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PricewaterhouseCoopers LLP – December 2008 1

Agent-based modelling

A new approach to understanding thehousing market

December 2008


Contents1

Page

Executive Summary 3Introduction 51. What is agent-based modelling? 62. Key features of our agent-based housing model 73. Behaviour patterns of baseline version of themodel

8

4. Sensitivity tests 115. Conclusions and areas for further research 14

Annex: Detailed model specification and references 15

1 This report has been prepared for general guidance on matters of interest only, and does not constitute professional

advice. You should not act upon the information contained in this report without obtaining specific professional

advice. No representation or warranty (express or implied) is given as to the accuracy or completeness of the

information contained in this report, and, to the extent permitted by law, PricewaterhouseCoopers LLP, its members,

employees and agents accept no liability, and disclaim all responsibility, for the consequences of you or anyone else

acting, or refraining to act, in reliance on the information contained in this report or for any decision based on it.

For more information about this report or related issues, please contact John Hawksworth by

e-mail at [email protected]


Agent-based modelling: a new approach to understanding the housingmarket2

Executive Summary

PricewaterhouseCoopers LLP, together with Professor Nigel Gilbert of the University ofSurrey, has developed a new approach to house price modelling based on computersimulations of the interaction of individual buyers and sellers (‘agents’) within the market.

This agent-based approach shows how realistic house price behaviour can be simulated bybuyers and sellers following relatively simple rules. The model allows users to change keyinput assumptions and see in ‘real time’ how this affects the evolution of prices and other keyvariables such as transactions numbers. The model display allows users to see how peoplemove around a schematic ‘town grid’ in which some new houses are built and othersdemolished over time. Key model parameters have been calibrated to match actual UK data.

Notable results of model simulations include the following:

both house prices and the number of housing transactions tend to be volatile in theshort term, helping to explain why short-term housing market forecasts are oftensubject to significant margins of error;

in the longer term, average house prices tend to show a stable relationship toaverage income levels for given levels of mortgage interest rates and loan-to-valueratios; if interest rates fall or maximum loan-to-value ratios rise, then the equilibriumhouse price to income ratio rises in response;

a key insight from the model, however, is that the interaction between these twoassumptions is critical, with the interest rate effect on house prices being muchweaker when the maximum loan-to-value ratio is lower;

in particular, the model suggests that moving from a 100% to an 80% maximum loan-to-value ratio, which is similar to what has happened recently in the UK mortgagemarket due to the credit crunch, can have a major depressing impact on house pricesthrough keeping first-time buyers with limited savings out of the housing market. Thiscan outweigh any positive effects on house prices and transactions volumes frominterest rate cuts;

increased inward migration puts significant upward pressure on house prices giventhat the supply of houses takes a long time to respond to such changes (and may beconstrained by the availability of land with planning permission to build on); thenumber of people seeking homes but unable to find affordable properties also tendsto increase significantly in such simulations; and

if there is a significant ‘yuppie invasion’ of migrants to an area with significantly higherincome levels than existing residents, the long-term effect is to price these residentsour of the market and push house prices up to a higher level but with the same ratioto incomes as before; the opposite tendency is evident with a large and persistentinflow of lower income inward migrants to an area.

2This paper was written by John Hawksworth and Paul Swinney of PricewaterhouseCoopers LLP and

Professor Nigel Gilbert of the University of Surrey. Tim Ogier provided helpful comments on an earlier

draft.


In policy terms, the model results suggest that:

building more new houses can reduce prices in the short-to-medium term, but asempty land is used up there is a strong tendency for house prices to return toprevious levels in the longer term; and

stamp duty changes do not seem to have a significant effect on house prices.

The model also shows how clusters of high house prices can arise over time due to a self-reinforcing tendency of a few high value houses in a particular area influencing valuations ofother nearby houses. This occurs even in a model where house prices are initially randomlydistributed across locations and there are no obvious locational advantages such as goodschools or access to transport links.


Agent-based modelling: a new approach to understanding the housingmarket

Introduction

The US housing market has been at the epicentre of the recent global credit crunch and theongoing downturn in the UK housing market remains one of the major concerns surroundingour economy. Understanding the housing market is therefore one of the major tasks ofmacroeconomists. The conventional approach to this problem is to use historic data toestimate an econometric model that relates house price movements to trends in incomes,interest rates and housing supply relative to household numbers.

This ‘top down’ approach is the most systematic way to produce quantitative house priceprojections and remains an ongoing area of PricewaterhouseCoopers LLP (PwC) economicresearch

3. In the present article, however, we explore a new ‘bottom up’ approach to

understanding the housing market based on using computer simulations to model directly theinteraction of individual households (‘agents’) who are seeking to buy and sell properties,including the role of intermediaries (i.e. estate agents or ‘realtors’). House prices emerge fromthis buying and selling process.

As far as we are aware, this agent-based approach has not been applied to the UK housingmarket before. As such, the research is necessarily of a somewhat experimental nature at thisstage. Nonetheless, our work to date suggests that this approach provides a usefulcomplement to conventional econometric techniques and should indeed have a wide range ofeconomic applications to markets other than housing.

The discussion below is structured as follows:

Section 1 provides a short general introduction to agent-based modelling;

Section 2 outlines our agent-based housing model and its key assumptions;

Section 3 describes the behaviour of house prices and other key variables in a baselineversion of the model;

Section 4 discusses the results of a number of sensitivity tests on key assumptions; and

Section 5 concludes and outlines areas for further research.

Further details of the model and methodology are contained in the Annex. A web-basedversion of the model is also being made available for readers to try out

4, since the model’s full

value can only really be appreciated through actually using it and seeing how the housingmarket evolves over time in different scenarios and how changing particular assumptionsaffects these market dynamics.

3See, for example, the article on probabilistic house price projections in the November 2007

PricewaterhouseCoopers UK Economic Outlook report.4

The model is written in NetLogo (Wilensky, 1999) and a demonstration version may be run as an

applet on the web at http://cress.soc.surrey.ac.uk/housingmarket/ukhm.html


1. What is agent-based modelling?

Agent-based models (ABMs) use computer simulations to explore the implications of theinteractions between agents within a particular environment over time. The modeller specifiesthe nature of the environment, the initial conditions and the rules which the agents follow. Thecomputer then simulates how the agents change and interact within the environment. Themodeller can observe the patterns that emerge at the macro level from this micro levelbehaviour and can see how these patterns vary with different initial conditions and agentbehaviour rules.

Many of the initial applications of ABMs were in the area of biology. Such models, for example,proved very useful in illustrating how ants could apparently achieve miracles of co-ordinatedbehaviour in gathering food and bringing it back to their nests using just a few simplemovement rules and scent trails. Or how, again using just a few simple rules, birds could flytogether in perfectly co-ordinated flocks (or fish swim together in schools). The dynamicevolutionary balance between carnivores, herbivores and limited natural food supplies couldalso be explored through such models, as could the spread of diseases through populationsof interacting animals or humans.

Transport systems can also be modelled in this way to help produce optimal designs tominimise congestion and ensure a smooth flow of traffic. Similar techniques have also beenused to optimise voice and data flows around telephone networks.

Initially, economists were not in the forefront of the use of ABMs, possibly because of thecontinued dominance at the theoretical level of economic models involving rational agentsmaking optimal decisions (rather than just following simple rules as in most ABMs) and at theempirical level of econometric techniques. But as ever increasing computer speeds havemade more sophisticated ABMs possible, and as user-friendly ABM software programs havebegun to appear (notably the NetLogo program used in the present study), so ABMs haveincreasingly begun to be used to model financial markets and simple economic systems. Insuch models, agents can be individuals, households, companies, governments or other typesof institution (e.g. central banks or regulators).

Housing is a particularly interesting area to which to apply ABM techniques5

given that:

location is critical to house prices at a micro-level, but conventional econometric housingmodels have no spatial dimension, whereas this is a key feature of ABMs;

estate agents play an important intermediary role in setting house prices, which is againrelatively easy to include in ABMs but is not taken into account in conventional economicmodels; and

econometric models have often struggled to explain fully the extent of the variation inhouse price to earnings ratios over time, which suggests that it is worth looking at analternative ABM approach to see if this adds any insight.

We are not suggesting that ABMs can replace traditional econometric models of housingmarkets, particularly in relation to quantitative forecasting. But we believe that they cancomplement these techniques, particularly in improving qualitative understanding of howhousing markets work and the factors that drive market dynamics.

5Past examples of related research include Otter et al (2001) and Filatova et al (2007), although the

approach of these papers is significantly different to that adopted here and they focus more on land use

than the determination of house prices and transaction levels.


2. Key features of our agent-based housing model

Our main objective in this research was to see if we could replicate key features of real worldhousing market behaviour using a simple stylised agent-based model. The technical details ofthe model are described in the Annex, which includes a screenshot of the model display.

The model presents results for a small residential ‘town’ with 2,500 land plots arranged in a50 x 50 grid. Some plots are initially empty (green spaces) while others have houses on them,the majority of which are occupied. Initially, house prices and the incomes of the householdsliving in them are randomly distributed across the grid. There are six estate agents (‘realtors’)positioned in a roughly circular pattern around the grid, some of which have overlappingcatchment areas and so compete for business from home sellers.

Homeowners seek to move either when forced to exit the area (e.g. due to death or a jobrelocation), or when their mortgages become too expensive for their income, when they try totrade down, or when their incomes rise to the point where they can comfortably afford a moreexpensive house. Having decided to sell, they approach one or more nearby estate agents forvaluations, which are based on the estate agent’s experience of recent price levels in thatlocality. The seller puts the house on the market at the highest valuation initially but reducesprice later if it does not sell.

Buyers are either people wanting to trade up or down or new entrants to the area. They lookfor a house that best fits their income level and make an offer. But offers only go through ifchains do not break down, just as in real life. The model works out which chains of offersremain intact and these people then move. Other offers fail as chains collapse. New entrantsbecome discouraged and leave the area after a certain period if they cannot find a propertythat matches their income.

House purchases are funded by mortgages subject to maximum loan-to-value ratios. Wherethe latter is set below 100%, buyers must pay deposits either from their savings (set as apercentage of incomes initially) or from net equity released from the sale of their existinghouses.

The model therefore captures many of the key features of the actual housing market,particularly in terms of the role of estate agents as market makers with better knowledge oflocal price histories than house buyers and sellers. It allows for entry and exit from an areaand also for some empty plots of land where new housebuilding can occur. There is a widerange of variables whose assumed values the user can change by adjusting ‘sliders’ (e.g.mortgage interest rates, maximum loan-to-value ratios, scale of income shocks, rate of entryand exit, rate of new housebuilding, length of search periods before buyers becomediscouraged etc).

The model is therefore very flexible in allowing the user to adjust initial conditions and keyassumptions to explore how these influence the dynamic behaviour of house prices (inabsolute terms and relative to income levels), the number of house sales, the number ofpeople seeking homes but unable to find them, the number of unsold houses on the marketand other variables of interest. The model can be run over hundreds of periods, each of whichmight be interpreted as representing around 2-3 months in real time.


3. Behaviour patterns of baseline version of the model

Figure 1 shows the evolution of the average house price to earnings ratio over time in thebaseline version of the model, while Figure 2 shows the volume of housing transactions in thiscase. Key assumptions in this baseline case include:

mortgage interest rates of 7% (broadly consistent with actual levels at the time thebaseline model runs were carried out in September 2008);

a maximum loan-to-value ratio of 80% (broadly reflecting recent market conditions);

new entrants to the town have the same average incomes as existing residents; and

new housebuilding of 0.33% of the existing housing stock in each period.

The implications of varying these and other assumptions are considered in Section 4 below.

Figure 1: Average house price to earnings ratio in the baseline case

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Figure 2: Number of transactions in the baseline case

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in the baseline case, Figure 1 shows that the house price to income ratio is initiallysomewhat above its long-run sustainable level, so transactions volumes are relatively lowat first; as sellers find they cannot find buyers, however, they reduce their asking pricesand transaction volumes then pick up (see Figure 2); and


after around 100 periods the model settles down into a long-run equilibrium with broadlystable house price to income ratios (of around 3-3.5 in this baseline case) andtransactions volumes; for sensitivity testing, we therefore generally allow the model to runfor 100 periods or more before applying shocks to parameter values; and

even once the model has settled into its long-term stable state, however, there is stillquite a lot of short-term ‘noise’ in the model, particularly around transaction volumes butalso to a lesser degree around house price to income ratios; this feature may help toexplain why short-term house price forecasting is so difficult in practice.

We can see from Figure 3 below that there is a tendency for the number of people looking fora house but unable to find one to rise sharply initially in this baseline case, far exceeding thenumber of empty homes for sale. But as some of those unable to find a home becomediscouraged and move out of the area, so prices adjust down relative to incomes over timeand eventually come broadly back into line with the number of empty houses for sale

6. The

model is therefore not characterised by full market-clearing due to a mis-match between theprices of some houses for sale and what some buyers can afford. Furthermore, sincetransactions can only be completed if they form part of an unbroken chain, there will alwaysbe (as in the real world) some chains that break down leading to unsatisfied buyers andsellers in any given period.

Figure 3: Unsuccessful home-seekers and empty houses in the baseline case

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Another interesting feature of the baseline model can be seen by looking at the relationshipbetween average asking prices and average sale prices. We find that asking prices aregenerally higher, but the gap fluctuates considerably in the early periods before again settlingdown to a stable level. In general, when asking prices are too high few sales occur due toaffordability constraints and asking prices then adjust back down. This is as you would expectand confirms that the price-setting mechanisms in the model are working in a sensiblemanner, but with some adjustment time lags.

Finally, we can note that, when run over long periods of time, the model shows a tendency forclusters of relatively high price and low price areas to arise (see the clusters of red in theright hand panel of Figure 4 below, which represent relatively highly-priced houses). This isperhaps surprising given that the initial distribution of house prices is random (see left-handpanel in Figure 4) and there is no obvious reason for some areas to be more attractive thanothers in our model (e.g. we have not introduced assumptions that areas differ according tofactors such as the quality of schools or access to transport links that may drive house price

6In practice, housebuilding might also adjust down, but this is assumed to be exogenous and so does

not happen in this version of the model.


variations by location in reality). It seems that when a particular locality happens by chance tofind itself with a cluster of relatively high or low house prices this may become self-reinforcingsince valuations of houses are, both in our model and in reality, influenced by the valuationsof neighbouring houses.

Figure 4: Emergent Neighbourhoods

Random at time 0 At time 1150Random at time 0 At time 1150

Note: Yellow dots represent the location of estate agents, with the yellow circles showing their

respective territories (see Annex for more details). Red areas indicate house price ‘hot spots’, while blue

areas indicate relatively low house prices (white or pink areas indicate intermediate relative price levels)

This is the kind of result that is quite typical of agent-based models, with emergent macropatterns that are not obvious from the rules of behaviour being followed by individual agents.Such clusters do take a long time to emerge in the model but, once established, show astrong tendency to persist.


4. Sensitivity tests

In the baseline case, our model therefore appears to settle into a relatively stable state afteran initial period of adjustment. To explore the properties of the model further, we have runseveral sensitivity tests on key assumptions relating to interest rates, maximum loan-to-valueratios, entry and exit rates, income levels of new entrants relative to incumbents, the rate ofnew housebuilding and stamp duty.

The first sensitivity test relates to a mortgage interest rate rise from 7% in our baseline caseto 10%. In general, this pushes house prices down due to reduced affordability as you wouldexpect (and vice versa for interest rate cuts). However, as illustrated in Figure 5 below, theimpact of the interest rate rise depends to a significant degree on the maximum loan-to-value ratio assumed in the model. While some such link would be expected, since smallermortgages will mean less exposure to mortgage interest rates, the difference in results in thetwo cases is very striking. The intuition seems to be that a 100% loan-to-value ratio makes itmuch easier for new entrants with limited savings to get into the housing market, so that theaffordability of mortgage interest payments becomes the key driver of house prices. If interestrates rise, this therefore has a large adverse effect on affordability and so on house prices(both in absolute terms and relative to incomes) as we can see from the sharp drop in theupper line in Figure 5 below after the shock (which occurs at period 200, as indicated by thedotted line in the chart).

Figure 5: House price to earnings ratio in response to an interest rate increase

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In contrast in the baseline case with an 80% maximum loan-to-value, new entrants to themarket are mostly constrained by their ability to find a deposit of at least 20% and onlysecondarily by their ability to afford interest repayments. Interest rate rises do still have somedownward influence on house prices, but it is much less marked in this case as the lower linein Figure 5 shows.

To some degree, these results reflect the fact that we assume a relatively high rate of newentry to the market combined with limited initial savings (only 50% of incomes). However, it isnonetheless interesting how the price and availability of mortgage credit are both potentiallyimportant for house prices, while also interacting in significant ways in the model. In thecontext of the current credit crisis, we might interpret the model results as suggesting that:

credit availability as represented by the maximum loan-to-value ratio does mattersignificantly for the house price to earnings ratio; and

if, as has happened during 2008, maximum loan-to-value ratios are reduced from100% to, say, around 80% then this will not only reduce house prices significantly butmay also reduce the significance of mortgage interest rate cuts in potentially revivingthe market – put simply, if first-time buyers (and other households with limited


savings) cannot afford a deposit, then the mortgage interest rate does not mattermuch to them.

The behaviour of the model is also sensitive to assumed entry and exit rates for households.Again, results are intuitively plausible with higher entry pushing up prices and vice versa. Atemporary rise in the number of new entrants produces an immediate increase in averagehouse prices, which is then slowly reduced as more houses come onto the market (see thepeak in house prices in the shaded area of Figure 6 when the temporary shock occurs).

Figure 6: Response of average house prices to a demand shock (temporary surge ofnew entrants)

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We also looked at the impact of new entrants with significantly different income levels toincumbents. We found, for example, that if there is a ‘yuppie invasion’ of newcomers withincomes twice the prevailing median level for existing residents then this drives up houseprices sharply (Figure 7) to restore price to earnings ratios to close to initial levels in the longterm, but with the lower income incumbents being pushed out of the market as a result.Conversely, if inward migrants have significantly lower than average incomes, then prices fallaccordingly and the higher income incumbents eventually move out. Both these effects arequalitatively similar to actual processes observed of areas moving up or down market overtime due to inward migration.

Figure 7: Response of house prices to an inflow of richer entrants (‘yuppie invasion’)

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We also looked at the effect of increasing the rate of new housebuilding, which had someimpact in dampening price levels but not as much as might have been expected. To somedegree, this may just reflect the limitations of the current model in treating new housebuilding


as an exogenous variable, rather than one that reacts to price signals in particular locations.One conclusion that may be more robust, however, is the finding from the model thatincreasing the housebuilding rate only has an impact on house prices in the short to mediumterm. Once all the green spaces in the town grid had been filled up with new houses

7, we

found that prices rose back to previous levels as dictated by model assumptions on incomelevels, mortgage interest rates and maximum loan-to-value ratios.

Finally, we also incorporated an option into the model to introduce stamp duty. However, thisdid not change the key results of the model (e.g. house price to earnings ratios or transactionlevels) in a significant manner. If, for example, stamp duty is set at 1% rather than zero thenthe impact on the average house price is barely noticeable on the charts from the model andis effectively lost in the short-term noise seen in house prices. The apparent corollary wouldbe that the temporary holiday on the 1% stamp duty rate for houses between £125,000 and£175,000 that was announced in early September seems unlikely to have more than amarginal impact on UK house prices compared with other market drivers like actual andexpected household income levels, mortgage interest rates and credit availability.

7In practice, this problem might be circumvented in part by building vertically to economise on land use,

which is not allowed for in our model. However, the experience of the tower blocks of the 1960s shows

that this strategy could have other drawbacks.


5. Conclusions and areas for further research

The aim of this research was to investigate the complicated interactions that characterise theUK housing market. We developed an agent-based model that behaves credibly in terms ofthe reaction of house prices and transaction volumes to shocks such as interest rate changes,shifts in maximum loan-to-value ratios and inward migration changes.

A particularly notable result in the context of recent UK economic and housing marketdevelopments is the way in which interest rate cuts may be less effective in boosting houseprices and transactions volumes in conditions where credit availability is seriously constrainedfor first time buyers and other potential homebuyers. The model also shows a tendency forclusters of high and low price houses to emerge over time in a self-reinforcing manner.

For this initial exercise it was desirable for the model to be as simple as possible, while stillshowing the required emergent behaviour. There are a number of features of real housingmarkets that could be covered in future research using an extended version of the modelincluding, for example:;

a rental sector; and

housebuilding that responds to demand, but with a lag for construction time.

It would also be desirable to reproduce a real location in order to validate the model and toaccount for spatial effects such as transport time to urban centres and key employmentlocations, and proximity to (good quality) schools and other local amenities. Nevertheless, wehave demonstrated that agent-based modelling of a housing market with credible qualitativebehaviour is both feasible and potentially useful in better understanding the dynamics of thesemarkets in response to economic and financial shocks such as the credit crunch.


Annex: detailed model specification and references

Below we describe the key features of the model. Names in bold refer to parameters that canbe varied by the model user.

1. Grid

There is a ‘town’ grid of 50x50 plots of land, of which some proportion (Density = say, 70%)will have houses on them and (1-Density) will be non-housing (e.g. parks and fields).

Of the houses, some proportion (InitialVacancyRate = say, 5%) are initially vacant andavailable to buy (at prices set by the highest valuation of the realtors covering the relevantarea as explained below). The values of the houses are initially distributed randomly acrossthe grid (although the model allows for other options if desired). Houses also have a qualityindex, set at the time they are constructed, which is the ratio of the average of the prices ofother houses in the locality to this house’s sale price. In this initial model, households haveonly one member for simplicity (including households of different sizes and allowing forhousehold size variations over time might be a useful future extension of the model).

The screenshot below shows how the model looks to the user during a run. The sliders on theleft of the grid are parameters whose value can be changed by the model user (e.g. interestrates, income shocks, entry and exit rates, housebuilding rates etc). The charts on the righthand side show how key variables (e.g. house prices, house price to income ratios,transaction volumes etc) evolve over time as the model is run.

2. Sellers

Each period a certain proportion (ExitRate) of homeowners exit the ‘town’ and seek to sell atthe price set by the realtor as described below. If they cannot sell in the current period, theirhouse remains empty and on the market.


Each homeowner initially has an income selected at random from a Gamma distribution (withparameters 1.3 and 5 x 10

-5multiplied by the set level of MeanIncome) and a mortgage of

value equal to the ratio of Affordability to the InterestRate multiplied by the homeowner’sincome. We assume here for simplicity that house purchases are financed using a repaymentmortgage of fixed duration (e.g. 25 years in our baseline case, although this can be varied inthe model). Borrowers have to find a deposit from their own resources in addition to themortgage. The amount of deposit required is determined by the MaxLoanToValue ratio.

Each period a set proportion of homeowners face positive or negative income shocks (+/-20%). These shocks permanently raise or lower incomes (subject to any further shocks).Homeowners facing negative income shocks trade down when mortgage interest becomesgreater than twice the Affordability ratio (which is set at 25% in the base case run), whilethose experiencing positive income shocks trade up when mortgage interest becomes lessthan half of this ratio.

When they decide to trade, sellers contact all realtors in the area covering their home and askfor valuations. They select the highest valuation, which becomes the ‘for sale’ price.

3. Estate agents

There are 3 designated areas of the town, each with a centre and with overlapping radiusesof coverage together encompassing most of the town. Estate agents (referred to in the modelas ‘realtors’) are located in the centre of each area, two to an area, to represent clustering.Most houses will therefore be covered by at least two realtors. Realtors have a radius ofcoverage given by RealtorTerritory. Houses not in any realtor’s territory take their valuationsfrom the nearest realtor.

Realtors know the prices of all houses they have recently sold. At the beginning of thesimulation run, the value of each house is lodged with one local realtor, to give realtors aninitial starting point for their valuations.

When asked for a valuation after the first period, the realtors use the median price of housesthat they have sold in the last RealtorMemory periods that are within a certain radius of thehouse for sale (the Locality) multiplied by the house’s quality index. If a realtor has no salesin the locality, it uses the median price of all sales in the Locality (whenever they were made)or if there were no sales, the average price of all houses in its territory. The valuation isboosted by the RealtorOptimism factor, which allows for realtors hoping that they can sell formore than the going rate.

If a house fails to sell during a period, the selling price is reduced by PriceDropRate per centand continues to be on the market for subsequent periods until it is sold.

4. Buyers

Each period there are new entrants to the town equal to a certain proportion (EntryRate) ofthe existing population of homeowners.

The new entrants and non-exiting sellers search randomly across the whole town for a setnumber of properties that they can afford (i.e, where the mortgage payments are no morethan their income * the Affordability ratio and where they have sufficient deposit to hand).They can also put any capital receipts from previous house sales towards the purchase price.They take off their list of potential properties any for which other buyers have already madean offer. They then choose the one property from the remaining set that comes closest totheir maximum affordable price, and make an offer at the price set by the seller. The firstbuyer to make an offer on a property has their offer accepted.

If an entrant has failed to purchase a house for a certain number of periods(MaxHomelessPeriod) after entry, he or she then exits the town.


5. Transactions

An offer only turns into a successful sale if the house being bought is either already empty orthe seller succeeds in moving to another house that they have purchased. Hence,transactions can fail if the chain collapses, just as in real world housing markets.

We start with the exiters moving out of their houses and then assume the potential buyer (ifany) who made a successful offer for this houses move in. This buyer’s house is then movedinto by the person making the successful offer for that and so on down the chain. Once allpossible transactions are complete, the next period starts.

When a house is sold, the seller gets the sale price and immediately uses as much of this asnecessary to pay off any remaining mortgage. If positive equity is left after paying off themortgage, this can be used as partial or full payment for the house that the seller is movinginto. If the price is insufficient to pay off the mortgage (i.e. negative equity), then the sale doesnot go through unless the seller has sufficient savings to pay off this negative equity.

The realtor concerned records details of successful sales and uses these records whenvaluing houses within the same Locality in the future.

If an offer fails to go through in one period, it immediately lapses.

6. New build and demolition

At each time step, new houses are added to the town at random empty locations, at a rate ofHouseConstructionRate per cent of the existing housing stock, unless there are no emptyplots. A house has a lifetime set at the time of its construction. At the end of its life, it isdemolished and the plot becomes vacant again and available for house building. A house isalso demolished if its sale price falls below one tenth of the median price of houses (which istaken as an indication it has become derelict). If there is someone living there, they attempt tobuy another house, but if they have not succeeded after MaxHomelessPeriod then they exitthe town.

7. Macroeconomic variables

As well as the mortgage InterestRate, a rate for income Inflation can be set. The interestrate may be varied over time (following a sine wave) using the CycleStrength indicator.

8. Model display

Houses are assigned a colour each period taken from one of ten shades from blue (lowest) tored (highest) according to their price. Red areas therefore indicate house price ‘hot spots’,while blue areas indicate low house price areas.

The model display includes charts showing how a range of key variables evolve over timewhen the model is run:

- The total number of houses, the number of empty houses and the number demolished ineach time period- The number of people without a house who are seeking one and the number with negativeequity- The total number of people in the town and the number trading up or down due to incomeshocks- Median house prices and the median house price to income ratio- Measures of income and house price inequality (e.g. Gini coefficients)- Transaction volumes- Number of empty homes and of people seeking a home who have not yet found one


For the current time period, histograms for distribution of incomes and house prices are alsoshown, as well as the distribution of capital accumulated by owners selling houses.

References

Filatova, T., van der Veen, A. and Parker, D. C. (2007), ‘Modelling of a residential land marketwith a spatially explicit agent-based land market model (ALMA)’, 2nd Workshop of MarketDynamics SIG, Groningen, Netherlands.

PricewaterhouseCoopers (2007), ‘Outlook for the UK Housing Market’, UK Economic Outlook,November 2007. http://www.pwc.co.uk/pdf/uk_economic_outlook_sec4_nov07.pdf.

Otter, Henriette S., van der Veen, A. and de Vriend, H. J. (2001), ‘ABLOoM: Locationbehaviour, spatial patterns, and agent-based modelling’, J. of Artificial Societies and SocialSimulation 4 (4) 2. http://jasss.soc.surrey.ac.uk/4/4/2.html.

Wilensky, U. (1999), NetLogo, Center for Connected Learning and Computer-BasedModelling, Northwestern University. Evanston, IL.http://ccl.northwestern.edu/netlogo/.

http://ccl.northwestern.edu/netlogo/


About PricewaterhouseCoopers

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About the authors

This report was written by John Hawksworth and Paul Swinney from the Economics practiceat PricewaterhouseCoopers LLP, together with Professor Nigel Gilbert. Helpful commentswere provided on an earlier draft by Tim Ogier.

Nigel Gilbert is Professor of Sociology at the University of Surrey. He is Director of the Centrefor Research in Social Simulation (CRESS) and the editor of the Journal of Artificial Societiesand Social Simulation. He has written or edited several books on research methods, includingAgent-Based Modelling (Sage Publications, 2008) and Simulation for the Social Scientist (withKlaus G. Troitzsch, Open University Press, 2

ndedition, 2005). For more details of his work in

this field see: http://cress.soc.surrey.ac.uk/

Economics

In addition to model-based analysis of the kind contained in this report, our Economicspractice provides a wide range of services covering competition and regulation issues,litigation support, bids and business cases, public policy and project appraisals, financialeconomics, brand economics, the economics of sustainability and business forecasting. Formore details about these economics services, please visit our website(www.pwc.co.uk/economics) or contact:

Tim OgierPartner, Economics+44 (0)20 7804 [email protected]

Thomas HoehnPartner, Economics+44 (0)20 7804 [email protected]

John HawksworthHead of Macroeconomics+44 (0)20 7213 [email protected]

© 2008 PricewaterhouseCoopers LLP. All rights reserved. “PricewaterhouseCoopers” refers toPricewaterhouseCoopers LLP (a limited liability partnership incorporated in England).PricewaterhouseCoopers LLP is a member firm of PricewaterhouseCoopers International Limited.

This publication (and any extract from it) must not be copied, redistributed or placed on any websitewithout PricewaterhouseCoopers’ prior written consent.

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