An Agent-Based Market Analysis of Urban Housing Balance in The Netherlands

Abstract

The Dutch housing market comprises three sectors: social-rented, private-rented, and owner-occupied. The contemporary market is marked by a shortage of supply and a large subsidised social sector. Waiting lists for social housing are growing, whereas households with incomes above the limit do not or cannot leave the social sector. Government policy and market regulations change frequently, not least for political reasons. In view of commonly recognised problems in the housing market, this article considers the ‘internal demand’ of those households that are dissatisfied with their current residence. We examine the effects of regulatory policy by means of an exploratory agent-based simulation. The results provide perspectives on how internal demand is impacted by regulations in a housing market that is suffering from a shortage, and allow decision makers to weigh the pros and cons of policy measures.

1. Introduction

The Dutch residential market is experiencing a profound housing shortage at the time of writing—an imbalance which is expected to grow in the medium term. The market comprises three sectors: social-rented (managed directly or indirectly by municipal governments), private-rented (regulated by a combination of municipal and national government), and owner-occupied (affected by the mortgage market) [1].

This article studies holistically the Dutch housing market and its tri-sector peculiarities. In particular, we examine the effects of government policy by means of an exploratory, agent-based simulation. The goal is to provide a path to greater transparency into the pros and cons of current and contemplated policy measures.

Among the contemporary problematic issues is the difficulty faced by younger people in entering the housing market. Regulations for the social housing sector and for mortgages have resulted in a situation where first-time home buyers (‘starters’) with a middle income in the market are both ineligible for social housing and unable to purchase a property [2]. Combined with the limited supply in private renting, this situation leaves a starter with very few options.

Starters who are eligible for social housing experience that the social-rented market has growing waiting lists in every major urban area [3]. We use the term external demand to refer to those wishing to enter the housing market, notably starters. On the other hand, occupying social housing are families with children living in one-bedroom flats, some waiting for their turn for a larger houses; others who are affected are who had their turn but are now ineligible for larger social housing because they earn above the maximum income to qualify, but who are also unable to afford to rent privately or to purchase a property [4]. We use the term internal demand to refer to those who have a home currently but are dissatisfied with it. On the other hand, at the same time, there are ‘empty nesters’—parents whose children have moved out, who keep living in social houses that are big enough to support a family with children [5].

Internal demand is of particular interest because it reveals a sort of inefficiency in the housing market, were citizens’ satisfaction could be increased without the need to build more houses. This is especially so as the speed at which houses can be built is limited, and house building is currently an environmental, economic, and social justice question in The Netherlands and other (European) countries. There are important political ramifications [6]. Moreover, internal demand is intertwined with contemporary questions about public housing policy, intergenerational differences, the ageing population, housing for refugees and asylum seekers, and equity [7].

The shortage of supply causes imbalance: some households will not have a home to own or will pay more for the few available dwellings than they would otherwise; some households under-pay and others over-pay; some households lack space while others have space to spare. The specific question we investigate is the following: How is internal demand impacted by regulations in a housing market that is suffering from a shortage? This question gains importance because of contemporary economic, social, and political debates in The Netherlands.

We address this question by developing an agent-based model (ABM) of the Dutch housing market—in particular, the city of Amsterdam. ABM is an appealing investigative methodology as it allows one to explore and estimate the effect of policy changes [8]. The simulation model intends to achieve three purposes: 1. Achieve a conceptual contrast with economical models through the use of a different modelling technique. 2. Investigate the effects of regulations on specific household groups. 3. Provide a flexible approach in which policy changes and new policies can be easily studied. Our modelling methodology emphasises a descriptive and data-initialised model, capturing as many of the realistic processes of the contemporary housing market as possible. This paper thus provides an ABM of the contemporary Dutch residential housing market, including the significant social housing sector.

Results from the simulation indicate that the following topics are interesting for further exploration: policy levers around tenant selection in the social sector, single versus double waiting time accumulation, the income limit, and demand restraint. Further, we identify the opportunity for more narrowly scoped ABMs to study specific policy questions.

The remainder of the article is structured as follows. Section 2 introduces the market to be studied. Section 3 provides a review of related work in light of the chosen methodology. Section 4 presents the agent-based model. Section 5 reports simulation results from the ABM on the question of interest. Section 6 concludes with a discussion of limitations and future work.

The subsequent appendices provide details about the market under study (Appendix A), full details of the model (Appendix B), and further experimental results (Appendix C).

2. Background and Context

This section provides the context of the Dutch housing market, together with an analysis from the academic literature and popular media addressing apparent problems. The following Section 3 will survey the relevant scholarly literature.

Since legislation and the market situation changes frequently—especially compared to the frequency at which household occupants move—we take January 2021 as our reference date. We use the term ‘house’ to refer to any of the stock of residential housing—whether this is a house, a flat, or a studio.

As introduced above, the market comprises three sectors: social-rented, private-rented, and owner-occupied. Under Dutch law, the social sector consists of all houses rented out at a price under the ‘liberalisation’ limit. Conversely, the private sector contains all houses rented out above the liberalisation limit. The owner-occupied sector consists of all houses that are occupied by the owner of the house. From 2013 to 2022, open market houses were a bull market, marked over-pricing occurring in 2020–2021. The bull market was finally tempered by rising interest rates in the second half of 2022.

We briefly describe each of the three sectors, reserving additional details to Appendix A. First, the social sector consist of all houses that, at the start of their contracts, were rented out under the liberalisation limit (set at around EUR 750 monthly), approximately 30% of the total. This is high rate—the highest rate in Europe—means that the social sector must be included in any model. Most of the social sector is organised by housing corporations. The goal of the social sector is to house the lowest-income households—hence the liberalisation limit. Rents in the social sector are bound by a ceiling depending on the quality of a house. The ‘Huurcommissie’ calculates a score using various properties of a house, and relates every score to a maximum rent [9]. Whereas the other sectors use a free market to match renters and landlords or buyers and sellers, the social sector generally uses a regulated, regionally centralised system to match houses and households.

Second, the housing that is rented privately comprises approximately 15% of the total [10]. While the private sector consists only of houses rented out above the liberalisation limit, not every house is allowed to be rented out at such a price. Similarly to how the Huurcommissie decides the maximum price of houses in the social sector, in limited cases, it can also enforce this for privately rented houses.

Third, the final of the three sectors, the owner-occupied sector, comprises approximately 55% of the total. The houses in the this sector can easily transition to a rental market when the owner decides to rent out the house. Similarly, a house in the rental sector can be sold to the occupant or a new owner who will occupy the house to move to this sector. Some municipal governments—especially in larger cities—have started to require owners to occupy their homes to prevent investors from buying new houses and renting them out [11].

The Dutch housing market described here suffers from contemporary problems. We give three examples of problems commonly perceived in the market. First, for starters with a middle income, the regulations for the social rental housing sector and for mortgages have resulted in a situation where these households are both ineligible for social housing and unable to purchase a property [2]. Combined with the limited supply in the private sector, this situation leaves a starter with very few options. In this paper, problems are approached with the egalitarian goal of satisfying as many households as possible in the existing system.

Second, satisfying all households’ preferences is not possible, due to scarcity of supply, but also due to opposing preferences. We describe the problems arising from two such cases. Firstly, there are those who live in too small a home and those living in a larger home than they need. Secondly, there are those who pay too much rent and those who pay too little rent.

For the first case, the ‘opposition’ is between expanding households where children are born, and households where all children have left (‘Lege nesters’, empty nesters) [12]. The expanding families are searching for a larger home, while the empty nesters occupy these larger homes. For the second case, the ‘opposition’ is between households that have increased their income but stay in the social sector, ‘Goedkope Scheefwoners’ (cheap-skewed renters), and households that are—partly due to a limited capacity in the social sector—paying too much rent ‘Dure Scheefwoners’ (expensive-skewed renters) [13]. The opposition is in the fact that the expensive-skewed renters could potentially have entered the social sector if the cheap-skewed renters had left the social sector.

Third, [14] reviews the government policy in the Dutch housing market and concludes that the current policy creates social inequality. Further, the author concludes: “Many citizens, and more specifically low-middle income groups and young households, do not understand the current policy choices which leads to an increasing distrust in government and to instability in society”. The social inequity is found to be increasing: [10] studies the rise in buy-to-let and its affect on—in particular—starters in the housing market.

3. Literature Review

Having introduced the market to be studied, we now survey the relevant literature. This section reviews previous work related to modelling the housing market, focusing on the systematic working of housing markets and the behaviour of actors that interact in the market. The broad variety of approaches in the literature include case studies [15], policy analysis [8], and agent-based models [16]. The majority of the literature considers the open market of private-rented and owner-occupied sectors. For succinctness, we refer to just ‘buyers’ and ‘sellers’, also including renters and landlords.

3.1. Considerations in Housing Market Modelling

We begin with buyer and seller searching strategies. The first step for a transaction in the housing market is that a buyer or seller looks for a partner(s) to negotiate with, i.e., a seller or buyer, respectively. The searching strategy for buyers is defined by a buyer reaching out to sellers. For example, a buyer anticipating more favourable market conditions might delay their search. The searching strategy for sellers can include when to sell, but also how long a seller waits for higher bids or at what price a seller advertises. Research on these strategies considers both a theoretical optimal strategy and real strategies applied in the housing market.

The authors of [17] compare two selling strategies (the stopping and number rule) under different market conditions using a theoretical simulation. They conclude that neither strategy dominates the other and that, rather than choosing one over the other, an adapting strategy would be most effective. The authors of [18] create a simulation to experiment with varying combinations of buyer and seller strategies. Their work highlights the importance of the interaction between different agent strategies.

Intertwined with searching strategies is the ‘system’ by which buyers and sellers find each other, which can be a deciding factor in the market. The authors of [19] provide an overview of matching models used to model this process for housing markets. The system is dependent on the spread of information and the speed of processes such as negotiation or requesting a mortgage. The authors of [19] also connect the matching progress to the role of the listing price, i.e., the price at which the seller places the property on the market.

The strategy of a seller is also dependent on the role of the seller. The authors of [20] considered the effects of the time on the market upon the selling behaviours of both private sellers and real estate agents. This was carried out by applying an estimation model on a dataset of a popular real estate marketing platform in Russia. They concluded that real estate agents are more impatient sellers than private sellers.

The listing price is the amount of money a home is advertised at—the asking price to purchase or rent the house. The authors of [21] compare two seller strategies that use the listing price differently. The listing price is the amount of money a home is advertised with. The first uses the listing price as a ceiling, while the other uses the ‘best-offer-over’ method, where the listing price functions more as a signalling device or a floor. They analysed 50,000 transactions in Rotterdam, The Netherlands, and found no clear difference in transaction price between the strategies.

The different usage of listing prices is a specific point of interest in the housing market, as the listing price can have very different meanings in different circumstances [19]. The listing price can communicate the following messages:

• I am willing to sell my home for at least X.
• I am willing to sell my home for more than X.
• I am willing to sell my home for X, but am willing to lower my price.

The listing price is especially interesting because the changing role is not explicit, but rather a gradually changing use of the same value.

The authors of [22] recognised a different role of the listing price during booms or busts and try to explain this behaviour with an econometric model. They conclude with the conjecture that a boom causes a change in the methods sellers use to price their houses which lasts beyond the initial boom. Earlier research of [23] and [24] conclude that the way the listing price changes the expected time before a sale depends on the market conditions.

Not only the market conditions change the role of the listing price. The authors of [15] observed a difference between the theoretically optimal and actual selling strategy for setting listing prices in Norway. The authors showed that the actual selling strategy was beneficial to estate agents, to the detriment of the seller they represent.

A third aspect of the housing market is the decisions of households. In particular, the amount of buyers and sellers on the market is dependent on the decision of households to sell or buy. Modelling this decision process can give more insight into how households react to changing market conditions.

The authors of [25,26] created agent-based models that consider the decision-making process of households in greater detail. The life events of a households provide a change in needs, while the household’s perception of the market informs them whether it is worth searching for alternative housing.

An interesting modelling choice is made by [27], who models households with an cultural component. This cultural component informs where a household wants to live. If there is no location that satisfies the cultural need of a household, they either leave the city or change their own cultural component depending on their economical situation. We note the idea that the state of the housing market can impose changes on a household.

After a household has decided to move and found a seller from which to buy a home, the buyer and seller proceed to negotiate a final transaction price. To understand this negotiation process, Ref. [28] investigated the influence of various factors on the outcome of the negotiation process for historical transactions. The authors found no evidence that first-time buyers have worse bargaining outcomes compared to repeat buyers.

The authors of [29] concluded that real estate agents may make agreements between buyers and sellers more difficult instead of easier. They also suggest that the cost of a real estate agent is paid by both buyer and seller and not only by the party making the formal payment. Finally, they highlight that a real estate agent should be considered as a (third) negotiation party, with its own self-interests, rather than part of one side of the negotiation.

3.2. Agent-Based Models for Housing Markets

The majority of research on the housing market is either social–anthropological [30] or economic [31] in nature, and carried out at a macro level. Econometric models analyse the relationships between housing prices and market fundamentals. These models can analyse specific policies, as long as those policies can be described in terms of the economic variables; however, econometric models cannot accommodate individual-level behaviour and results. Because of this, these models struggle to predict emergent patterns caused by policy [16,26,32] (compare the point of [33]).

This paper adopts agent-based modelling [34,35] with the rationale that the ABM methodology allows a focus on the choices of and effect on individual households within the regulations—renters, buyers, and sellers—and the emergent city- and national-level effects. The choice of ABM as a methodology is recommended by [8], who highlight the influence of regulations in both the rental and home-ownership sectors on tenure choice. Additionally, ABM allows one to explore and estimate the effect of policy changes, and the use of ABM allows unexpected interactions between regulations to emerge [36].

We are not the first to recognise ABM as a proven choice for studying housing markets. Existing studies have a wide range of foci—from reproducing historic events [26] to comparing buyer and seller strategies [18]. However, to our knowledge, there are no models which include the Dutch social sector.

An important precedent for ABM is the model of the home-ownership sector in England, UK, presented in [16]. The authors show that a simplified model of the housing market can replicate key behaviours observed in the real market. Their model provides effective ways to model income and home-owner behaviour when income changes. However, from a spatial perspective, Ref. [16] assume that buyers that cannot buy a home leave the local market to some alternative municipality. However, if this alternative does not exist, such as in a scarce market, these buyers would not leave the market and keep providing pressure on the market. The second reason that the model of [16] cannot be used for our research question is that it does not consider the rental sector.

The authors of [37] focused on the choices of individual households. They included renovation and emigration as additional choices for a household. The agents in their model proactively and reactively gather imperfect information about the market and take into account how a residential location affects their (daily) budget.

The authors of [25] created a model that focuses on the decision of households to enter the market if they expect to be able find a better home. The households also take into account the expected sale price. This results in a dynamic model in which households react to the state of the market.

In response to a financial crisis, Ref. [26] created an extensive model of the Washington, D.C., housing market. Their design reproduces historical data based on rich micro datasets; as an example, the number of households is matched to census data. Notably, they model both home-ownership and renting.

The authors of [38] created a model of the Danish housing market and studied the effect of income and interest shocks. The households vary their characteristics mainly with age. Most notably, the households change their preferences with age, but do not explicitly change their needs.

The authors of [18] set up agents with different strategies to research how strategies affect each other. In this model, agents are only a buyer or a seller, not both, and no new agents enter over the simulation time.

The authors of [39] created a model that combines the purchasing, renting, and investing sectors into one model. The first part simulates the demographics and provides triggers for households to look for a different home. The second part models the process of matching between offering agents and the agents that received triggers. While there is both a rental and buying sector, they both use the same system.

The authors of [40] study the effects of government fiscal policy instruments on regulating the housing market by means of a data-driven ABM, presenting a case study of the Korean market.

A number of other works model aspects of the housing market or urban housing development using ABM (e.g., [41]). To our knowledge, none address the case of a Dutch municipality setting with all three of social-rented, private-rented, and owner-occupied dwellings. Section 2 summarised the unique features of this market.

The closest are [42], who look at negotiation in Dutch property purchases using ABM, and [32], who look at the peer-to-peer rental market in Amsterdam, again using ABM.

Our work is different from both of these. The authors of [42] present a short, non-archival paper about bidding strategies. The market considered in that work is simple, and notably does not include social housing, and the simulation briefly reported is highly stylized. That work is focused on buyer’s bidding strategy in the private owner-occupied sector. We focus on the dynamics of the market across all sectors.

The authors of [32] look at the Amsterdam housing market but with a firm emphasis on the ‘Airbnb effect’ and policies to counteract it. They are not interested in the dynamics of the three sectors of the market, they do not consider housing shortages per se, their treatment of the social housing sector is superficial, and their time frame is shorter. By contrast, we do not consider tourists and short-term Airbnb-like rentals. A comparison of our work with that paper is thus not meaningful.

3.3. Simulating Households over Time

The initial population of households for the housing market can be generated with the known data of the current population. However, as simulating the housing market for the purpose of this paper requires a medium–long time span, it becomes necessary to also simulate the future population. In The Netherlands, future households are predicted yearly by the Dutch statistics agency (Centraal Bureau Statistiek, CBS). The CBS method for prediction is in itself a simulation model [43]. The CBS model does not model households but rather people, in terms of their position in a household and ‘Burgerlijke Staat’ as their state.

The possible household positions are the following:

• Child living with parents.
• Single-person household.
• Living with a partner without a child living at home.
• Living with a partner with a child living at home.
• Parent in single-parent household.
• Other members of a private household.
• Member of institutional household.

The ‘Burgerlijke Staat’ can be one of four states: never married, married, widowed, or divorced. (In this system, registered partnership and marriage are treated the same).

To model the state of a person in the next simulation step, transitions between states are utilised. For every possible transition, the frequency is estimated from measured data in combination with assumptions. The frequency is further separated by age, gender, and the current simulation year. The assumption is made that the transitions are only dependent on the factors of age, gender, and the state of a person. Besides the transitions between the different states, births, deaths, and migration are modelled to have persons enter and exit the simulation. Births are based on the female population present in the simulation.

4. Model Design

Having introduced the system to be studied, and having surveyed related work, especially in ABM, in this section, we next describe the methodology and the data collected and overview the ABM constructed. The following section employs the ABM in simulation.

4.1. Methodology

Since the focus of the main research question is on the demand caused by individual households, the methodology is agent-based modelling [34], as indicated in Section 3. This choice is made because, in order to investigate the internal demand in a housing market—caused by the mismatch between a households needs (or wants) and the properties of the house they current inhabit—it is necessary to use a methodology that can model individual households and houses. Further, the methodology needs to be able to differentiate between different motivations for internal demand to give better insight into possible solutions or causes. ABM fills these need through its focus on individual agent behaviour.

Section 2 described the working of the Dutch housing market. We aim to create a descriptive model [44], using the available documents, data sources, and interviews with real estate agents.

Our approach to construct the ABM has two parts. The first part of the modelling process fills in the technical parts of the model, finding out which rules form the systems in the housing market. The second part of the modelling process fills in the data-initialised and social–logical parts of the model.

A challenge is that data about the points of interest in the housing market are often (publicly) unavailable, disconnected, or possibly non-existent. Additionally, the data that do exist is are often private information divided over many parties. Due to these factors, the choice was made to make a model that is restricted by the available data. For this reason, some less central aspects of the system were excluded: see Section 4.2 below, Section 6, and Appendix B.

As we explain below, household agents form the core of the ABM. The model description follows the ODD (overview, design concepts, details) protocol [45]. The model was implemented using NetLogo [46], and is available at DOI doi.org/10.4121/21757244.

We retrieved datasets from the CBS, the municipality of Amsterdam, the Dutch citizen financial advice agency (Nationaal Instituut voor Budgetvoorlichting, Nibud), and Nul20, a platform for information about housing policy and urban development in the Amsterdam metropolitan area. Additional data originally published in ‘Maandstatistiek van de bevolking’ were requested from the CBS and can be found in [47].

For the initialisation of households, the most recent available CBS datasets were used. For the generation of the initial incomes of households, the dataset retrieved from CBS (www.cbs.nl/nl-nl/visualisaties/inkomensverdeling (accessed on 2 September 2021)) was fitted to a Gaussian distribution following [16]. (The choice of a Gaussian distribution for households’ income, though following the literature, is recognised as an approximation. Typically, this distribution is log-normal, except for very high incomes. It would be interesting to see whether the ABM could also incorporate these very high incomes. However, the particular behaviour of such households needs to be taken into account in the model.)The data were separated between households with one or two money-earners. For the transitions of households, data from the five most recent years, for which all points of interest were available, were used. Since there is no centralised public dataset for the supply of houses that includes the desired features, the data for houses were selected to be the most recent data available about the housing supply in Amsterdam (data.amsterdam.nl (accessed on 2 September 2021)). For the calculation of the maximum mortgage, data as per 2021 were retrieved from [48].

Lastly, we retrieved qualitative data from the Dutch central government (Rijksoverheid), ‘Woningnet Regio Amsterdam’ (the central allocation system for the social sector in Metropolitan Amsterdam), and Dutch legal documents. Specific (legal) sources used are reported in [47].

4.2. High-Level Conceptual Design

We built an ABM to capture the salient processes in the Dutch housing system. Thus, the observed system is decomposed into separate components and structured to show the relationship between them. The result of this process is shown in Figure 1.

First, the agents that act in the model are identified. On the one hand there are households, which are groups of people that live together and search for houses collectively. On the other hand, there are the suppliers of houses: the housing corporations, landlords, real estate agents, and owner-occupants looking to sell. These agents can be abstracted to a strategy that is used to sell a particular house; in this way the ‘house’ becomes an agent. This abstraction retains the ability for these groups to use the fact they own a large share of the supply in their strategy.

Households have two interactions. They decide whether they search for a different house when conditions change, and they apply to houses for rent and bid on houses for sale. Houses also have two interactions. They set and advertise a (sale of rent) price, and select a winner when bids or applications have arrived.

Second, the systems representing the environment are considered. Grouped together as ‘Household Progression’ are the systems that represent the change households experience over time. These systems simulate the life of persons through birth, ageing, and death—the financial situation is simulated through income changes and mortgages; the composition of households is simulated through children moving out to create their own households and relationships, which either combines two households who start a relationship or splits a household because a relationship ends.

The other environmental systems are forced migration—simulating migration that forces households to move, such as being evicted—and the system to simulate new houses being built during the simulation.

Third, the systems to initialise the agents and the support processes are added. The ‘House Transfer Protocol’ decides how houses are transferred from (n)one household to another; the ‘Communication Protocols’ ensure agents understand each other’s messages, and that they only have knowledge of information the other agent willingly exposes; and the ‘House Generator’ creates new houses when needed.

Some factors have been considered but intentionally excluded from the model. Firstly, the periodical changes of systems are excluded—most notably, the mortgage calculation and possible mortgage options offered by banks. Their decision-making process is too complex to predict. Secondly, systems related to money are excluded: this comprises savings, interest, houses needing repairs, and eviction. Our research question does not need the prices in the model to representative of the real future, as the goal is to measure motivations; while households are motivated to move by high rents, and in reality savings and eviction are influential, these factors are excluded to reduce complexity. Finally, the model is designed under the assumption that the composition of the housing market does not change (during the simulation), as the focus is not on construction policies. We discuss limitations and extensions of the model at the end of the paper.

A full description of the model in ODD format is provided in Appendix B.

4.3. Verification

We perform a set of actions to check whether the NetLogo software implementation of the ABM design is correctly implemented. First, the NetLogo program has been verified by reviewing the code, varying the parameters, and running the simulation during the implementation process. Second, the program checks for incorrect states or attributes of households multiple times in each simulation step. A check function was introduced that checks whether the state of the household is correct with its attributes and whether all attributes are set to a valid value. The benefit of this function is that every run that it completes has not violated these constraints, even if the code can reach an invalid state in other scenarios. Third, the outputs of the model were reviewed by Dutch real estate agents. It was not the intent that the model mimics historical market developments, or predicts the future, but the professionals agreed that the outputs were reasonable in their opinion.

5. Simulation Results and Discussion

We undertake a set of simulation experiments to explore different settings and simulated policies. The experiments fall under three categories: first those that pertain to policies set by corporations and the government; such policies can be changed by the policy maker relatively easily. Second, experiments exploring the different behaviours of households; such behaviour changes might be hard to incentivise in practice, but simulation can explore the consequences without having to consider how the behaviour could happen. Third, experiments exploring changes in the environment; these changes can only result from a large or time-consuming process, but can be of great importance.

The ABM is run 100 times with a simulated time period of 75 years. As there was no sufficiently detailed national dataset of houses in The Netherlands, and the social market functions differently per region, the model uses Amsterdam as a basis for its default settings.

Table 1. Default values for input variables.

Variable	Value	Remark
seed	0	Setting seed to 0 generates random seeds
plot?	disabled	Disabling plots improves performance
maximum_simultaneous- _reactions_social_market maximum_simultaneous- _reactions_lottery_social_market	8 8	Simulates the 2 reactions per week as 8 reactions per month.
supply_lottery	10%
maximum_income_social- _rental_market	40,024	The maximum income for the social market is set to 40,024 according to current Dutch law [49].
mortgage_length mortgage_type mortgage_interest	360 months annuity 0.0210
population_size	1000	A compromise between population size and simulation length
housing_supply	951
free_housing_supply% private_housing_supply% home_ownership- _housing_supply%	18 51 31	Based on the reported composition for Amsterdam in [50].
Size1/2% Size3% Size4% Size5%	31.29 34.35 23.69 10.67	Calculated using ‘Woningvoorraad naar stadsdelen en aantal kamers per woning, 1 januari 2021’
social_rent_432.51% social_rent_432.51_to_619.01% social_rent_619.01_to_663.40% social_rent_663.40_to_737.14%	21.22 53.37 11.16 14.25	Calculated using ‘Corporatiebezit naar huurklassen en stadsdelen. 1 januari 2020’
house_worth_to_221000 house_worth_221000_to_310000 house_worth_310000_to_385000 house_worth_385000_to_511000 house_worth_511000_plus	12.21 22.18 22.48 22.48 20.65	Calculated using ‘Woning voorrraad naar stadsdelen en waarde van de woning, 1 janurari 2020 (procenten)’
new_houses_monthly new_houses_type	0.84 flat	Follows the plans reported in the construction goal in [51], scaled down with the house supply in the simulation
social_leave old_large_house_leavers spouse_waiting_time building_waiting_time migration migration_type	disabled disabled ‘always’ ‘while_searching’ 0.00 percentage of households	Other values for these variables are used to introduce variations
shocked% shock_size	20% 20%	These values are set according to the defaults in [16], from which the income shock system originates.

summarises all input variables, their default values, and—if applicable—the motivation for the value.

Before discussing the experiments, the default configuration of the simulation is investigated with a sensitivity analysis.

5.1. Sensitivity Analysis

To have a better understanding of the effect of the input variables on the model outcomes, we perform a global sensitivity analysis using the Sobol method [52]. For Sobol, for each input variable of interest, a range of values needs to be provided (see

Table 2. Overview of the input variables analysed; for each value range, a data type is indicated.

Variable	Range	Type
seed	[100,000, 200,000]	Integer
maximum_simultaneous_reactions_social_market	[1, 16]	Integer
maximum_simultaneous_reactions_lottery_social_market	[1, 16]	Integer
supply_lottery	[0, 100]	Float
maximum_income_social_rental_market	[35,000, 45,000]	Float
social_leave	[True, False]	Boolean
old_large_house_leavers	[True, False]	Boolean
spouse_waiting_time	[always, never, divorce]	String
building_waiting_time	[while_searching, always]	String
new_houses_monthly	[0, 2]	Float
housing_sector_combinations	[0, 5150]	Integer
size_combinations	[0, 176,850]	Integer

). For values that require a boolean or string, a uniform distribution is mapped to the possible options.

Sobol assumes independent variables for its analysis, but the input settings for the sizes of houses and the sizes of the three sectors are represented as percentages. These variables need to add up to 100% and thus are dependent variables. Instead, it is possible to represent a set of dependent variables through a single independent value. The ability to see the the impact of each separate variable is lost; instead, only the impact of the set of variables together is known.

Due to the large amount of output variables, the results are summarised in

Table 3. Overview of the output variables measured.

Variable (NoH = Number of Houses)	Major Contributor (ST > 0.4)	Minor Contributor (ST > 0.25)
NoH wanting to move out	new_houses_monthly	housing_sector_combinations
NoH motivated by divorce	housing_sector_combinations	new_houses_monthly
NoH motivated by too small homes	size_combinations	housing_sector_combinations
NoH motivated by social_leave	social_leave x housing_sector_combinations
NoH motivated by old_large_house_leavers	old_large_house_leavers
NoH motivated by high_rent	housing_sector_combinations
Avg. age private sector	old_large_house_leavers
	housing_sector_combinations
Avg. age social sector	housing_sector_combinations
Avg. age owner-occupied sector	housing_sector_combinations
Avg. age homeless	housing_sector_combinations
	new_houses_monthly
Avg. rent private sector	old_large_house_leavers	size_combinations
Avg. mortgage size owner-occupied sector	housing_sector_combinations
Avg. % of income spent in private sector	housing_sector_combinations	old_large_house_leavers
Avg. % of income spent in social sector	housing_sector_combinations
	social_leave
Avg. % of income spent in owner-occupied sector	housing_sector_combinations
Number of Households	seed
	housing_sector_combinations
Avg. waiting time of searching households		old_large_house_leavers
		building_waiting_time
		housing_sector_combinations
Avg. waiting time of successful renters	housing_sector_combinations	new_houses_monthly
Avg. waiting time all households	building_waiting_time
Avg. waiting time low-income households	housing_sector_combinations	building_waiting_time
Highest waiting time	old_large_house_leavers	housing_sector_combinations

; the full results are provided in [47]. Mostly notable is the fact that the distribution of houses across sectors is often the most influential factor. While this is an interesting factor, its dominance makes the analysis of the lesser factors difficult. For the number of households, the interaction of the seed and the division of the market sector is most influential; the importance of the seed suggests that there is no connection between the inputs and the number of households. The large confidence intervals temper strong conclusions from the analysis.

In the measurement for the average waiting times of all households, it is notable that the building_waiting_time input fundamentally changes how waiting time is accrued: this makes other factors less significant relatively easily. For policy changes, we therefore have to consider that it may not be possible to simultaneously—or with the same metrics—evaluate them.

5.2. Experiment 1: Changing Policy

Since regulation and policies are created and used by centralised organisations—principally national and local governments—policies are comparatively easy to change. However, decision makers request insight into the implications of contemplated changes on the housing market and citizens.

Four different policies present in the Dutch housing market are explored: 1. The size of the supply that is handed out using lotteries instead of selection; 2. The option for couples to posses two independent waiting times; 3. The number of reactions each person can use in a week; 4. The maximum income limit in the social sector. For conciseness, additional figures are provided in Appendix C.

5.2.1. Lotteries for Social Housing

In Amsterdam, social sector houses are assigned with two methods: lottery and selection. The selection prioritises the households with the longest waiting time while the lottery randomly selects from all eligible households that applied. As these systems are used side by side in practice, the question of how the simulation changes when a different amount of the supply is dedicated to the lottery is investigated.

For a higher degree of lotteries, Figure 2B shows that the social sector is younger. Conversely, Figure 2A,C shows that the ‘homeless’ and private rental households are older on average. Figure 3A,B show that, with a higher degree of lotteries, households with a lower waiting times are successful, and the average waiting time is higher.

5.2.2. Divorce and Secondary Waiting Times

In the social market in The Netherlands, any person can be signed up twice: one time as registrant and one time as co-registrant. A co-registrant does not build up any time, but it does allow one to search for a home for both the registrant and the co-registrant. This results in a couple having two separate waiting times by both independently signing up and being each others co-registrant, potentially giving an advantage over a single-person household.

The benefit of this system is that, should these partners divorce or split, the partner that was a co-registrant does not have to start building their waiting time from zero. To investigate the potential impact of this benefit for couples, an experiment with alternative systems for the waiting time of the co-registrant is created.

Consider Figure 4. Firstly, one can see the variation effect on households with the motivation ‘relationship ended’ in Figure 4B. If the second waiting time is dedicated to divorce, then the fewest households are searching with this motivation; if the second waiting time is not used, then the most households are in this category. The differences seen in Figure 4A in waiting times are higher for divorce, because the waiting times function differently in each variation—some waiting times are reset less often in the ‘divorce’ variant.

5.2.3. Maximum Number of Reactions

The social market assigns houses using selection rules to assign a house to households appropriately. A limitation to this system, however, is that a house will be assigned only to one of the households that reacted to the house. This means that the household that theoretically would be the best fit for the house might not have reacted to it. Altering the number of maximum reactions a household can make leads to it being more or less likely that the best-fitting household is able to react to the house, changing how efficiently the houses are utilised.

Slight differences are seen in total number of searching households in Figure 5B, where the scenario with 12 monthly reactions is slightly more favourable. It should, however, also be considered that a larger amount of reactions can be impractical due to households not being required to accept a house and needing time to inspect it.

5.2.4. Increased Income Limit for Social Housing

In The Netherlands, households with middle incomes have a hard time purchasing a house; for this problem, increasing the income limit of social housing is proposed as a solution. This experiment changes the income limit to investigate the effects.

Most clear are the results in Figure 6; the group of ‘homeless’ households is slightly younger, while the social sector is slightly older.

5.3. Experiment 2: Changing Behaviour

Having studied policy changes, in the second set of experiments, we study how the simulation outcomes change if behaviour is modelled differently. We look at two concepts: (1) a different way for households to accumulate waiting time; (2) a willingness to help other households. Creating a bottom–up change in behaviour may be more difficult in reality than changing top–down policies, as the choice of every individual household matters. Nevertheless, it is valuable to consider whether the change in behaviour is effective before considering how the behaviour could be changed.

5.3.1. Waiting Time for Social Housing

As a default, the assumption is made that households are always signed up for the social sector, as this is the optimal strategy if the sign-up fee is disregarded. If a household is signed up, then the household passively builds up waiting time, regardless of their circumstance. The only way for the waiting time to be reset is if the waiting time is used, or the registration lapses. In this experiment, we investigated what happens if, instead, households can only build up waiting time while they are actively searching in any market. This prevents households that are currently happy in their home from building up waiting time pre-emptively, and can—to a certain extent—model households in the social sector that do not sign up again after receiving a social house.

Figure 7A shows a clear decrease in the waiting time present in the simulation as the time in which waiting time can be built up is limited. Figure 7B shows that younger households obtain access to the social sector.

5.3.2. Willing Social Market Leavers

In the Dutch housing market, there are two common occurrences which lead to inefficient or unintended usage of houses. First, the cheap-skewed renters, which are households that live in the social sector but now earn above the maximum income to enter the market. They are not part of the target group of social housing, but still use a resource for this group. Secondly, empty nesters, who are parents whose children have moved out but who still inhabit a large house that could house a family instead. These households could be incentivised to search for more fitting homes. In this experiment, we investigated what would happen if all these households would be successfully nudged to start searching.

The first observation, as shown in Figure 8A, is that an increase in rent occurs for both variations where older households try to free family homes. Figure 8B also shows a longer waiting time for households which are able to enter the social sector for these variations. For the variation (true, false)—where only households intentionally leave the social sector—the waiting times in Figure 8B are decreased compared to the baseline.

5.4. Experiment 3: Changing Environment

The final set of experiments study variations in the environment, in order to understand their impacts. The simple migration mechanism is considered first to examine how influential its inclusion can be. Then, different supplies of houses are considered: the sizes of houses and the size of market sectors are varied.

5.4.1. Migration

In this experiment, the impact of migration is tested: households that leave due to, moving out of the city for a new job, for example. We note that migration was previously excluded from the sensitivity analysis due to its large impact on run time.

While motivations to move are decreased by increased migration rates, the total number of searching households increased, as seen in Figure 9. The additional figures in Appendix C show differences in the motivations for agents’ searching, reported in (Figure A7e).

5.4.2. Varying Size Compositions

Recall that the default composition for houses in the system is the composition in Amsterdam (Table 1). As the composition does not change over time, we investigated whether a different composition of houses can decrease the desire to move in the market. In this experiment, the size compositions are altered, as a tuple of percentages (Size 1/2%, Size 3%, Size 4%, Size 5%).

Figure 10 shows that fewer households with larger houses are searching for new homes. The compositions (0, 0, 0, 100) and (10, 20, 30, 40) have similar performances. The full maximum size house composition (0, 0, 0, 100) actually prevents more people from moving out but has no problems regarding the size of houses. In contrast, the (10, 20, 30, 40) composition has fewer problems when relationships end or when people want to move out (compare [53]); but in return, there is a problem with too-small houses. Additionally, Figure 10 shows a much lower private renting ratefor the (0,0,0,100) composition.

5.4.3. Varying Market Compositions

The default composition for houses in the system uses the composition in Amsterdam. As the composition does not change over time, we investigated whether a different composition of houses can decrease the desire to move in the market. In this experiment, the market compositions are altered.

Figure 11A shows that, for both variations with an increased owner-occupied sector, there are more searching households. Figure 11B shows that, for private rentals, a larger private sector (and smaller owner-occupied sector) has the lowest private rental rate. Notably, in the latter sub-figure, one can see an apparent temporal reversal in the role of sector composition. This is interesting for future study.

5.5. Discussion

Summarising this section, the experiments indicate that the ABM is effective in considering the effect of different scenarios on the demand of households. The clearest results are seen in Section 5.2.2—the secondary waiting time is influential in the success of divorcees finding a different home—and in Section 5.3.2, which suggests that empty nesters leaving large homes have a bigger negative effect through an increased demand. This is in comparison with the positive effect they have on utilisation due to families using their large homes. Furthermore, the results on selection versus lottery in Section 5.2.1 are interesting—that lotteries favour starters to the detriment of those families who have been waiting longer for social housing. The results for the income limit for social housing in Section 5.2.4 are also interesting; this adjustment helps older starters and older (non-starter) households, to the detriment of poorer or younger households. Other results have less significant outcomes, in line with the exploratory nature of this work.

5.5.1. Limitations

The significance of the conclusions from the other scenarios is lower, due to the current scale of the simulation. The ABM reported in this paper is detailed, and includes modelling of (medium/long-term) population growth and the addition of new housing stock. Increasing the scale and time span can be achieved by abstracting some market details. Indeed, to further investigate cyclic demand–supply behaviours and long-term consequences, an alternative model design can be considered in which the number of houses is defined in relation to the size of the population as a cyclic function. This would allow for the stronger control of an expected supply of houses over a simulation course.

A second limitation with the implemented model is the disentangling of specific causes of internal demand. Here, there are two points to note. First, because only one motivation can be reported at any given moment, the experiments cannot show that a specific demand has reduced since households may have a different kind of demand preventing the targeted demand from being reported. Second, because the motivations are aggregated, the detail at the household level is lost. This manifests with no measured difference between a small group of households experiencing problems over a long period of time and a large group of households experiencing problems for a short period. To resolve this issue, the temporal extent of motivations also needs to be measured. It may also be useful to expand motivations to measure the reasons households are unable to find a home in addition to why they are unhappy with their current home.

We note that the primary research question is largely unaffected by these points, as the specific cause of demand does not change the total demand. Further, the ABM methodology is successful in flexibly examining policy changes and new policies. Only some policy changes cannot be covered by existing household behaviour, such as the different styles of secondary waiting times allowing for different long-term strategic behaviours. Researching this particular aspect is better served by algorithmic or game-theoretic approaches, which can explore which strategies are effective.

In all three experimental sets, a trend is seen in the number of households—the number of households rapidly increases after roughly 45 years. This coincides with the moment in which the number of houses temporarily exceeds the number of households. The cause of this phenomenon is partly the way in which relationships function. (When relationships are ended, one partner might maintain custody of all children, while the other one becomes independent. The split-off partner might then form a new relationship and choose to have more children in this relationship. Additionally, relationships can form between two households with many children, which might end, leaving another person without children.) An option to mitigate this is to introduce gender as a factor in the analysis; here, the number of children accounted for might depend on how many children a woman has had before. This can contribute to the number of children born independently of a current relationship. We also note that, in the model, the lack of a house does not prevent childbirth; this might not be the case—and could be more restricting—in real life.

Finally in terms of the limitations of the current model, there are two (smaller) design limitations which became apparent during the experimentation. First, the simple market mechanisms for the private rental and owner-occupied sector are not flexible enough to function well during, e.g., an abundance of houses. Second, childbirth is only dependent on the age of the household and number of children currently living at home. When all children are moved out, this can cause children to be born that are not born in reality, especially as the model considers that children look for their own home early in adulthood.

5.5.2. Validation

For the kind of ABM that this paper develops, as [34] points out: “The real outcome of the model is not the experimental results so much as an increased insight and knowledge and that outcome can be validated through several different methods”. Part of the knowledge pertains to the model design and the pointers to follow-on the ABMs discussed above. Part of the knowledge applies to the real Dutch housing market. Here, we can say that policy makers have a broad simulation tool. For examining specific policy questions, further modelling and experiments with more narrowly scoped ABMs are recommended; we discuss these opportunities in the next section.

We remark that validation via historical replay is difficult due to the lack of data; it is more likely to be the case for more narrowly scoped models. Moreover, the ABM developed thus far is a long-term, forward-looking simulation. In this regard, there is not an obvious path to compare with the market in, for instance, 2050.

6. Conclusions and Future Work

In the context of the Dutch housing market, this paper argues that the interaction between choices of households and regulations in the social-rented, private-rented, and owner-occupied sectors shapes the choices of households. The goal is to provide a path to greater transparency into the pros and cons of current and contemplated policy measures. The specific question we investigate is the following: how is internal demand impacted by regulations in a housing market that is suffering from a shortage? The behavioural interaction between households motivates the approach of developing an agent-based model. With it, we examined the effects of regulatory policy by means of exploratory simulations. To our knowledge, this is the first ABM that captures the important social rental sector of the Dutch market.

The simulation results find that, in the social sector, selection may be preferable over lottery due to the bias of the latter towards households that already own a home. These households leave a home which then, in turn, can satisfy a different household. This first satisfies a part of internal demand, and then creates a new opportunity to fulfil other demand. What is important to consider here is the impact on specific parts of the housing market. For example, lottery is preferable for younger households without a home. It is important that, when considering internal demand, those who are not yet part of the housing market are still considered; policies should not only prioritise those who are already part of the sector. Policies that focus only on ‘fixing’ internal demand might end up shuffling people in the sector instead of allowing new entrants into the sector.

The metric of ‘secondary waiting time’ can be effective in helping split households to find a home, but has unclear effects on other households. This metric focusses on a specific type of internal demand. An open question is the impact of households using the secondary waiting time in a strategic manner to gain an advantage; the benefit of secondary waiting time for divorcees might not weigh up against the downside of its strategic use by (other) households. Here, the focus is on a specific type of internal demand, and we note also the ‘gap’ between what the rules allow and what households might—in principle—do, as strategic exploitation of secondary waiting time requires intentionally and effort.

Increasing the income limit for the social sector is found to favour older households. We note that such a ‘solution’ to the housing shortage, namely increasing income limits, does not address root causes: it does not address any internal demand or systematic issues (as all data points between scenarios converge over time) but rather temporarily shifts the burden onto younger households. Perhaps more promising, and more direct, specific policies for older households, namely encouraging them to move from larger houses or apartments to smaller ones, have been introduced in Amsterdam at the time of writing.

Market policies that encourage a change to behaviours—designed to increase housing stock utilisation—can instead spur demand. An example is the just-cited policy of downsizing for older households. With respect to behaviour changes, further study is warranted, as experiments could measure households’ motivations more carefully; triangulation with household survey and panel data is a promising direction.

Since an ABM is a deliberate abstraction of reality, it should be noted that the presented model does not intend to predict the fiscal future of the housing market. While rich in descriptive detail, the developed model is somewhat limited by its smaller scale and shorter simulation time span than originally envisioned, together with some design limitations that have been found. In this regard, there is a case for a less detailed—but not overly simplified—model if the whole system is to be simulated [44,54]. Such a more narrowly scoped model or models might also result in more significant outcomes. Nevertheless, the experiments reported here have led to some interesting suggestions for the original research question and multiple directions for future work.

First, it is recommended that alternative designs for the way the population is simulated are considered, in order to improve the scaling of the execution time with an increased simulation time span. This will allow experiments to consider the effects over multiple generations. With this, the measurement of motivations can be expanded to measure multiple motivations and to consider the length of time that households hold these motivations.

Second, the composition of the housing sector neglected the small ‘senior housing’ part of the social rental sector. A recent government policy is to build more homes that are dedicated to older couples or singles. Further, one can allow the relative size and distribution of house sizes to change over time; indeed, the three sectors can be expected to expand at decoupled rates.

Third, some policies can be examined with a restricted model that encompasses only the social sector. A narrower, social-only ABM with a greater degree of abstraction would allow us to study the consequences of agents needing time to inspect houses (and possibly refusing a house after an inspection)—a salient factor to correctly understand the practical limitations of an assignment system. Additionally, agent preferences and the existence of multiple separate regions in the social sector could be considered. Likewise, a narrower, private-only ABM could examine the shift to temporary rental agreements in the private sector [55].

Fourth, a contemporary debated political question is where and how many new houses to construct, to address the fundamental imbalance of greater medium-term demand than housing supply. The results in Section 5.4.2 suggest that larger houses reduce demand, as expanding families do not need to move. Building larger houses, however, requires more space, resulting in a smaller total supply. This can be investigated in two steps: the trade-off between house size and the amount of houses—which can consider both monetary cost and spacial cost—followed by using the trade-off to setup different scenarios for either a model or simply to compare the results to the known demand.

Fifth, the consequences of couples being able to utilise two separate waiting times can be explored further through the view of optimal strategic behaviour. A related point is that different regions use different selection rules to select winners. The (strategic) consequences of these different policies are ripe for study [56].