An Unintended Consequence of Mortgage Financing Regulation – a Racial Disparity

Black et al. (1978) and Munnell et al. (1996) represent early studies focusing on the issue of credit allocation. Holmes and Horvitz (1994), Tootell (1996), and Ross and Tootell (2004) are examples of studies emphasizing the issue of redlining, analyzing whether the racial composition of an applicant’s neighborhood affects loan credit allocations. A few recent studies investigate the existence of disparate treatment by mortgage loan originators (Ross et al. 2008; Hanson et al. 2016) using experimental methods. Turner and Skidmore (1996), Ladd (1998), LaCour-Little (1999), and Ross and Yinger (2002) provide thorough and detailed reviews of previous studies.

The focus of our review of the literature is to examine racial and ethnic disparity in loan pricing. For literature on racial discrimination in credit allocations, please see Turner and Skidmore (1996) and Ross and Yinger (2002) for the summary.

An overage is defined as “a difference between the price at which a loan closes and the minimum price acceptable to the lending institution as quoted on the lender’s rate sheet”. For details, see Black et al. (2003).

The default and prepayment hazards are estimated using two separate models.

See Fang and Munneke (2016) for a discussion on why the discrete-time competing-risks loan hazard model can solve the issue of left truncation and right censoring.

The multinomial logit model is chosen with the independence of irrelevant alternatives (IIA) assumption that the odds ratio for any pair of choices is assumed to be independent of any third alternative (one event is not informative to the other conditional on all of the covariates in the model), and choices at any point in time are independent of those at any other point in time. Based on the IIA assumption, a widely adopted approach was utilized here to estimate this multinomial logit model in which we estimated default hazard and prepay hazard separately. Hence, it is not necessary to estimate default and prepay hazard models within a simultaneous equation framework, especially given the findings that studies show separate models perform well for most of the data (Allison 2010). The advantage of estimating default and prepay hazard models separately also includes the flexibility in having different specifications for different hazard models.

For other time-varying covariates, we either used the actual values if we were able to observe them, or extrapolated values from the known values, whichever seemed more reasonable and appropriate.

This 10-year treasury constant maturity yield is widely used as the benchmark for the mortgage interest rate of 30-year fixed-rate residential mortgage loans in practice.

Though several studies in asset pricing argue other interest rate models perform better than the CIR term structure model with respect to out-of-sample prediction, those models could only be employed to forecast the mean, not the density of the spot interest rate needed here. In addition, the CIR term structure model is the standard model used in mortgage literature.

The parameters in Equation (2) were estimated with the use of 4 time series of yields with different maturities from 1987 to 2007 within the framework of the single-factor CIR term structure model. Those 4 time series are 6-month T-bill yield, 1-year Fama-Bliss bond yield, 3-year Fama-Bliss bond yield, and 5-year Fama-Bliss bond yield. Data were obtained from CRSP. The reason we chose this estimation period (from 1987 to 2007) is many studies have found there was a shift in Federal Reserve monetary policy in the early 1980s (Duan and Simonato 1999) and the loan data in this study ends in 2007 based on loan origination year. We used the GAUSS code offered by Jin-Chuan Duan on his website to implement the estimation, the one he used to yield the results in Duan and Simonato (1999). We would like to acknowledge this help from him.

Notice here, this study forecasts the conditional density of the future spot interest rate rather than the simple conditional mean to account for all of the possible path of future interest rate. For the transition density of the spot interest rate, see Cox, Ingersoll, Ross (1985). Here, a normal distribution was used to closely approximate the true transition density.

Note here, as we use the forecasted conditional density not the forecasted conditional mean to calculate the predicted probability of each event at time t (\( {\widehat{p}}_{kt},k=1,2 \)), the future market mortgage interest rate at time t (the future 10-year yield here, y_t(r(t))) could be any positive value in the spectrum. For each specific value of y_t(r(t)), the predicted probability of each event at time t based on that specific value could be calculated as p_kt[y_t(r(t))]. As in the single-factor CIR model, the whole term structure is driven by the spot interest rate r(t), the distribution of the future 10-year yield at time t is determined by the distribution of the future spot interest rate at time t specified as dF(r(t)| r(0)). Therefore, considering all of the possible values of y_t(r(t)), the predicted probability of each event at time t is calculated as in Equation (3) and (4).

In this study, we chose a 10-year span instead of a 30-year span because in reality, most of the 30-year fixed rate mortgage loans are prepaid within the first ten years if they were not defaulted upon. Notice here, a capital P is used to distinguish total loan termination probabilities from time-specific loan termination probabilities. The subscript k tells the type of the event, 1 for default and 2 for prepayment.

The FIRREA amendments in 1989 expanded the coverage of HMDA to many independent non-depository lending institutions, in addition to the previously covered savings associations, banks, and credit unions. For detailed information on who is required to report HMDA data, see the descriptions on the Federal Financial Institutions Examination Council (FFIEC) website https://​www.​ffiec.​gov/​hmda/​reporter.​htm.

HMDA-LAR data from 1989 to 1991 used the 1980 census tract boundaries, data from 1992 to 2002 followed the 1990 census tract definitions, and data from 2003 to 2012 adopted 2000 census tract definitions.

Each mortgage loan was matched to property sales in the pool with replacements requiring that the gap between the appraised value of the property in the loan data and the transaction price of the property in the property sale data to be the minimum one in the pool. If multiple property sales were matched to a loan and those multiple properties were located in the same census tract, this loan is treated as having a unique property sale match, and its census tract identification number is identified as the common one for those multiple properties.

As the loan amount in HMDA-LAR data is in thousand dollars, we allowed loan amount to differ by up to $1000. Lien status is a new field added to the HMDA-LAR data beginning January 1, 2004.

In this study, if there are multiple HMDA-LAR matches for a loan that meet those matching criteria above, and if those multiple matches have exactly the same race and ethnicity information on the borrower and the co-borrower, this loan is allowed to be identified as having a unique HMDA-LAR match, since the goal of the data matching is to obtain the race and ethnicity information on the borrower(s).

Avery et al. (2007) discussed several hierarchies to solve this issue, and this study adopted one hierarchy that is reasonable here given the demographic characteristics of the population in Miami-Dade County, FL.

In this study, the census-tract level aggregated HMDA data is preferred rather than the decennial census survey data to generate the time-varying variables describing the demographic characteristics of a census tract, because the aggregated HMDA data is updated every year and is believed to be more accurate than census survey data which is updated every ten years. Those measures include the median applicant income, the proportion of African American applicants, the proportion of non-Hispanic white applicants, and the proportion of Hispanic applicants. The applicant income is inflation adjusted by a GDP per capita deflator. All income is defined in 2009 dollars. The racial and ethnic group of a loan application is identified using the hierarchy described above.

The data on the pool of property transactions are sales from 1990 to 2013 in Miami-Dade County, FL.

The housing sale price is inflation adjusted by a GDP per capita deflator. All prices are defined in 2009 dollars.

Recent housing price appreciation rate at origination is defined as the ratio of the median housing sale price in a neighborhood in a three-year period prior to the month of loan origination to the median housing sale price in the same neighborhood in another three-year period prior to the three-year pre-origination period, then minus 1.

The traditional Public Securities Association (PSA) schedule is not used because previous studies argued this schedule did not describe the pattern of actual prepayments well, for more details, see Kau et al. (2004).

A yield at time t lagged by 2 periods is used because in practice there is usually a gap between a borrower’s decision and actual termination, and borrowers typically rely on past information to make their decisions. Notice here, for the first mortgage month and second mortgage month, the 10-year yield at loan origination (at time 0) is used as the 10-year yield at time t lagged by 2 periods.

Contract rate spread at origination is defined as the gap between the contract rate and the 10-year yield at origination. We chose the contract rate spread instead of contract rate itself because the 10-year yield as the benchmark mortgage interest rate varied considerably within our study period, and this spread allows us to make comparisons across mortgage vintages.

Heterogeneity in housing sale price at time t was measured by the standard deviation of housing sale price within a three-year window prior to time t in a neighborhood. Housing occupancy rate and poverty rate in a neighborhood at time t are from the census survey data. Median income of loan applicants in a neighborhood at time t is generated by the aggregated HMDA data described in the data subsection. In order to reflect the rank of each census tract in terms of median applicant income in Miami-Dade County, FL at time t, the ratio of the median applicant income in a census tract at time t to the median applicant income in Miami-Dade County, FL at time t was calculated and included in the model.

We also tested whether those excluded variables affect the corresponding hazard respectively. None of the coefficient estimates of those variables are statistically significant.

This set of covariates are included in this loan contract rate determination model mainly for the identification purpose. We tested whether the main results change if those covariates are excluded. The main results remain the same.

The FICO linear spline function was specified as follows: FICO_{(FICO ≤ 700)} = minimum (FICO, 700); and FICO_{(FICO > 700)} = maximum(FICO, 700)-700. Therefore, the coefficient on FICO_{(FICO ≤ 700)} measures the effects of FICO score on dependent variable when FICO≤700; while coefficient on FICO_{(FICO > 700)} measures the marginal effects of FICO score when FICO>700. We tested whether the results are robust to the specification of the FICO score knot point by conducting the same analysis with a knot point at 720 or 750, and results are robust.

The proportion of African American borrowers in the sample of this study is slightly lower than the proportion of African American residents in Miami-Dade County, FL indicated by the census survey (approximately 20% in 2000 census survey data). This leaves a research question for future study on whether African Americans face more difficulties having access to credit than borrowers in other racial and ethnic groups. As we do not have data on loan applications, this research question is beyond the scope of this study.

Points are not included in the data set.

A prior study by Mayer et al. (2013) provided evidence for this explanation.

This argument is supported in a few prior studies analyzing loan termination patterns of minority borrowers. Deng and Gabriel (2006) using a competing-risks loan hazard model found minority borrowers prepay their mortgage loans more slowly, but defaulted more. However, considering both default and prepayment risks, they revealed that the elevated default risks of loans by minority borrowers are more than offset by the damped prepayment speeds of those loans. Therefore, they argued that those damped termination risks of loans by minority borrowers should be reflected in the pricing of those loans, and the efficient risk-based pricing of loans should serve to enhance mortgage and housing affordability among those minority populations.

The average original loan size and the average contract rate in the sample of this study are approximately $180,000 and 8% respectively.

The matching conducted here is similar to propensity score matching that is conducted based on a predicted propensity score (Rosenbaum and Rubin 1983). However, it is not exactly the same as the typical propensity score matching, as the loans are matched based on the predicted termination probabilities instead of the probability of a borrower being in a particular racial and ethnic group.

For a single continuous variable x, the standardized difference of the mean is defined as \( SD=\left({\overline{x}}_{group1}-{\overline{x}}_{group2}\right)/\sqrt{\left({s}_{group1}^2+{s}_{group2}^2\right)/2} \), where \( {\overline{x}}_{group1} \)and \( {\overline{x}}_{group2} \) denote the sample mean of this variable in racial and ethnic group 1 and group 2, respectively, whereas \( {s}_{group1}^2 \)and \( {s}_{group2}^2 \)denote the sample variance of the variable in racial and ethnic group 1 and group 2, respectively. For a dichotomous variable, the standardized difference of the mean is defined as \( SD=\left({\overline{x}}_{group1}-{\overline{x}}_{group2}\right)/\sqrt{\left({\overline{x}}_{group1}\times \left(1-{\overline{x}}_{group1}\right)+{\overline{x}}_{group2}\times \left(1-{\overline{x}}_{group2}\right)\right)/2} \).

A caliper is applied to impose a tolerance level on the maximum distance on a matching criterion variable between two groups. Specifically, the caliper is defined as\( Caliper=\pm \rho \sqrt{\left({s}_{group1}^2+{s}_{group2}^2\right)/2} \), where ρ is the caliper radius, \( {s}_{group1}^2 \)and \( {s}_{group2}^2 \)denote the sample variance of a matching criterion variable in target and control groups.

Applying the same diagnosis technique to other variables included in the loan contract rate determination model (Eq. (6)) reveals that the neighborhood traits variables are typically unbalanced, providing justification for the regression adjustment to be applied.

Woodward and Hall (2010, 2012) note that borrowers may suffer an informational disadvantage compared to the brokers and fail to recognize that more upfront cash payments (more points) should lead to a lower interest rate. Under such a scenario, they find that minority borrowers pay significantly higher total origination fees including points than similar white borrowers.

In this “color neutral” world, although the contract rate estimation results based on the full sample (Table 5) show that African American borrowers pay a significantly higher contract rate than non-Hispanic white borrowers, this racial disparity disappears with the matched samples in which borrowers in the two racial groups are more homogeneous in terms of loan termination risk (Table 7).

A caliper is applied to impose a tolerance level on the maximum distance on a matching criterion variable between two groups. Specifically, the caliper is defined as\( Caliper=\pm \rho \sqrt{\left({s}_{group1}^2+{s}_{group2}^2\right)/2} \), where ρ is the caliper radius, \( {s}_{group1}^2 \)and \( {s}_{group2}^2 \)denote the sample variance of a matching criterion variable in target and control groups. Austin (2011), Cochran and Rubin (1973), and Rosenbaum and Rubin (1985) all examine the extent to which the caliper radius (ρ) reduces the bias between the two groups.

Although LTV is a continuous variable, the loans in the sample tend to fall on common LTV ratios (e.g., 80%, 85%, 90%, etc.). Thus, we convert the LTV ratios into three categories based on the original LTV ratio: loans with original LTV ratio below 80, loans with original LTV ratio above 80 but below 100, and loans with original LTV ratio above 100. Matched loans must fall in the same original LTV ratio category.