The Borrower at the Boundary
Mortgage affordability is not uniform even when borrowers face the same national 30-year mortgage rate. This chapter focuses on the boundary created by the relationship between a proposed loan, current income, and other payment obligations: why a rate change can leave one borrower comfortably eligible while pushing another toward a smaller loan or out of the market. The goal is to diagnose that exposure without treating loan-to-income as an exact measure of debt-to-income.
A common rate meets unequal loan sizes
The relevant comparison is not simply one household’s mortgage rate with another’s. In the United States, a national 30-year mortgage rate can be broadly common across cities at a point in time, while the size of the loan needed to buy a home varies sharply. A high-cost city may require a large mortgage relative to the income available to service it. A lower-cost city may allow a household to buy with a smaller loan even when the quoted rate is identical.
The paper uses loan-to-income, or LTI, to make this exposure visible. LTI is the loan amount divided by the borrower’s annual income. It is not the same as debt-to-income, or DTI. DTI compares scheduled debt payments with income, so it is closer to the actual payment test a lender applies. But for mortgages with the same term and rate, a larger loan relative to income generally produces a larger payment relative to income. LTI is therefore a useful city-level proxy for the likelihood that DTI constraints will bind, not a substitute for measuring the payment ratio itself.
That distinction becomes especially important when rates rise. Two borrowers can have the same LTI at one rate, but their payment-to-income ratios will increase when the rate rises. The borrower with more room under the lender’s payment boundary may remain eligible. The borrower whose payment already consumes much of current income may cross the boundary. LTI helps identify where that crossing is more likely, but it does not tell us exactly which borrower will be approved. Taxes, insurance, other debts, credit characteristics, down payments, income stability, and lender rules can all affect the final decision.
The paper’s Houston and Los Angeles examples show the threshold effect. Consider a relatively expensive Houston mortgage of about $500,000 for a household earning about $125,000. The loan-to-income ratio is about four. At a 3 percent mortgage rate, the annual payment is roughly $25,000, or 20 percent of income. At 7 percent, it rises to about $40,000, or 32 percent of income. That is a substantial increase, but it remains below the 45–50 percent DTI cutoff the authors use to illustrate where lenders may stop approving a loan, even before considering other monthly debts.
Now consider Los Angeles, where the example uses a mortgage of about $1.2 million for a household earning $200,000. The LTI is about six. At 3 percent, the annual payment is roughly $61,000, or 31 percent of income. The same loan becomes unaffordable under the example once the rate rises above about 6.4 percent, because the payment ratio passes 45 percent. The difference between the two cases is not that Los Angeles receives a different national rate. It is that a larger loan relative to income places the borrower closer to the payment boundary before the rate moves.
The paper reports a pattern consistent with that contrast. Average 30-year mortgage rates rose from 3.0 percent in 2021 to 6.8 percent in 2023. Loan-to-income distributions shifted down in both Houston and Los Angeles, but the shift was not identical. The number of loans issued from 2021 to 2023 fell 27 percent in Houston and 50 percent in Los Angeles. These figures are descriptive comparisons, not by themselves a city-level causal estimate. House prices, local incomes, employment, buyer composition, and other conditions can change at the same time. Their value is that they illustrate the prediction the broader analysis examines: a common nominal rate should have a larger affordability effect where high loan sizes make payment constraints more likely to bind.
The boundary is therefore a threshold, not a smooth tax applied equally to every household. Below the threshold, a higher payment can be absorbed without changing the approved loan. Near the threshold, the same dollar increase can force a discrete decision: reduce the principal, change the home being considered, bring more funds to the purchase, or stop qualifying. The underlying desire for housing need not change in the same proportion as the financing opportunity. The contract has changed what the household can carry under the lender’s current-income test.
The city comparison also clarifies why a simple national time series is difficult to interpret. Nominal and real mortgage rates often move together, and an economy-wide shock can affect rates, housing sentiment, incomes, and demand at once. If the nominal rate appears to rise when mortgage issuance falls, that pattern alone does not show whether the cause was the nominal payment, the real cost of borrowing, expectations, or another macroeconomic force. The cross-city prediction adds a more specific test: after accounting for the real rate, the nominal-rate effect should be stronger in places with higher LTI and, by implication, more binding payment constraints.
The numbers in the two examples show why an average response can hide a threshold response. In Houston, moving from 3 percent to 7 percent raises the illustrative payment ratio from 20 percent to 32 percent of income: a 12-percentage-point increase that still leaves room below a 45–50 percent boundary. In Los Angeles, the borrower starts at about 31 percent, and a rate above roughly 6.4 percent crosses 45 percent. The same direction of rate movement therefore produces different decisions: one borrower may keep the loan size, while the other must reduce the principal or lose eligibility. This is not a claim that every Houston or Los Angeles borrower matches the example. It is a way to see why the effect can become much larger near a qualification threshold than it appears for borrowers well below it.
What a borrower’s distance from the boundary can change
A useful way to apply the mechanism is to ask where the payment boundary is, not to treat the mortgage rate as a complete affordability measure. Start with the proposed loan relative to current income. A larger principal creates a larger scheduled payment at the same rate and term. Then consider the obligations that are included in the payment-to-income calculation. The paper’s examples include mortgage payments alongside other household debt payments and property taxes. A borrower who appears safe when viewed through the mortgage alone may be closer to the limit once the other obligations are counted.
Next consider the distance to the threshold. The relevant question is not only whether the current payment ratio is below a cutoff. It is how much room remains if the rate used to price the new loan rises. A household at 20 percent of income in the Houston example and a household at 31 percent in the Los Angeles example are not equally exposed to a move toward a 45 percent boundary. The latter has less room, so a similar rate movement can change the feasible loan more abruptly.
This is the practical meaning of “at the margin.” The highest-risk affordability change is not necessarily carried by the household with the highest quoted rate. It is carried by the household whose proposed payment is close to the relevant limit. A borrower with a smaller loan, higher income, fewer other obligations, or more room under the lender’s test may remain eligible at the same rate. Conversely, a borrower can move closer to the limit without a rate change if the desired loan grows, income falls, or other debts increase. The rate is one input to the boundary; it is not the boundary by itself.
A rate change can also alter the choice among homes without producing a clean yes-or-no rejection. A borrower may still qualify, but only for a smaller principal. That can mean a different price range, a larger required down payment, or a decision to wait. These are all responses at the financing margin, and they can reduce the number of loans originated even when many applicants remain technically eligible. The paper’s mechanism is therefore compatible with a gradual market response made up of many discrete household adjustments, not only a population of applications that are either accepted or denied.
A down payment illustrates the same interaction. A larger down payment can reduce the principal that must be financed, which can reduce the payment-to-income ratio for a given home and rate. That does not mean every household can produce more cash, or that the paper estimates how wealth changes the nominal-rate effect. It means that the contract-level mechanism operates on the financed principal. Wealth, liquidity, and the price of the target home can therefore alter exposure even when the quoted mortgage rate is identical. The supplied evidence does not provide a complete distributional estimate across wealth or income groups, so these are mechanisms to keep in view, not quantified conclusions from the paper.
The timing of the loan is equally important. A person applying for a new fixed-rate mortgage faces the rate available when the payment schedule is set. If the rate rises before origination, the same proposed principal requires a larger payment, and a payment-constrained borrower may no longer qualify. If the borrower keeps the same loan size, the payment boundary is more likely to bind; if the borrower reduces the principal, the purchase may remain possible at a different scale.
An existing borrower with an unchanged fixed-rate mortgage is in a different position. A market-rate increase does not, through this particular mechanism, immediately rewrite the nominal payment already fixed in the contract. That borrower may still experience indirect effects through employment, house prices, refinancing decisions, or other debts, but those are separate channels. The paper’s direct affordability argument is strongest for new originations and for contracts that are being reset or replaced. The supplied evidence does not quantify how adjustable-rate mortgages, refinancing, cash purchases, or household wealth modify the overall incidence.
LTI is useful precisely because it captures one part of this exposure at a scale where direct DTI data may not be available for the full historical period. The paper notes that detailed DTI ratios are available at the loan level only from 2018, while LTI can be constructed over a longer city-level sample. The two measures are strongly correlated in the paper’s 2019 cross-city data, as are average LTI and the share of loans with LTI above five. But a correlation between LTI and DTI does not make them interchangeable. A higher interest rate changes the payment associated with a given LTI, and borrowers with different terms or obligations can have different DTI ratios at the same LTI.
The proxy is used at the city level, not as a claim about every person in a high-LTI city. The paper groups CBSAs into terciles by average LTI, with the highest tercile representing places where the typical loan is larger relative to income. Within that group, some households will be far below a payment limit and others will be close to it. The average LTI does not reveal each borrower’s credit profile, contract term, taxes, insurance, or other debts. It instead provides a way to test whether the average market response is stronger where the payment constraint should be more relevant.
This choice also creates a meaningful trade-off in the evidence. A direct loan-level DTI measure would more closely match the proposed mechanism, but it is not available for the full period used in the city analysis. LTI offers longer coverage and a transparent relationship to payment exposure, at the cost of measurement precision. If the proxy captures many local features unrelated to payment constraints, the interaction could be harder to interpret. The paper’s reported correlations and controls make the proxy useful, but they do not turn it into a perfect instrument or establish that every observed city difference comes from underwriting.
That is why the city examples should be read as a diagnosis of exposure rather than as an underwriting calculator. They answer: where would the nominal-rate channel plausibly be strongest, given loan sizes relative to incomes? They do not answer: will a particular application be approved, how much cash should a particular household commit, or how much a city’s house prices must change. Those questions require borrower-level terms, lender rules, and market data not supplied here.
The borrower at the boundary is the key to unequal affordability effects. A rate increase can be economically meaningful without forcing every household to change its purchase, because only some borrowers are close to the payment ceiling. This prediction turns the contract story into an empirical question: do high-LTI cities experience a larger reduction in new mortgage issuance when nominal rates rise, after the real rate and other relevant conditions are considered? The checkpoint that follows will use that prediction to connect the household mechanism to the evidence.