There is mounting evidence that households make suboptimal savings and investment decisions. For example, Choi, Laibson, and Madrain (2011) show that less-than-optimal contributions to 401(k) plans may lead to more than $500 in financial losses. Agarwal, Skiba, and Tobacman (2009) and Bertrand and Morse (2009) document that borrowers take payday loans with astronomical APRs when cheaper forms of credit are available. Moreover, consumers with multiple credit card offers often fail to choose the right credit card (Agarwal, Chomsisengphet, Liu, and Souleles, 2015).

In a similar spirit, this note presents novel evidence that many mortgage borrowers appear to have failed to apply for mortgages that give the lowest interest rates. Specifically, we find that nearly 10 percent of prime borrowers who applied for their loans jointly could have lowered their mortgage interest rate at least one eighth of 1 percentage point if the mortgage was applied for by the applicant with a higher credit score and an income high enough to qualify for the mortgage. Furthermore, among the joint applicants with a lower credit score below 740, for whom mortgage interest rates are most sensitive to credit scores, more than 25 percent could have significantly reduced their borrowing cost by having the individual with a higher credit score apply. This is due to the fact that when lenders price mortgages with joint applications, the interest rates are determined by the lower score of the two--often known as the minimum FICO rule. We estimate that such borrowers could reduce their annual interest payment by between $220 and $1,400. Consistent with the existing literature, we find that couples who appeared to have left money on the table tend to have lower credit scores and be much younger and less financially sophisticated.

1. The Minimum FICO Rule and Data Description
FICO score, a proprietary credit score by Fair Isaac and Company, is one of the most frequently used credit scores in household credit markets. It is routinely examined in underwriting and pricing home mortgages. Under the minimum FICO rule, when two borrowers (typically a couple) jointly apply for a mortgage, only the lower of the two credit scores is considered in the underwriting and pricing of the loan by originators, mortgage insurers, and secondary market guarantors such as Fannie Mae and Freddie Mac.² The rule leads to a somewhat complicated relationship between the income and credit scores of the applicants and the interest rate. On the one hand, most mortgage underwriting and pricing decisions take into account the debt-payment-to-income (DTI) ratios. A front-end ratio (calculated using only mortgage payments) lower than 28 percent and a back-end ratio (calculated using all debt payments) lower than 45 percent are extensively used as underwriting and pricing criteria.³ Notably, in reinforcing conventionally prudent risk management, these ratios are used to define the so-called Qualified Mortgages, as mandated by the Dodd-Frank Act. Thus, if both applicants have an income, applying jointly will lower these ratios and increase the borrowing limits.⁴ On the other hand, in a scenario where the credit scores of two applicants are far apart, the borrowers cannot benefit from the higher score because the mortgage interest rates are determined by the lower score. To examine whether some joint mortgage borrowers may qualify for a lower interest rate if the applicant with high credit score applied for the loan individually, we focus on borrowers of whom the higher-credit-score individual's income alone qualifies the amount of the loan applied for jointly.

The main data used in this analysis is a 30 percent random sample drawn from the population of all mortgages securitized by an anonymous national insurer during the years between 2003 and 2015. We apply the following sample selection criteria to this large pool of mortgages. First, we keep only the mortgages taken to purchase owner-occupied single-family homes, where borrowers can be either first-time homebuyers or existing homeowners. Second, we keep only the mortgages that are fully documented and fully amortized 30-year fixed-rate conforming loans.⁵ Third, we focus on the joint mortgages borrowed by couples by removing the loans in which age differences between the two applicants are greater than 18 years (likely parent-child pairs). For each of these mortgages, we observe the information at origination, such as loan-to-value (LTV) ratios, credit scores (FICO), front-end and back-end debt-to-income ratios, loan balances, and note rate (loan interest rate at origination). We also match the loans to borrowers' mortgage application information, which includes a borrower's level of education, gender, marital status, and verified income in particular.

All told, our sample consists of 603,989 joint-applicant mortgages. Table 1 shows the frequency with which certain combinations of incomes and credit scores appeared in the data. Approximately 18 percent of joint applications require the combined income of both applicants to satisfy the front-end ratio criterion. The remaining 82 percent of applications could have qualified with the single income of one or the other applicant. For the joint applications in which one income could have satisfied the front-end ratio criterion, the applicant with the higher income did not always have the higher FICO score. Finally, for the joint-applications where both individuals' income qualifies, a small fraction of them have equal FICO scores. Note that two conditions are necessary in order to benefit from switching to single-borrower applications: (a) one borrower has a higher FICO than the other one and, (b) the borrower with a higher credit score can satisfy the income eligibility by his/her own income. This leads to a pool of 248,680 (=152,082 96,600) eligible loans.

2. How Much Money Might Be Left on the Table?
To evaluate the extent to which borrowers may lower their interest rates by applying for the loan individually and qualifying for the same amount of credit, we consider the following conceptual framework. Let $$FICO^H$$ and $$FICO^L$$ denote the higher and lower FICO score between the two applicants jointly applying for a mortgage. The observed note rate of a joint mortgage can be represented as $$i^J = \lambda (FICO^L, LTV, Rate^{Avg}) + \varepsilon $$, where $$\lambda $$ represents a pricing function, $$Rate^{Avg}$$ is the average U.S. mortgage rate in the loan origination month, which reflects the general financial cost conditions in the mortgage market, and $$\varepsilon$$ is the loan-specific shock term that depends on, among other factors, borrowers' shopping and searching efforts. In such a framework, the expected note rate of a mortgage being applied for by the applicant with a higher credit score can be written as

$$$$ E[i^S] = \lambda (FICO^H, LTV, Rate^{Avg}). $$$$

The expected borrowing cost reduction of switching from joint to individual application thus can be estimated as

$$$$ E[i^J] - E[i^S] = \lambda (FICO^L, LTV, Rate^{Avg}) - \lambda (FICO^H, LTV, Rate^{Avg}). $$$$

To estimate the pricing function $$\lambda$$, we consider the following linear specification using the pooled joint- and individual-application mortgages

$$$$ E[i] = \alpha + \beta LTV \times FICO + \gamma Rate^{Avg}, $$$$

where $$i$$ is the observed note rate and $$LTV \times FICO$$ denotes the interaction term of $$LTV$$ and $$FICO$$ bucket dummies. Note that for joint mortgages, $$FICO = FICO^L$$. The estimation has an R-squared above 90 percent.

Using the estimated coefficients, we estimate the expected note rates of joint applications using the lower FICO scores and estimate the expected counterfactual rates of the corresponding individual applications using the higher scores. The difference between the two rates measures the foregone arbitrage loss of joint applications from applying alone. We find nearly 10 percent of all eligible joint applications (24,158 out of 248,680) could have received a lower interest rate of at least one eighth of 1 percentage point annually. The average annual interest savings are reported by FICO and LTV overlays in Table 2. Among the borrowers who can lower their interest rates by more than 1/8 of a percentage point, annual interest payment savings range from \$220 to \$1,400, depending on the configuration of the applicants' credit scores, the size of their loan, and the LTV of the loan. On average, these joint applicants could have reduced their interest payments by \$400 per loan (or about 2.4 percent).

3. Characteristics of Borrowers Who May Have Left Money on the Table
We next explore the characteristics of the borrowers of joint mortgages who appear to have left money on the table. Because the statistics in Table 2 reveal that no borrowers with credit scores above 720 can lower their borrowing costs more than one eighth of a percentage point by switching to single-applicant loans, our estimation will focus on borrowers with lower credit scores. Specifically, we estimate a logit model among the 61,253 eligible joint applicants whose minimum FICO scores are below 720, with the dependent variable equal to one if the borrowers could have reduced borrowing costs more than one eighth of a percentage point by applying individually. The independent variables include an array of credit score bins (the lower score of the joint applicants to be lower than 620, 620-639, 640-679, with 680-719 being the omitted group); an array of dummies of loan and borrower characteristics, including high LTV (above 90 percent), first-time homebuyer, young household (the first borrowers' ages younger than 35), marital, educational attainments (with high school dropouts being the omitted group); and household income bins (with high income households being the omitted group). In addition, we control for state and year fixed effect in our estimation. The estimated odds ratios implied by turning the dummy variables to equal one are reported in Table 3, with an odds ratio greater than one indicating that a joint-applicant mortgage with the dummy variable equal to one is more likely to be able to reduce the borrowing costs by switching to individual-applicant.

Our analysis indicates that, even among the borrowers with relatively low credit scores (FICO < 720), there remains a rather steep credit score gradient regarding the likelihood of leaving money on the table. For example, joint borrowers with lower scores below 620 are seven times as likely to be able to significantly reduce their borrowing costs by switching to the high-score individual alone applying for the mortgage. In addition, consistent with our expectations, borrowers with high-LTV mortgages, first-time home buyers, and younger borrowers are all subject to greater likelihood of reducing borrowing costs by switching to individual applications, whereas married borrowers are less likely to be so. Moreover, relative to both low- and high-income borrowers, middle-income borrowers appear to have a greater chance of reducing borrowing costs by using individual-applicant mortgages. Interestingly, once the above characteristics of the loans and the borrowers are controlled for, relative to borrowers with lower educational attainments, joint mortgage applicants who have college degrees appear to have a great chance of saving money by using single-applicant loans.

References
Agarwal, Sumit, Souphala Chomsisengphet, Chunlin Liu, and Nicholas Souleles, (2015). "Do Borrowers Optimally Choose Credit Contracts?" Review of Corporate Financial Studies, 4(2), pp. 239–57.

Agarwal, S., P. M. Skiba, and J. Tobacman (2009). "Payday Loans and Credit Cards: New Liquidity and Credit Scoring Puzzles?" American Economic Review, 99(2), pp. 412–17.

Bertrand, M., and A. Morse (2009). "What Do High-Interest Borrowers Do with Their Tax Rebate?" The American Economic Review, 99(2), pp. 418–23.

Calvet, Lurent E., John Campbell, and Paolo Sodini, (2009). "Measuring the Financial Sophistication of Households," American Economic Review 99(2), pp. 393–98.

Campbell, J. (2006). "Household finance," The Journal of Finance 61(4), pp. 1553–1604.

Choi, James J., David Laibson, and Brigitte Madrian (2011). "$100 Bills on the Sidewalk: Violations of No-Arbitrage in 401(k) Accounts," The Review of Economics and Statistics 93(3), pp. 748–63.

DellaVigna, S., and U. Malmendier (2006). "Paying Not to Go To the Gym," American Economic Review, 96(3), pp. 694–719.

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Please cite this note as:
Li, Geng, Weifeng Wu, and Vincent Yao (2016). "Do People Leave Money on the Table? Evidence from Joint Mortgage Applications and the Minimum FICO Rule," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, March 28, 2016, http://dx.doi.org/10.17016/2380-7172.1718.