The Federal Reserve Bank and the Bank of England left their policy interest rates unchanged this month.^{1} But an interest rate lift-off in the near future remains on the table in both the US and the UK, provided the headwinds from China ease off and there is further evidence of improvements in the domestic economy. However, inflation still hovers stubbornly at around 0% in both economies.

Interest rates set by central banks influence the economy through various transmission mechanisms. But one channel affects the typical household directly – the cost of servicing mortgage debt. Standard mortgage loans require homeowners to make nominal installments — regular interest and amortisation payments — calculated to ensure that the loan is fully repaid by the end of its term. Changes in the interest rate set by the central bank affect the size of mortgage payments, but differently for different types of loans. In addition, the real value of these payments depends on inflation. In a new paper, we provide a general equilibrium characterisation of these channels in a model with incomplete financial markets (Garriga et al. 2015).

## Mortgage contracts and debt servicing costs

Fixed-rate mortgages – characteristic of the US – have a fixed nominal interest rate and thus constant nominal installments for the entire term of the loan, typically 15 or 30 years. Fixed-rate mortgage interest rates are determined at origination on the basis of the mortgage lenders’ expectations of the future path of the central bank interest rate.

In contrast, the interest rate of adjustable-rate mortgages – a standard contract in the UK – changes every time the central bank interest rate changes. The nominal installments of adjustable-rate mortgages loans are thus recalculated on each such occasion, to ensure the full repayment of the loan by the end of its term.^{2}

While mortgage contracts specify nominal installments, either fixed or adjustable, the real cost of servicing mortgage debt depends on inflation. The effects of the lift-off on homeowners will therefore depend not only on the mortgage type and the future path of interest rates, but also on what happens to inflation during the lift-off.

It is instructive to illustrate the effects of the lift-off on homeowners in terms of changes in mortgage debt servicing costs — nominal mortgage payments deflated by inflation as a fraction of household real income. This variable provides a metric of the burden of mortgage debt to homeowners, as it measures the fraction of real income homeowners have to give up to meet the mortgage payment obligations of their contract. The numerical examples below illustrate these points. Various papers consider different channels through which homeowners’ decisions then transmit into the wider economy (e.g. Boldrin et al. 2013, Auclert 2014, Di Maggio et al. 2014, Garriga et al. 2015).^{3}

## Liftoff scenarios

Figure 1 considers two alternative paths for the central bank interest rate: a slow lift-off and a fast lift-off from the current near zero lower bound. In both cases, the interest rate is assumed to revert to 4%, the pre-2007 crisis average. In the fast lift-off case, it reaches the halfway mark of 2% in two years’ time, whereas in the slow lift-off case this mark is not reached until about eight years from the start of the lift-off.

Figure 2 plots debt-servicing costs in the case of the lift-off scenarios under the assumption that there is no increase in inflation. As a result, the paths of the nominal interest rate in Figure 1 coincide with paths of the real interest rate. Figure 3 contrasts this case with a situation where the increase in the central bank interest rate is assumed to be accompanied by a one-to-one increase in the inflation rate. The real rate therefore stays unchanged at 0% and the paths of the nominal interest rates in Figure 1 are equivalent to paths of the inflation rate. While both assumptions are extreme, they demonstrate how the effects of the lift-off on homeowners with mortgages depend on the inflation rate and put bounds on what we may expect to happen.

**Figure 1**. Paths for short-term nominal rate

In both figures, the debt-servicing costs under the various lift-off scenarios are compared with a baseline case, in which both the central bank interest rate and the inflation rate stay unchanged at 0% (blue dotted line), approximately the current situation. In this case, debt-servicing costs are about 20% due to the lenders’ markup of three percentage points.

## A liftoff without inflation

When inflation stays at 0% during the lift-off (Figure 2) the real mortgage payments of existing homeowners with fixed-rate mortgages loans stay unaffected. This is because the fixed-rate mortgage interest rates have been fixed at origination before the lift-off and inflation stays at 0%. However, new fixed-rate mortgage loans will be priced according to the expected path of the central bank interest rate in Figure 1 and will therefore carry a higher interest rate. The faster the lift-off, the higher the new fixed-rate mortgage interest rate. In the case of the fast lift-off, the higher fixed-rate mortgage interest rate implies debt-servicing costs of almost 30%; under the slow lift-off, debt servicing costs will be 25% (the solid red lines in Figure 2).

With adjustable-rate mortgages, the lift-off affects both existing and new homeowners. The dashed green lines plot debt servicing costs for new adjustable-rate mortgage homeowners and essentially track the paths of the central bank interest rate — debt-servicing costs gradually increase from 20% to 32% under the fast lift-off and to 27.5% under the slow lift-off. For existing homeowners with adjustable-rate mortgages, the effects depend on when the loan was originated. The more recently originated the loan, the more the path of debt servicing costs will resemble that for new loans. Debt-servicing costs of loans that are almost repaid will be nearly immune to the lift-off. This is because mortgage payments in later periods of the life of the loan are mostly amortisation payments, rather than interest payments.

**Figure 2**. Liftoff with no inflation

## A liftoff accompanied by one-for-one inflation

When the lift-off is accompanied by equivalent increases in inflation, and no change in the real rate, the impact of higher nominal interest rates on debt-servicing costs is attenuated (Figure 3). First, existing fixed-rate mortgage homeowners gain from higher inflation and these gains grow over time as persistent inflation deflates the real value of the nominal payments, which under fixed-rate mortgages are constant. Those with the more recently originated mortgages gain the most over their homeownership tenure (the dash-dotted red lines in the figure show the case of a mortgage with 119, out of 120, quarters remaining – that is 29 years and three quarters). New fixed-rate mortgage borrowers, however, will face a higher mortgage rate and, as a result, initial debt-servicing costs of almost 30% in the fast lift-off case (solid red line). But the real value of those payments will also gradually decline over time.

For adjustable-rate mortgage homeowners, both existing and new homeowners, there are two opposing forces in place. On the one hand, higher nominal interest rates increase nominal mortgage payments. On the other hand, higher inflation reduces their real value. The first effect is stronger initially but the second effect dominates over time. Furthermore, the point where the second effect starts to dominate depends on the speed of the lift-off. While in the fast lift-off case the first effect is stronger for the first eight years (32 quarters), increasing debt-servicing costs to up to 25%, in the slow lift-off case it is very small and short-lived (dashed green lines). The speed of the lift-off is thus especially important for those at early stages in their homeownership lifecycle such as first-time buyers, as these households are the ones with the highest exposure to the first effect.

**Figure 3**. Liftoff with a one-for-one increase in inflation

## Policy implications

To sum up, the effects of the lift-off on homeowners depend on three factors:

- The prevalent mortgage type in the economy (fixed-rate or adjustable-rate mortgages);
- The speed of the lift-off; and
- What happens to inflation during the course of the lift-off.

If inflation stays constant at near zero then in the US, where fixed-rate mortgage loans dominate, the lift-off will affect only new homeowners. In the UK, where adjustable-rate mortgage loans dominate, the negative effects will in contrast be felt strongly by both new and existing homeowners.

However, if the lift-off is accompanied by sufficiently high inflation as in our examples, the negative effects will be weaker in both countries. In the US, the initial negative effect on new homeowners will be compensated by gradual positive effects on existing homeowners. And in the UK, provided the lift-off is sufficiently slow, neither existing nor new homeowners would face significantly higher real costs of servicing their mortgage debt. But if the lift-off is too fast, both types of homeowners in the UK will face higher real mortgage costs in the medium term, even if the lift-off is accompanied by positive inflation with no change in real rates.

Therefore, if the purpose of the lift-off is to ‘normalise’ nominal interest rates without derailing the recovery, central bankers in both the US and the UK should wait until the economies show convincing signs of inflation taking off. Furthermore, the lift-off should be gradual and in line with inflation.

*Disclaimer: The views expressed herein do not necessarily reflect those of the Federal Reserve Bank of St Louis or the Federal Reserve System.*

## References

Auclert, A (2014), “Monetary policy and the redistribution channel”, mimeo.

Boldrin, M, C Garriga, A Peralta-Alba, and J M Sanchez (2013), “Reconstructing the Great Recession”, Working Paper No 2013-006B, Federal Reserve Bank of St Louis.

Di Maggio, M, A Kermani and R Ramcharan (2014), “Monetary policy pass-through: Household consumption and voluntary deleveraging”, mimeo.

*Financial Times* (no date), “When rates rise”, available at http://ig.ft.com/sites/when-rates-rise/.

Miles, D (2004), “The UK mortgage market: Taking a longer-term view,” special report, HM Treasury.

European Mortgage Federation (2012), “Study on mortgage interest rates in the EU”, Brussels.

Garriga, C, F E Kydland, and R Sustek, (2015), “Mortgages and monetary policy”, Working Paper No 751, School of Economics and Finance, Queen Mary, University of London.

Scanlon, K, and C Whitehead, (2004), “International trends in housing tenure and mortgage finance”, Special report for the Council of Mortgage Lenders, London School of Economics.

## Endnotes

1 In the UK, the typical mortgage is the so-called standard-variable rate mortgage, which has an interest rate fixed for the first year or two. After this initial period, the interest rate can vary at the discretion of the lender, but usually the resets coincide with changes in the Bank Rate, the Bank of England policy interest rate. A ‘tracker mortgage is explicitly linked to the Bank Rate. Here we abstract from these details. European Mortgage Federation (2012) and Scanlon and Whitehead (2004) provide further institutional details of mortgage markets in developed economies. Miles (2004) focuses on the details of the UK market.

2 The examples assume that a homeowner’s real income does not change throughout the life of the loan, the loan at origination is four times the homeowner’s income, its term is 30 years (120 quarters) and the mortgage lender’s mark-up over market interest rates is three percentage points. The fixed rate mortgage interest rate is also calculated to be consistent with no-arbitrage pricing in bond markets, given the future path of the central bank interest rate.

3 This is effectively a scenario under the Fisher effect.