that credit risk is driven primarily by underwrit- ing. However, it would be more accurate to say that underwriting is the process of selecting the best borrowers among those who are interested in getting loans. Thus,

the primary drivers of risk may actually be the conditions that change the consumers’ perspectives on their financial risks. Therefore, consumer risk appetite determines the pool of interested borrowers. Underwriting selects from those. When interest rates are falling, homes are more affordable, and naturally conservative consumers come to the market to borrow. When interest rates rise, demand from conservative consumers dries up, and we are left with those consumers who are riskier in ways not always visible to bureau scores and other typical underwriting factors.

From the perspective of understanding the housing bubble, this suggests that the financially conservative consumers withdrew from the market in 2005 just as the problems with poor underwriting were taking hold. The pool of interested borrowers had a high proportion of risky consumers, and lenders went deeply into that pool. A disaster was in the making.

5 CONCLUSION

Although many explanations have been offered for the US mortgage crisis, our research advocates that shifts in consumer risk appetite were a major contributing factor. In our approach, we used an APC model to capture trends in the population odds. The age and period functions were then included in a generalized linear model of delinquency, which also included all available scoring factors. The original cohort function was thereby replaced with the scoring factors and a series of fixed effects to capture any residual structure. Although we had normalized for product life cycles, macroeconomic conditions by state and all available scoring factors, the remaining vintage fixed effects were both significant and persistent through multiple segments.

The residual vintage fixed effects demonstrated a strong credit risk cycle, but cor- relations with external information suggest possible causes. Using the SLOOS, we found that self-reported changes in underwriting standards did not correlate with the vintage fixed effects. This is reasonable because those changes in underwriting might already be captured in the scoring factors incorporated into the model. Surprisingly, the changes in consumer mortgage demand reported by the SLOOS correlated strongly with the vintage fixed effects, suggesting that periods of high demand correspond to low-risk vintages, and periods of low demand correspond to high-risk vintages.

Further investigation of the SLOOS-reported changes in demand showed that both demand and the vintage fixed effects correlate strongly with long-term changes in interest rates. This suggests that declining interest rates drive increased demand from a broad spectrum of consumers, including the important low-risk borrowers. When interest rates are rising, the low-risk consumers no longer want mortgages, so the resulting vintages are lower in volume but much higher in risk.

Modern risk management relies heavily on statistical models. Often models are estimated over a short time horizon that does not cover a full cycle or a cycle with a sufficiently severe downturn period. Our paper emphasizes the importance of estimat- ing models over a full cycle whenever possible. It is also vital to pay special attention to the credit cycle when conducting model validation and for the analysis of model risk in particular. Regulatory guidance on model risk from the Board of Governors of the Federal Reserve System and Office of the Comptroller of the Currency (2011) highlights the increased awareness of regulatory agencies on this subject. Further, the Basel II framework and Comprehensive Capital Analysis and Review framework emphasize the use of models for effective supervision and surveillance. Our analysis stresses the importance of accounting for the credit cycle as an important element of model development, implementation, validation and control. It is of particular impor- tance for bank supervisors to improve their understanding of the credit cycle as a catalyst of credit bubbles and its effects on the procyclicality of capital.

DECLARATION OF INTEREST

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper. Any remaining errors or omissions are their own. The views expressed in the paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. An early draft of this paper, including the appendix, is available free of charge at www .philadelphiafed.org/research-and-data/publications/working-papers.

ACKNOWLEDGEMENTS

We thank Sharon Tang for outstanding research support and Amy Sill for outstanding logistic support. We are particularly grateful to William W. Lang for his support and assistance on this project. We also gratefully acknowledge the assistance of the Editorial Services team at the Federal Reserve Bank of Philadelphia.

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