A speech by Andy Haldane Chief Economist at the Bank of England – The Dappled World– for the Shackle Biennial Memorial Lecture included a section on modelling the UK housing market using Agent-Based Models (ABM). It makes interesting reading. What you will see is a gradual heating-up of the mortgage market over the past few years, with a clear epicentre of London and the South-East.
The housing market has been one of the primary sources of financial stress in a great many countries (Jorda, Schulerick and Taylor (2014)).
Chart 6: UK House Prices: 1846-2015, Annual Long Range Distribution
Not coincidentally, this market has also been characterised by pronounced cyclical swings. Chart 7 runs a filter through UK house price inflation in the period since 1896. It exhibits clear cyclicality, with peak-to-trough variation often of around 20 percentage points. Mortgage lending exhibits a similar cyclicality.
Chart 7: Long-run UK house price growth 1846 to 2015
Source: Hills, Thomas and Dimsdale (2016); Bank calculations. Notes: The chart shows the Hodrick-Prescott trend in annual house price growth data (where lambda=6.25). Data during WWI and WWII are interpolated.
House prices, like other asset prices, also exhibit out-sized booms and busts. Chart 6 plots the distribution of UK house price growth since 1846. It has fat-tails, with the probability mass of big rises or falls larger than implied by a normal distribution. For example, the probability of a 10% movement in house prices in any given year is twice as large as normality would imply.
Capturing these cyclical dynamics, and fat-tailed properties, of the housing market is not straightforward using aggregate models. These models typically rely, as inputs, on a small number of macro-economic variables, such as incomes and interest rates. They have a mixed track record in explaining and predicting housing market behaviour.
One reason for this poor performance may be that the housing market comprises not one but many sub-markets – a rental market, sales market, a mortgage market etc. Moreover, there are multiple players operating in these markets – renters, landlords, owner-occupiers, mortgage lenders and regulators – each with distinctive characteristics, such as age, income, gearing and location.
It is the interaction between these multiple agents in multiple markets which shapes the dynamics of the housing market. Aggregate models suppress these within-system interactions. The housing market model developed at the Bank aims to unwrap and model these within-system interactions and use them to help explain cyclical behaviour (Baptista, Farmer, Hinterschweiger, Low, Tang and Uluc (2016)).
Specifically, the model comprises households of three types:
- Renters who decide whether to continue to rent or attempt to buy a house when their rental contract ends and, if so, how much to bid;
- Owner-occupiers who decide whether to sell their house and buy a new one and, if so, how much to bid/ask for the property; and
- Buy-to-let investors who decide whether to sell their rental property and/or buy a new one and, if so, how much to bid/ask for the property. They also decide whether to rent out a property and, if so, how much rent to charge.
The behavioural rules of thumb that households follow when making these decisions are based on factors such as their expected rental payments, house price appreciation and mortgage cost. These households differ not only by type, but also by characteristics such as age and income.
An important feature of the model is that it includes an explicit banking sector, itself a feature often missing from off-the-shelf DSGE models. The banking sector provides mortgage credit to households and sets the terms and conditions available to borrowers in the mortgage market, based on their characteristics.
The banking sector’s lending decisions are, in turn, subject to regulation by a central bank or regulator. They set loan-to-income (LTI), loan-to-value (LTV) and interest cover ratio policies, with the objective of safeguarding the stability of the financial system. These so-called macro-prudential policy measures are being used increasingly by policy authorities internationally (IMF-FSB-BIS (2016)).
The various agents in the model, and their inter-linkages, are shown schematically.
Figure 17: Agents and interactions in the housing market model
Source: Baptista et al (2016).
This multi-agent model can be calibrated using micro datasets. This helps ensure agents in the model have characteristics, and exhibit behaviours, which match those of the population at large. For example, the distribution of loan-to-income or loan-to-value ratios on mortgages are calibrated to match the UK population using data on over a million UK mortgages. And the impact on the sale price of a house of it remaining unsold is calibrated to match historical housing transactions data.
One of the key benefits of the Agent-Based Models (ABM) approach is in providing a framework for drawing together and using, in a consistent way, data from a range of sources to calibrate a model. For example, a variety of data sources were used to calibrate this model, including:
- Housing market data: FCA Product Sales Data, Council of Mortgage Lenders, Land Registry and WhenFresh/Zoopla.
- Household surveys: English Housing Survey, Living Cost and Food Survey, NMG Household Survey, Wealth and Asset Survey, Survey of Residential Landlords (ARLA) and Private Landlord Survey.
Micro-economic data such as these are essential for understanding the impact of regulatory policies – for example, macro-prudential policies which affect the housing market. For example, the Bank has been making use of the FCA’s Product Sales Database to get a more granular picture of the mortgage position of households. This is a very detailed database, covering over 13 million financial transactions by UK households since 2005. By combining these data with land registry data, it is also possible to build up a regional picture of pockets of indebtedness.
Chart 8 documents the evolution of high (more than 4.5 times income) leverage mortgages since 2008, on a regional basis. Warmer colours suggest a higher fraction of loans at or above that multiple. What you will see is a gradual heating-up of the mortgage market over the past few years, with a clear epicentre of London and the South-East in the run up to the macro-prudential intervention made by the Bank of England’s Financial Policy Committee (FPC) in June 2014.
Chart 8: Proposition of mortgages with a loan-to-income ratio greater than 4.5Source: FCA Product Sales Database; Land Registry; Bank calculations.
One of the key features of an agent-based model is that it is able to generate complex housing market dynamics, without the need for exogenous shocks. In other words, within-system interactions are sufficient to generate booms and busts in the housing market. Cycles in house prices and in mortgage lending are, in that sense, an “emergent” property of the model.
Chart 9 shows a simulation run of the model, looking at the dynamic behaviour of listed prices, house prices when sold and the number of years a property is on the market. The model exhibits large cyclical swings, which arise endogenously as a result of feedback loops in the model. Some of these feedback loops are dampening (“negative feedback”), others amplifying (“positive feedback”).
For example, when mortgage rates fall, this boosts the affordability and the demand of housing, putting upward pressure on house prices. This generates expectations of higher future house price inflation and a further increase in housing demand – an amplifying loop.
Ultimately, however, affordability constraints bite and dampen house prices expectations and demand – a dampening loop. We can use the simulated data from Chart 9 to construct distributions of house price inflation over time (Chart 10). This simulated distribution exhibits fat-tails, if not as heavy as the historical distribution. Nonetheless, the model goes some way towards matching the moments of the real-world housing market.
Chart 9: Model simulations of the housing market
Source: Baptista et al (2016). Notes: Blue is the list price index, red the house price index and green the number of years a house is on the market.Chart 10: The distribution of house pricesSource: Baptista et al (2016); Hills, Thomas and Dimsdale (2016); Bank calculations. Notes: The blue diamonds show the distribution of simulated house price growth for over 160 years from the model. The red diamonds show the distribution of real house price growth between 1847 and 2015.
This same approach can also be used to examine the impact of various macro-prudential policy measures, whether hard limits (such as an LTV limit of 80% for all mortgage contracts) or soft limits (such as an LTI cap for some fraction of mortgages). These policies could also be state-contingent (such as an LTV limit if credit growth rises above a certain threshold).
As an example, we can simulate the effects of introducing a loan-to-income (LTI) limit of 3.5, where 15% of mortgages are not bound by this limit. This simulation is similar, if not directly comparable, to the macro-prudential intervention made by the Bank of England’s Financial Policy Committee (FPC) in June 2014.
Chart 11 looks at the simulated impact of this policy on the distribution of loan-to-income ratios across households, relative to a policy of no intervention. The incidence of high LTI mortgages (above 3.5) decreases, with some clustering just below the limit. With some borrowers nudged out of riskier loans, a greater degree of insurance is provided to households and the banking system. Another advantage of these class of models is that they allow you to simulate the longer run impacts once the second round and feedback loops have taken effect. Chart 12 shows that the distribution of house price growth narrows under the scenario relative to the baseline.
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