1 

Overview 

In early 2009, a government-sponsored 

program—Making Home Affordable (MHA)—

was established to provide foreclosure 

alternatives to homeowners impacted by the 

financial crisis. The Home Affordable 

Modification Program (HAMP), the first and 

largest program under MHA, provided a 

standard for mortgage modifications that 

crossed servicer and investor types, with the 

goal of reducing struggling homeowners’ 

monthly mortgage payments to an affordable 

and sustainable level. With the termination of 

these programs at the end of this year, the U.S. 

Department of the Treasury (Treasury) in 

conjunction with the U.S. Department of 

Housing and Urban Development (HUD) and 

the Federal Housing Finance Agency (FHFA)—

together the Agencies—are working with 

stakeholders to maintain strong loss mitigation programs going forward. There is, however, more work to be 

done. With some exceptions, servicers will no longer be required to evaluate homeowners for a standard 

mortgage modification like HAMP. Instead, servicers and investors will need to utilize proprietary loss 

mitigation programs, and determine the appropriateness of such programs in a more economically stable, 

post-crisis environment. Since post-modification DTI greatly correlates with the reduction in a homeowner’s 

monthly payment, it is necessary to use an econometric analysis to properly control for payment change and 

other variables known to impact modification performance to properly answer questions about the 

importance of DTI. 

Research Questions and Analysis 

The following analysis is part of a Lessons Learned Series which provides insight into the success of the 

Making Home Affordable (MHA) program. Fannie Mae, as Treasury’s financial agent, performed an analysis 

of the Importance of Debt-to-Income Ratio for Modified Loan Performance on behalf of Treasury in order to 

answer two questions about the performance of HAMP modifications: 

 Is the post-modification front-end debt-to-income ratio (DTI) a significant indicator of modification 

performance? 

 Does the importance of DTI as an indicator of post-modification performance change depending on 

the borrower’s income level (i.e., is the performance of HAMP modifications for low-income 

borrowers more sensitive to DTI than those for higher-income borrowers)? 

Researching these questions required a dataset of HAMP modifications with meaningful differences in postmodification DTI. This requirement ruled out use of HAMP Tier 1 modifications since all such modifications 

have the same 31% DTI target. HAMP Tier 2, however, primarily targets payment change and allows for DTI 

between 10% and 55% and those modifications were able to provide the necessary dataset. 

MHA LESSONS LEARNED SERIES: 

IMPORTANCE OF DEBT-TO-INCOME RATIO (DTI) 

FOR MODIFIED LOAN PERFORMANCE 

October 20, 2016 
 2 

Fannie Mae used a method of statistical analysis, called logistic regression, to control for the effects from 

other variables before measuring the relationship between DTI and modification redefault. Fannie Mae 

started with a baseline model of redefault at 6 and 24 months using 16 control variables for measuring risk of 

the borrower and local housing market. If DTI is a predictive indicator of redefault, we would expect that 

adding it to the regression would improve the accuracy of the model predictions (i.e., “model fit”). However, 

the addition of DTI to the regression failed to improve the model fit. Fannie Mae performed an additional test 

to determine if DTI had significance specifically for the subset of borrowers below the median income. This 

“DTI plus income” test also failed. 

INTERPRETATION 

This analysis found that within HAMP Tier 2, the post-modification front-end DTI does not have a statistically 

significant impact on modification redefault. In other words, the measured effect was so small that it fell 

within the margin of error. 

The limited context of this analysis is important to understand. 

First, out of necessity, our analysis was limited to HAMP Tier 2 modifications. MHA program rules require 

that HAMP Tier 2 is only offered to borrowers who do not qualify for, or have already failed a HAMP Tier 1 

trial or permanent modification. The possibility also remains that borrowers determined to be eligible for 

HAMP Tier 2 may be particularly insensitive to DTI. 

Secondly, within the HAMP dataset, DTI data is limited to front-end DTI. One might hypothesize that backend DTI, which includes all of a borrower’s monthly debt burden, would be a better predictor of modification 

redefault, but reliable measures of back-end DTI were not available to us. This outcome may provide an 

opportunity for further analysis using data from other, non-HAMP loan modification programs. 

Conclusion 

As noted in “Guiding Principles for the Future of Loss Mitigation”, sustainability and affordability are key 

points of convergence for successful mortgage modification solutions. Payment reduction—whether fixed 

plan versus flexible step-up plan—is a necessary component to achieve the best possible outcome for 

struggling homeowners. It is readily apparent that singular variables do not reliably predict redefault 

performance in this analysis. 

Because none of the added variables improved the model fit relative to our baseline model, we can conclude 

that neither DTI nor income level—taken alone or together—are statistically significant factors in predicting 

the redefault performance of Tier 2 HAMP modifications. 

Even if the results had been significant, they still would have been viewed as weak. We illustrate this below 

using the modeled 6-month redefault rate. If we were to use the estimated DTI coefficients to illustrate the 

effect of altering DTI on a single hypothetical median loan, the redefault probabilities fluctuate by less than 

1%. 
 3 

 

APPENDIX: Modeling Approach

LOAN POPULATION 

Tier 1 HAMP modifications target a 31% DTI as part of the modification structure. With no meaningful variation in DTI, 

traditional Tier 1 HAMP modifications are not suitable for answering these questions. By contrast, Tier 2 HAMP 

modifications focus primarily on payment reduction and allow for the resulting DTI to fall between 10% and 55%. As a 

result, we limited our analysis to Tier 2 HAMP modifications. 

MODEL ESTIMATION 

When a HAMP modification becomes 90 days delinquent, it is considered to have lost good standing, an event also 

referred to as redefault. After a loss of good standing, investor, servicer and borrower incentives stop, and loan 

performance is no longer reported into IR/2, the program’s official system of record. 

We began by fitting a logistic regression model to predict redefault using a familiar set of control variables from previous 

research in the HAMP vs. non-HAMP Performance Study1

 and The Effects of Principal Reduction on HAMP Early 

Redefault Rates2

. We used control variables for 

 Post-modification LTV 

 Investor Category (Private Label Security, Held on Portfolio) 

 P&I Payment Change (% of original payment) 

 Loan Delinquency at time of trial 

 Credit Score 

 Origination LTV 

 Months since origination 

 Principal Forgiveness 

 Property Occupancy Status (Owner, Tenant, Vacant) 

 Unit Count (1-4) 

 Capitalized UPB 

 Months Spent in Trial 

 12 Month HPI Change 

 State (12 states) 

 Servicer (9 servicers) 

 Modification Effective Date (by quarter) 

NULL HYPOTHESIS: DTI 

Our null-DTI hypothesis is that post-modification front-end DTI is not a significant factor in the performance of a modified 

loan. Controlling for other risk factors, modified loans with lower DTIs will not have a lower probability of redefault. 

To test our null-DTI hypothesis, we constructed an alternate model (“A-Model”) building upon the baseline by adding a 

set of 4 categorical indicators of DTI ranges between 10% and 55%. We compared the models using a likelihood ratio 

test for relative goodness of fit. The alternate “A-Model” fails the test with a relative p-value of 0.2883, offering little 

reason to reject the null-DTI hypothesis.

 

1 Scott, Walter L. "Treatment Effects of Subprime Mortgage Modifications Under the Home Affordable Modification Program." 

Mar. 2015. https://www.treasury.gov/initiatives/financial-stability/TARP-Programs/housing/mha/Pages/Surveys.aspx 2

 Making Home Affordable, “The Effects of Principal Reduction on HAMP Early Redefault Rates.” Jul. 2012. 

https://www.hmpadmin.com/portal/programs/docs/hamp_servicer/MHAPRAReasearch.pdf 
 4 

Table 1: Regression coefficients for DTI (“A-Model”). 

Analysis Of Maximum Likelihood Parameter Estimates 

Parameter Value DF Estimate Standard 

Error 

Wald 

ChiSquare

Pr > 

ChiSq 

LN_AFT_MDFC_FRNT_RTO_PCT c [10,20) 1 -0.0708 0.0523 1.83 0.1757

LN_AFT_MDFC_FRNT_RTO_PCT d [20,30) 1 -0.0238 0.0522 0.21 0.6487

LN_AFT_MDFC_FRNT_RTO_PCT e [30,40) 1 0.0075 0.0593 0.02 0.899

LN_AFT_MDFC_FRNT_RTO_PCT f [40,55] 0 0 0 . . 

Table 2: Log likelihood ratio test against baseline model 

BASELINE A-Model 

Log Likelihood DF Log Likelihood DF Pr 

-20122.9682 71 -20121.0871 74 0.2883

NULL HYPOTHESIS: INCOME 

Our second null hypothesis is that lower-income borrowers are as sensitive to the impact of DTI on post-modification 

performance as higher-income borrowers. 

To test the null-income hypothesis we created a dummy variable to identify modifications to borrowers with gross 

monthly income below $3,333—the median for our population of HAMP Tier 2 modifications. We then created our “BModel” of redefault by adding the lower income flag to our baseline redefault model. We then added DTI as a separate 

variable, and also connected it with the low income flag (“C-Model”). In order to reject the null-income hypothesis, Cmodel would have to provide a better fit than our baseline and both models A and B. 

C-Model fails all of these tests with p-values above the customary threshold of 5%. Indeed, none of the model variants 

represent an improvement in fit over the baseline or any of the simpler model specifications. These results do not 

support rejection of the null-income hypothesis. 

Table 3: Relative log likelihood ratio tests against nested model 

Test Pair 

DF 

diff 2 * | LL2 - LL1 | Pr 

BASELINE A-Model 3 3.7622 0.2883 

BASELINE B-Model 1 0.0282 0.8666 

A-Model C-Model 4 2.1964 0.6997 

B-Model C-Model 6 5.9304 0.4310 

BASELINE C-Model 7 5.9586 0.5446 

Table 4: Comparison of model predictions using rejected control variables for DTI and income. 

HAMP Tier 2 Redefault Probability at Month 6 

Modeled without DTI or Income Group 

Baseline 8.4% 
 5 

HAMP Tier 2 Redefault Probability at Month 6 

Modeled with DTI & Income Group 

After Mod DTI 

Below Median 

Income 

Above Median 

Income 

c [10,20) 8.0% 7.6%

d [20,30) 8.3% 8.5%

e [30,40) 8.6% 8.5%

f [40,55] 8.9% 8.2%

To illustrate this another way, we can calculate the relative importance of the variables from our rejected C-Model 

regression. Initial delinquency, payment change and credit score have the strongest impacts. DTI has very little 

predictive power. 

Figure 1: Relative importance at 6 months and 24 months after modification completion.