What goes up must come down: modelling the mortgage cycle

Kristina Bluwstein, Michal Brzoza-Brzezina, Paolo Gelain and Marcin Kolasa.

Mortgages matter. For the individual, borrowing to buy a house can be the biggest debt decision of a lifetime. For the economy, mortgages make up a large fraction of total debt and are a main driver of the financial cycle. Mortgage debt exceeds 80% of UK household debt (see Figure 1), so it is important to understand mortgage market trends, how they link to the macroeconomy and the implications for monetary policy. This post uses a novel model to do just that. In particular, it introduces a rich description of the housing sector into an otherwise standard ‘DSGE’ Model. It focusses on the role of fixed rate mortgages, the mortgage cycle, and how they affect monetary policy transmission.

Figure 1: UK household debt to income ratio

Source: Bank of England Financial Stability Report (2018)

The problem is that it is hard to understand and predict a credit bust (or a boom, for that matter) without the right tools – in our case: the right models. Since the financial crisis, many economists have made up for lost time by developing a huge arsenal of new models that boast features from housing, to fixed interest rate mortgages, to non-linear effects. However, when looking at each of these factors in isolation, none of them alone can explain the evolution of mortgage debt. We address this problem in a recent working paper, in which we construct a model that includes several such features and allows us to replicate and explain the nature of the mortgage debt boom-bust cycle. The paper also shows that the transmission of monetary policy depends on the stage of the housing cycle and the length of fixed interest rate mortgages.

Modelling non-linear effects and fixed interest rates is essential to explain the data on mortgage debt

A standard macro model with housing often assumes that mortgages last for only one period. It might sound counter-intuitive to assume that a loan is continuously taken out and repaid every period, but as mortgages in these models always have variable interest rates, it is not as unrealistic of an assumption as it sounds. It is equivalent to taking out a mortgage each period and paying the current interest rate.

We expand upon this model by making three crucial and realistic extensions: (i) Loans can be held for longer than one period. To make things more interesting these mortgages can be taken out as fixed interest rate mortgages. This means that the interest rate on the mortgage is not affected by changes in the central bank’s interest rate for a specific duration of time. There is a large variation among countries in how long the fixed rate period can last, with the US on the longest side of the spectrum with an average duration for which the interest rate of a mortgage is fixed of around 27 years (see Figure 2), and the UK on the shorter side of the spectrum with an average duration of fixed interest rate mortgages of only 3 years.

(ii) We also assume that banks cannot ask for their loans to be repaid any faster, as the repayment schedule is fixed. This means that banks cannot reduce the amount of the already taken out loans any faster than that repayment schedule allows.

(iii) Finally, we assume that borrowers occasionally face limit on how much they can borrow (i.e. occasionally binding constraints). In normal times, the amount available to borrow is equal to a specific proportion of what their house is worth. However, they also do not have to borrow up until that maximum amount and can borrow less. Also, in extreme circumstances, their mortgage loan could become larger than what their house is currently worth, something that is known as being ‘under water’ in the US. This can happen when house prices fall, but the original mortgage was taken out while prices were still high. These three extensions all sound pretty intuitive, but can be tricky to model, especially when it comes to estimating these models with data. We choose US data, as it allows us to look at what happens when the duration of fixed interest rate mortgages is at the most extreme end.

Figure 2: Average Initial Fixed Period for Mortgages by Country.

Source: Campbell (2012).

In our new paper, we show that only by including all of these features can we predict the path of US mortgages reasonably well (see Figure 3, black bold line). In contrast, a standard model without these extensions would predict that mortgages would track house prices (grey dotted line), as people would always borrow as much money as their house is worth, and reduce their debt immediately if their house loses value. Instead, our model manages to match the slower increase in mortgage debt, and can capture the fact that households do not always take out the maximum possible mortgage amount they can just because their house has increased in value. We also qualitatively show that once house prices go down, mortgages tend to decline more slowly and with a large delay, as banks cannot just ask borrowers to pay them back more rapidly.

Figure 3: The evolution of the stock of real mortgage debt in the US

Source: US Flow of funds.

The series is linearly de-trended and presented in percent deviation from mean (bold grey line). Our full non-linear model (bold, black line) manages to match the slow increase and the partial decline of the data. In contrast, the basic linear model without our extensions (grey dotted line) follows the evolution of house prices and thus overestimates the peak and slow decline in mortgage debt.

Monetary policy could be less effective with fixed rate mortgages and at the peak of the cycle

Now that we have a more realistic model in place, we can use it to analyse the effects of monetary policy. For households, prevailing interest rates lie at the heart of mortgage decisions. They determine the cost of taking on new debt and of servicing the stock of existing mortgages.  Changes in the interest rate therefore have potentially large effects on the economy. The strength of these effects will depend on the structure of the mortgage market and notably the prevalence of fixed versus floating rates.   

We find that both the mortgage market structure and the stage of the housing cycle matter for the conduct of monetary policy. Increases in the policy rate have a smaller effect on the rates households pay when mortgage interest rates are fixed for a longer time. As the increase in the interest rate is not passed on as strongly, it might affect one of the transmission channels of monetary policy: namely, the cash-flow channel that would normally imply that households reduce their consumption to meet higher mortgage payments, and thereby effectively reduce pressure on prices. While this means that the cash-flow effect of monetary policy is dampened, it also protects borrowers from increases in their mortgage repayments.

We also find that the transmission of interest rate rises is weaker when house prices are at their peak, as borrowers have room to smooth their consumption by taking out bigger loans.

Our analysis demonstrates that it is critical for economists and policymakers to understand the drivers of the mortgage credit cycle. On the one hand, it is important for policymakers to know how the housing cycle and mortgage structure affect the transmission of monetary policy. On the other hand, spotting the signs of a potential mortgage market slowdown early on might help to avoid some of the detrimental impacts from future events similar to those that took place a decade ago.

Kristina Bluwstein works in the Bank’s Macroprudential Strategy and Support Division, Michal Brzoza-Brzezina works at Narodowy Bank Polski, Paolo Gelain works at Federal Reserve Bank of Cleveland and Marcin Kolasa works at Narodowy Bank Polski.

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Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.

3 thoughts on “What goes up must come down: modelling the mortgage cycle

  1. Oh the agony of seeing Denmark and Belgium included in Figure 2, but the Netherlands omitted! Disregarding the fact the Netherlands is twice as large as either, the Netherlands also has the highest mortgage density in the world. So, as a Dutchman, I naturally feel offended 😉

  2. Has your model considered the impact of US mortgage holders having the option to refinance their mortgage and that this is a rational decision when interest rates fall? Valuation models for mortgage debt assume that a proportion of home owners do this in a path dependent way.

  3. Thank you for publishing the article, the impact of fixed rate mortgages and house prices was particularly engaging. I had a question regarding the penultimate paragraph:

    “We also find that the transmission of interest rate rises is weaker when house prices are at their peak, as borrowers have room to smooth their consumption by taking out bigger loans.”

    How would borrowing more allow households to smooth consumption? Does this assume that households are expecting an increase in income in the future?

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