PolicySpace2: modeling markets and endogenous housing policies
PPolicySpace2: modeling markets and endogenoushousing policies
Bernardo Alves Furtado ∗ Institute for Applied Economic ResearchNational Council for Scientific and Technological Development
February 25, 2021
Abstract
Policymakers decide on alternative policies facing restricted budgets and un-certain, ever-changing future. Designing housing policies is further difficult givingthe heterogeneous characteristics of properties themselves and the intricacy ofhousing markets and the spatial context of cities. We propose PolicySpace2 (PS2)as an adapted and extended version of the open source PolicySpace agent-basedmodel. PS2 is a computer simulation that relies on empirically detailed spatialdata to model real estate, along with labor, credit and goods and services markets.Interaction among workers, firms, a bank, households and municipalities followthe literature benchmarks to integrate economic, spatial and transport literature.PS2 is applied to a comparison among three competing municipal housing policiesaimed at alleviating poverty: (a) property acquisition and distribution, (b) rentalvouchers and (c) monetary aid. Within the model context, the monetary aid, that is,a smaller amounts of help for a larger number of households, makes the economyperform better in terms of production, consumption, reduction of inequality andmaintenance of financial duties. PS2 as such is also a framework that may befurther adapted to a number of related research questions.
Keywords:
Real estate market, Housing policies, Agent-based modeling, Simula-tion, Spatial analysis, Metropolitan regions.
JEL Clasification:
C630, R3 ∗ The author acknowledges receiving grant 304489/2019-0 from the National Council for Scientific andTechnological Development (CNPq) [email protected] – Corresponding author a r X i v : . [ c s . M A ] F e b Introduction
Real estate markets suffer influence of (a) economic cycles, interest levels and liquidity,(b) households inter-temporal decisions and changes, (c) local and foreign investors’interest, (d) land-use and zoning regulation and permits, (e) construction dynamics,and (f) location, location, location: such as job market proximity, amenities and neigh-borhoods. Besides this vast amount of interconnections, the dwelling as a marketablegood itself pertains some singular characteristics. They are durable and expensive,usually indivisible and with elevated transactions costs; mostly heterogeneous and withmonopolistic relative location.There is a large and consistent literature that handles most of these intricacies ofthe market. From urban economics and macroeconomics specifically, a vast array ofstudies follow the framework of DiPasquale and Wheaton [1]. More recently though, inthe aftermath of the subprime housing crisis it has become clear that traditional modelsare insufficient to handle empirical volatility and excessive price variance [2, 3, 4, 5].These observed inefficiencies of typical modeling fostered alternative lines of in-vestigation based on more empirical approaches [2, 6, 7] and with an emphasis oncomputational simulations [8, 9]. These models aim at replicating patterns and pro-cesses so that they may be useful tools in comprehending mechanisms and evaluating ex-ante policies. Real estate market models specifically have focused on macropru-dential analysis in order to inform monetary authorities on how to prevent or reduceexcessive volatility in the housing market. [10, 11]. Policy-makers indeed face a daunt-ing task of providing housing market stability at the national scenario as well as ofinsuring that citizens have adequate, serviced and affordable housing at the local level.Given this context, we propose PolicySpace2 (PS2) as a primarily endogenouscomputational agent-based model (ABM) that includes mortgage loans, housing con-struction, taxes collection and investments, with firms and households interacting inreal estate, goods and services and labor markets. PS2 is applied to 46 metropolitanregions in Brazil and serves the purpose of comparing local policies’ investments overthree alternative household poverty alleviating mechanisms: (a) housing acquisition,(b) rental payments over two years, and (c) a transfer of monetary aid.Moreover, PS2 integrates three venues of modeling: macroeconomics ABM [9],land-use change [12] and transport and urban planning [13]. In fact, we have noknowledge of any other model that (a) is open source, (b) uses intraurban official datafor a number of metropolitan regions, (c) applies explicit spatial rules for three differentmarkets, (d) includes a tax system at the municipal level (e) is based on firms andhouseholds decision-modeling, and (f) whose policy experiment is implemented fromendogenous demand and offer processes.These features enable PS2 to observe the dynamics of the real estate market draw-ing from most of its influences: (a) households composition and location, (b) firmsproductivity and location, (c) migration, new household formation and demographics,(d) credit and financial liquidity, (e) labor market and selection processes that simulta-neously consider qualification, distance, and access to public or private transport, and(f) the dynamics of construction.Validation and verification of the model comes from a successive and cumulativenumber of steps. Processes and rules are based on literature of previous models. Rules2re tested in a structural sensitivity analysis [14]. Parameters are also exhaustivelytested and perform robustly through a great variation of scenarios coming from differentmetropolitan regions settings. Results are presented as an average of simulation runs.Further, 66 indicators help follow different aspects of the simulation.Amidst all of the processes involved in the simulation, we were able to calibratePS2 to provide reasonable macroeconomic indicators: GDP, inflation, unemploymentand Gini coefficient that remain within expected values. Furthermore, even withoutthe inclusion of any data referring to the real estate market itself, such as propertycharacteristics, we are able to replicate very well the first half of the prices distributionfor the case of Brasília, for which we had empirical data to compare.Running PS2 evidentiates the fact that the model captures the relevance of thehousing market to the economy as a whole. Increase in households’ savings, an influxof households, elevated productivity or a higher participation of households in themarket all increase GDP and quality of life within the model. The policies’ experimentsuggests that the monetary aid distributed among a larger number of households ismore powerful than both property acquisition or rental payments in increasing GDPand reducing inequalities.Besides this introduction, section 2 presents the modeling approaches to real estatemarket analysis and agent-based modeling and refers back to how PS2 contributes toexisting literature. Section 3 describes the model and the policy experiment design. Wethen present the sensitivity analysis and validation (section 4), the results of the simu-lation and policy tests (section 5) follow. We conclude with some final considerations.
Housing is a major component of capital stock [15]. The residence is also households’most expensive purchase [16], which may involve mortgage payments for a number ofyears. Affordability of financial costs or rental burden is a larger problem for countriesin development, such as Brazil [17]. Preventing volatility, sudden cycles and disruptiverental markets may be socially desirable goals [18, 19].Besides the weight of housing on households’ budget and a country’s wealth, “[t]hehousing market is a dynamic system of intricately woven interdependent processes”[20, p.511]. In addition to the specificities of the characteristics of the dwelling itselfand the financial market as such, other mechanisms make real estate market analysiscomplicated: (a) neighborhood’s perception, the buzz and in its impact on valuation[21, 22, 23], (b) the ever-changing spatial urban context and scale in which the dwellingsits [24, 25, 26], and (c) the long-run dynamics of these continuous altering landscape,with rigid, slow-adjusting stock [1, 27].Location relative to other residences [28, 29] as well as to the transport [30] systemare also relevant to price dynamics. On top of it all, individual activities’ time allocationand mobility management also play a role on households decision-making towardshousing [31, 32, 33]. 3raditional modeling [16] suggests a spatial equilibrium in which all of these condi-tions clear: (a) supply and demand in the purchasing and rental markets, (b) appreciationof the estate’s value equivalent to premium of interests of the economy, and (c) salariesand amenities balance across other localities.Glaeser and Nathanson suggest that empirical data do not follow all of these con-straints mainly because of relevant momentum, mean reversion and "excessive variancerelative to fundamentals" [5, p.1]. Moreover, differently to what is seen on the assetmarkets, for example, real estate is operated mostly by amateurs who venture into themarket once in a while. Thus, using historic data to make price forecasting is a ratherdifficult task that depends heavily on the amount and precision of available information.The literature suggests that real estate markets are inherently complex, encompass-ing the financial market, future expectations, intrinsic features of the property itself,location, the utility to households and investors, altering spatial context. At the sametime, theoretical tools seem to be insufficient to maneuver all of these elements together.PS2 aims at incorporating most of these influencing factors within a single modelingplatform, including a number of endogenous processes in a data generator scheme thatincludes dynamics and feedback effects. We briefly list these elements. Full modeldescription follows in section 3.1. Uncertainty towards property valuation is assessed locally using limited knowl-edge by the buyer. Initial listing price reflects size and quality of the property andits endogenous dynamic location influence. Actual transaction price evaluatesalso the size of current housing offer and buyers endogenous savings.2. Entering the market is an exogenous decision [15]. However, transaction occursonly when the household has enough savings or can access mortgage loans(endogenous).3. The dynamics of the neighborhood depends on the activities’ of firms in thevicinity which is endogenous and depends on the consumption of households.4. Construction is also endogenous. Firms calculate most profitable regions – givencurrent prices – and check its capacity of construction, available land plots andthe size of offer to decide on new projects.5. Households’ dynamics – including demographics (aging, mortality and fertility) –new marriage (endogenous) and migration (exogenous) are present in the market.6. Endogenous labor market, along with distance and public and private mobilitycosts also influence the real estate market.
Agent-based model (ABM) refers to the construction of computational models in whichagents follow explicit, formal rules and interact with other agents and the environment.One of the first application to economics was the El Farol problem proposed by Arthur[34] to discuss bounded rationality. By early 2000s, a consensus had consolidatedaround its meaning and usability [35, 36]. Dawid and Gatti described benchmarks and4est practices in what they called ’families’ of macroeconomic agent-based models inthe end of the 2010s [9].A more recent definition of ABM suggests that a model should contain a ’sufficient’number of individual heterogeneous entities that posses attributes that are exclusiveto themselves and that engage in interaction that alters the states of other entities[37]. Along with the definition, and the listing of benchmark practices and choices ineconomics, the modeling community has agreed on a support for clear communicationof models as well as availability of simulation code [38, 39] ABM has been used on some real estate market analysis [10, 11, 14, 40, 41, 42, 43,44], mostly evaluating macroprudential initiatives towards curbing volatility. One ofthe first ones is an abstract model for the United Kingdom market proposed by Gilbertet al. [45]. The authors aim at replicating real estate stylized facts, including the role ofthe broker. Prices are fixed in the short-term and demand is driven by new comers. Themodel suggests that lower loan-to-value (LTV) limits curb prices, whereas exogenousdemand drives prices up.A series of papers focused on the subprime bubble bursting and boom analysis,started with the proposal of Geanakoplos et al. [11]. Baptista et al. [10] and thenGoldstein [14] develop the model for the Washington, DC case, whereas Axtell et al.[41] applies it to the United Kingdom. The emphasis of Baptista et al. is on learningmore about the behavior of investors who buy-to-let, besides discussing the impositionof limits to leveraging. Goldstein studies the influence of the percentage of incomethat is directed towards the real estate market. The papers all suggest that there is astrong relationship between LTV and the occurrence of more volatility. Carstensen [43]takes the modeling to Denmark in order to investigate effects of shocks on interests andsalaries. His work suggests that increases of debt-to-income (DTI) ratios may lead tothe collapse of the market.Ge [40] adds to the literature discussing volatility in the real estate market, howeverwith a more detailed focus on the bank as an agent that decides on mortgage levels. Thebank performs an endogenous calculus that considers the value of collaterals and theprobability of default to set mortgage rates. Shocks on the model include the numberof investors that act speculatively. She shows that those are sufficient conditions togenerate endogenous bubbles in the market.Other authors focus on spatial changes and evolution. Prunetti et al. [46] designa utility analysis associated with a land-use and land cover model to represent spatialdynamics. Moeckel [32] associates a model of land use change to a transport model totackle households’ simultaneous constraints. Huang et al. [42] review decision-makingreal estate models that are associated with land-use dynamics.PS2 includes a bank that collect clients’ deposits, pays interests and offers mortgageloans for prospect buyers. Spatial rules mediated by access to public or private transportare present in the labor market – as criteria for candidates choosing firms –, in the goodsand services market as criteria for consumers choosing firms – along with prices –, andas an influence of properties’ price-setting mechanism. Administrative space is alsorelevant as five different taxes are collected and transferred to the municipalities fol-lowing tax distribution rules. Households and firms are generated following intraurban PolicySpace2 full code is available at GitHub.com/BAFurtado/PolicySpace2
PolicySpace2 (PS2) is an economic model that emphasizes spatial elements – regional,municipal and intraurban – of a complex market, that of real estate, whose dynamicinfluences are (relatively) not fully understood, although the market produces permanenteffects on households and the society as a whole. We adapt and extend the original,open-source model [47, 48] that in turns follows the tradition of Gaffeo [49] andLengnick [50]. Lengnick is one of the macroeconomic agent-based models familydescribed by Dawid and Gatti [9].We added extensive changes and adaptations to the original model. We includedthe credit and rental markets. Construction firms now produce endogenous dwellingsfollowing profitability, land availability and supply size. Neighborhood effects, supplysize and the time the property has been on the market also influence prices. Mortgageloans as well as bargaining make real estate market negotiations more dynamic. House-holds make decisions on consumption and savings based on their permanent income[9]. Empirical data follows intraurban information for the year 2010.The purpose [51] of PS2 is to illustrate a potential explanation as how alternativepublic investments in housing and monetary aid among citizens impact the economyand inequality in the long-run. Additionally, PS2 is a descriptive model that enablesanalogies [39] among distant facets of analysis, correlating labor productivity to realestate markets or household savings, for instance. Finally, PS2 makes it easy to endoge-nously reason about the real estate market as an integrated component of the economicsystem.The purpose of explanation is verified as a comparison of simulated versus empiricaldata and the analysis of the policy experiment. The purpose of description and analogyis discussed in the presentation of the sensitivity analysis and the comments on behaviorreplication. TRACE methodology [38] recommends that besides the purpose and answers, the modeler shouldalso provide the target public and the extent to which the model may be expanded. PS2 serves mainly
6e detail the model providing the context of agents and scale and then we use thesequence of events to describe the decision-making processes, the related equations andthe supporting literature.
Agents.
PS2 contains individuals who work, commute, age, die and are born, getmarried and divorce. Individuals are organized in households (families) and reside indwellings that have fixed location. Households may move among residences and areconsidered as a collective of individuals making decisions on consumption. Firms –also fixed in space – hire individuals, produce and participate in the goods and servicesmarket. Construction firms also hire individuals and supply new dwellings in the realestate market. There is one bank that collects deposits, pays interests on them and offersmortgage loans. Municipalities have actual geographical coordinates, collect taxes onfirms and workers, consumption, properties and transactions within their own territory.
Scale.
PS2 runs monthly from January 2010 to January 2020 in the standard simu-lation. It may be configured to go up to 2030 and start either in 2000 or 2010. Eachsimulation is run for a single metropolitan region of Brazil, out of 46 available withinthe model , being Brasília the standard run. Generator of agents.
The model either loads previously saved agents or generatesthem from official census block data. We also use official intraurban geograph-ically delineated regions. Municipalities are a set of regions. Dwellings aregenerated so that there is an exogenously assigned number of vacant residencesin the model. Agents, households and dwellings follow each census block’spopulation percentage (pop) for a given starting year. Agents are allocated intohouseholds and households into dwellings, either as an owner or a rental, ran-domly distributed.
2. Each region lists the number of available land plots or licenses. Constructionfirms need to purchase a license in order to build a new property.3. Following exogenous empirical data, new firms enter the simulation.4. Firms ( 𝑖 ) update their inventory with goods and services ( 𝑄 𝑖 ) each month ( 𝑡 ) basedon workers ( 𝑙 ) qualification ( 𝑞 ) [49] and two exogenous parameters ( 𝛼, 𝛽 ) (seeequation 1). Firms produce homogeneous products with fixed technology [50]. policymakers and academics interested in real estate and economic dynamics. PS2, however, can also bethought as a platform that contains a wide number of elements. As such, one could detail specific modulesof PS2 and use it for further analysis. Actually, we consider only the urban core of metropolitan regions, named by the Statistics Bureau asAreas of Concentration of Population (ACPs). Please, check the GitHub repository for a full list. Parameters and their standard value are described on Appendix A. 𝑄 𝑖,𝑡 = 𝐿 ∑︁ 𝑙 𝑞 𝛼𝑙 𝛽 (1)5. Demographics.
Mortality, fertility, new marriages and aging take place accordingto exogenous probabilistic official data by state. Each agent receives a month ofbirthday in which all demographic processes occur. When female agents withinfertile age (14-50) give birth, the child is incorporated at the mother’s household.6.
Migration and marriage.
Migration occurs when necessary to maintain exoge-nously observed population growth. Households coming into the municipalityonly stay if they are able to find residence through the real estate market. Mar-riage occurs probabilistically. Agents leave their now old household (and houseproperty) behind, if not the only adult. Otherwise, they bring any children (andproperty) they may have with them. Newly formed households persist only ifeither adult brings a house (or a rental) or if they succeed in the market. Whenthe last member of a household dies, a search for relatives – members from thehousehold the deceased may have belonged to originally – receive any wealth orproperty. When there are no known relatives, any property is randomly allocatedto another household.7.
Consumption at the goods and services market.
Households choose from anexogenously determined sample size ( 𝜍 ) either the firm that is the closest or the onewith the cheapest product ( 𝑃 ( . ) ). The consumption amount is determined by thehousehold’s simplified permanent income ( 𝑃𝐼 ℎ,𝑡 ) [9], with an extra assumptionthat expected future income is an average of all previous permanent income (seeequation 2). When gathering consumption money, households search first forcash available with each member. If collected cash is not enough to make thepermanent income, households try to withdraw from their reserve money ( 𝑅 ℎ ) orsavings ( 𝑆 ℎ ) from the bank. 𝑃𝐼 ℎ,𝑡 = 𝑖 𝑡 ∗ 𝑌 ℎ,𝑡 − 𝑡 + 𝑖 𝑡 ∗ 𝑌 ℎ,𝑡 − 𝑡 𝑟 𝑡 + 𝑤 𝑡 ∗ 𝑟 𝑡 (2)where 𝑖 𝑡 is 𝑟 𝑡 /( + 𝑟 𝑡 ) and 𝑟 𝑡 is the baseline interest of the economy, 𝑌 ℎ,𝑡 − 𝑡 isthe household’s members average monthly income for all available periods and 𝑤 𝑡 is the sum of properties values, reserve money, savings and loans in the bank.Any income the household may have (or gain via rentals or sales) in excess ofpermanent income is deposited as savings in the bank, but for a reserve wagegiven as 𝑅 ℎ = ∗ 𝑃𝐼 ℎ,𝑡 . Simply put, household consumes a bit more than totalwages if they have savings and a bit less when their total wealth is negative. Permanent income is "a linear function of current and expected future incomes and of financial wealth."[9, p.78]
8. The bank calculates and collects payment for loans. If the household fails to pay infull, the debt accumulates for the next month. Note that the bank pays exogenousbaseline economy interest on deposits ( 𝑟 𝑡 ), but applies (also exogenous) marketmortgage interest rates on loans.
9. Firms check their revenue, pay taxes and calculate profit. Calculate wages, paytheir employees and decide whether to update prices.
Firms’ decision on prices.
Blinder [52] identifies via survey a number of differentstandards firms use when setting prices under uncertainty. His findings supportthe idea that firms do not evaluate the market every month. PS2 follows Seppecheret al. [53] in observing the size of the firms’ inventory in order to update pricesand it does so not every month, but according to an exogenous parameter ( 𝜁 ). Ifthe amount sold in the previous month was above produced quantity, then firmsupdate prices by a markup percentage ( 𝜋 ). Firms’ decision on wages.
Firms decide on wages ( 𝜔 𝑙,𝑡 ) based on total revenue( 𝑇 𝑅 𝑖 ) discounted of taxes on labor ( 𝑡𝑎𝑥 𝑙 ) and global unemployment ( 𝑈 𝑡 ) (seeequation 3). 𝜔 𝑙,𝑡 = 𝑇 𝑅 𝑖,𝑡 ∗ ( − 𝑈 𝑡 ) ∗ 𝑞 𝛼𝑙 (cid:205) 𝐿𝑙 𝑞 𝛼 ∗ ( − 𝑡𝑎𝑥 𝑙 ) (3)10. Planning new dwellings.
Construction firms operate their property planningprocess considering availability of land plots, profitability and current supplysize. They also check for finished previous construction plans and when so listthe new properties in the market. First, the firm checks whether their contractedamount of work ( (cid:205) ℎ 𝑐𝑜𝑠𝑡 ) is smaller than a fixed number of months ( 𝑛 ) timestheir current monthly production ( 𝑄 𝑖,𝑡 ). If so, they may start a new constructionproject. Next, the construction firm checks whether it has enough funds to buythe license plots and separates the regions where it can afford and that actuallyhave available licenses. The firm then tests whether to continue with the plansdrawing a number from a uniform distribution and checking that it is higherthan the global vacancy percentage. That means that the higher the offer on themarket the less likely the construction firms start new projects. Building sizeand building quality is chosen randomly. Next the firm gets a sampled price ofhouses that have similar size (within 10 absolute distance) and quality (within 1absolute distance) for each available region. Cost is calculated as dwelling size( 𝐻 𝑠 ) times quality ( 𝐻 𝑞 ) times a random productivity factor that is a function ofmarkup ( 𝑓 ( 𝜋 ) ). Region profitability ( 𝑁 𝜋,𝑚 ) then is the mean prices of similardwellings deduced by calculated building cost and license price ( 𝑁 𝑚 ) times lotcost (1 + 𝜐 ) (see equation 4). When there are no profitable regions, the firm doesnot start a new construction. Otherwise, it chooses the most profitable one andstarts construction. 𝑁 𝜋,𝑚,𝑡 = 𝑃 ask ,𝑚,𝑡 − ( 𝐻 𝑠 ∗ 𝐻 𝑞 ∗ 𝑓 ( 𝜋 ) ∗ 𝑁 𝑚,𝑡 ∗ ( + 𝜐 )) (4)11. Labor market.
All individuals ( 𝑙 ) who are between 16 and 70 years old and See Ge [40] for an example of an endogenous mortgage rate mechanism. Firms ( 𝑖 ) do not enter the marketoffering positions every month. Rather they evaluate probabilistic whether to doso following an exogenous parameter ( 𝜄 ). When in the market, they may eitherfire a randomly chosen employee, when their profit is negative, or open a posi-tion otherwise. Candidates and firms are shuffled. Some of the posts available,depending on an exogenous parameter ( 𝜂 ), will use a proximity criterion whereasothers will make a decision based on qualification of candidates. All positionsinvolve a sample of candidates ( 𝜎 ). The candidates at the pool for each positionevaluate the post themselves considering the wage ( 𝜔 ) paid and the distance fromthe firm to their residence ( 𝑑 ℎ − 𝑖 ), mediated by the cost of transport ( 𝑐 𝑡𝑟 ) (seeequation 5). Having access to private transport depends probabilistic on the decilof income of the candidate’s last wage. All offers are sorted based on the score.Firms paying higher wages choose first in descending order. For every pair offirm-candidate – conditional on the candidate having not being chosen earlier– positions are filled successively and firm and candidate leave the market forthat month. The market closes when there are no more positions or no morecandidates. 𝑠 𝑙,𝑖,𝑡 = 𝑞 𝑙 + ∑︁ 𝑖 𝑤 𝑙,𝑡 − 𝑑 𝑙,ℎ − 𝑖,𝑡 ∗ 𝑐 𝑡𝑟𝑙,𝑡 (5)12. Real estate market.
A sample of households ( 𝜙 ) exogenously determined enterthe real estate market monthly. Prices ( 𝑃 ask ) for all properties are updated andthose unoccupied are listed and divided between rental and sales market by anexogenous parameter. Rental.
Rental market happens first. Households are sorted by permanent income( 𝑃𝐼 ℎ,𝑡 ). Given a random sample of fixed size ( 𝜎 ), households ( ℎ ) choose a rentalthat is within their budget randomly. Otherwise, they propose a discounted valueon the cheapest rental available in the sample. Sales.
On the sales market, households are sorted by purchasing power ( 𝑃 offer ),including an estimate of possible mortgage credit ( 𝐿 ℎ ). Then, each householdtries to buy the most expensive property on their sample [14]. Asking prices.
The asking price is calculated considering the dwelling sizeand quality ( 𝐻 𝑠,𝑞 ) and the neighborhood quality of life index ( 𝑁 ) which differsby region ( 𝑚 ) and changes monthly depending on taxes collected and popula-tion proportion (see below item 15). Additionally, an extra comparative effect ofneighborhood may be added. A parameter ( 𝜏 ) may be set that brings the influenceof a normalized index of neighborhood households average income ( 𝑁 𝑞 ∈ [ , ] )into prices [40]. Finally, a discount for time on the market is incorporated intoprices with a bounded value ( 𝛾 ) and a decay factor ( 𝜅 ), depending on the numberof months the property has been listed ( 𝑇 ) (see equation (6)). Bank mortgage criteria.
The bank follow three simple criterion to provide mort-gage loans: (a) the bank needs to have positive balance; (b) the household cannothave a current mortgage and (c) total loans already offered cannot be higherthan the percentage of total deposits ( 𝜈 ) as established by monetary authorities. Neugart and Richiardi [54] have proposed an ABM of the labor market. 𝐿 ℎ ) the bank provides depend on the maximumcapacity of monthly payment the household can make, restricted by a limit ( 𝜒 )of permanent income ( 𝑃𝐼 ℎ ∗ 𝜒 ) times the maximum number of months ( 𝑚 ) (360)or the number of months before the oldest member of the family reaches 75, sothat 𝐿 ℎ = 𝑃𝐼 ℎ ∗ 𝜒 ∗ 𝑚 Negotiation.
When the property’s price is below the household’s savings, thetransaction is made with final price ( 𝑃 ) set as a simple average of asked priceand household’s savings [55]. When property’s price requires mortgage loan( 𝐿 ℎ ), the buyer requests the loan on the difference between savings and askedprice. If successful on getting the mortgage loan, the offer price ( 𝑃 offer ) is savingsplus estimate mortgage (see equations (7) and (8)). Otherwise, when the loanis declined by the bank, the household leaves the market. When the savings arebelow the asked price, but above an exogenous parameter limit ( 𝜌 − ), the buyermakes an offer with their total savings. The chance that the seller will acceptdepends probabilistically on the size of the supply market (see equation (11)).When both savings and savings with mortgage are below property asked price,and the discount was not possible or not accepted, households try the next houseon the list. Constraints.
There are some constraints imposed on prices. The ratio savings,price is upper-bounded by an exogenous parameter ( 𝜌 + ) and there is a loan-to-value parameter (LTV) on mortgage requests (see equations (9) and (10)). 𝑃 ask = 𝐻 𝑠,𝑞 ∗ 𝑁 𝑚,𝑡 ∗ ( + 𝜏 ∗ 𝑁 𝑞 ) ∗ (( − 𝛾 ) ∗ 𝑒 𝜅 ∗ 𝑇 + 𝛾 ) (6) 𝑃 offer = 𝑆 ℎ ∨ 𝑆 ℎ + 𝐿 ℎ if 𝑃 ask < 𝑃 offer (7) 𝑃 = ( 𝑃 ask + 𝑃 offer )/ 𝐿 ℎ / 𝑃 < = LTV (9)if 𝑃 ask / 𝑃 offer > 𝜌 + −→ 𝑃 = 𝑃 offer ∗ 𝜌 + / 𝑃 ask > 𝑆 ℎ > 𝜌 − −→ 𝑃 = 𝑆 ℎ | 𝑃 ( ∑︁ Listed / ∑︁ ℎ ) (11)13. Decision on moving.
Households will move to the best dwelling (most expensive[14]) when at least one member is employed. Otherwise, they will move to theworst one (enabling the listing of the most expensive in the next month).14. Households invest. The bank keeps the date to calculate interest at the exogenousrate ( 𝑖 𝑡 ).15. Municipalities invest in Quality of Life Index improvement ( 𝑁 𝑚,𝑡 ). All taxescollected at each market, respectively: consumption, labor, firm profits, prop-erty transactions and properties, are transferred to the municipalities budgetaccording to tax rules distributions in Brazil, following the original model[47]. Investments are linear and transformed via an exogenous managementefficiency global index ( 𝜓 ) and population (pop 𝑚 ) difference, such that: 𝑁 𝑚,𝑡 + = (cid:205) 𝑚 𝑡𝑎𝑥 𝑡 ∗ 𝜓 ∗ pop 𝑚,𝑡 − / pop 𝑚,𝑡
16. Statistics and output are calculated and saved.11 .2 Policy experimental design
The policy experiment is applied using endogenously collected taxes by municipality( 𝑚 ). Instead of investing full budget to the investment in quality of life ( (cid:205) 𝑚 𝑡𝑎𝑥 ), apercentage ( 𝛿 ) is diverted to either one of three policy investments.When applying a policy, the first action is to register all households whose per-manent income ( 𝑃𝐼 ℎ,𝑡 ) has been below an exogenous quantile ( 𝜃 ) of the householdsof the metropolitan region in the previous year and currently still reside within themunicipality. Households are then sorted according to permanent income so that thepoorest of all municipal household is the first in line.1. Property acquisition and distribution.
The municipality lists all properties in theregion that construction firms have finished but have not sold yet and sorts themby the cheapest to the most expensive. The list of households registered includesonly those who do not own any property. Then, the municipality purchases theproperty from the selling firm, excluded of transaction tax, and transfers theproperty to the household next on the list, for as long as the monthly availableallotted funding, properties and households last.2.
Rental payment vouchers.
The municipality lists all households that do not ownany properties and are in the policy register. Thus, as long as there is enoughfunding and households the municipality issues 24-month rental vouchers thatshould cover the current household rental price. If the household decides to leavethe residence, it gives the remaining vouchers, if any, back to the municipal-ity. Households can only apply for new vouchers after they have expended allpreviously received and the criteria to be listed still hold.3.
Monetary aid.
In this policy scenario, the municipality divides all monthlyavailable funding equally into a single payment for all households listed at thatmoment in the policy register.4.
No policy – baseline.
In this case, no money is invested in policy and all resourcesgo into investment in municipal quality of life ( 𝑁 𝑚 ). We aim at validating PolicySpace2 through a series of successive steps. First a seriesof macroeconomics indicators have to behave reasonably within expected values. Eventhough these indicators have been calibrated to be in such a way, they happen to bewithin reasonable boundaries simultaneously. That means the Gini coefficient, inflation,unemployment among other indicators are all sensible.Brasília – which is our baseline case – observers Gini coefficient of 0.4705, totalinflation for the 10-year period is 43.32% and unemployment 12.39% which are withinexpected values for the case of Brazil. Apart from that, extensive variations in theparameters or the metropolitan regions change final values but do not lead to thecollapse or explosion of the model. 12econd, most rules, procedures and parameters come from literature or data. Firms’decisions on prices, wages and production, for example, are based on previous works.Price setting in the real estate market follow hedonic and urban economics baselines withalso some support from urban studies. Labor market does not have a clear predecessor,despite the contributions of Neugart [54], but has based itself on commuting costs andactivities’ time allocation. Parameters follow observed data as much as possible.Moreover, a number of new rules implemented in PolicySpace2 are tested in thesense that they can easily be turned on and off. This happens for example with theinfluence of global unemployment ( 𝑈 𝑡 ) on wage decision-making, the cost of commut-ing, the neighborhood effect on prices, if any, the influence of distance on hiring, thediscounts on the negotiation processes and time on market, the size of hiring samplesize or firms consulted for consumption. All parameters are tested with a variation ofcombinations. That helped verify the robustness of the results as well as to gain insightson the operational emergence of results of the model. Considering the purpose of the model – that is to investigate "alternative householdpoverty alleviating mechanisms", all tested rules and parameters maintained the bulkof the results presented.Thirdly, the validation itself is done by comparison of data collected for the Brasíliareal estate market that never goes into the model. It was gathered independently fromlisting offers available on internet sites mostly during 2020. Model data, however, onlyuses information from Census and official data, mostly from 2010 (although it is alsopossible to run with 2000s data).We compare normalized prices over space for Brasília using data from the lastmonth of the simulation (see figure 1). Results are spatially similar and the simulateddata is able to replicate the lower half of the distribution of the real data. Observedprices are more volatile and ragged comparatively to simulated prices which are morecontinuous with less pronounced peaks. Simulated data also follow more closely thelocation of firms whereas observed data is rather scattered over space.However, considering that no description of properties size, quality or price isincluded in the model, the similarity we were able to achieve, given a market thatincludes heterogeneous properties (central, small one-bedroom high valued properties,but also, large, distant, sophisticated properties) seem to be sufficient to hold thecomparison and thus serve the purpose of the model.
Results clearly show that from an endogenous perspective, the best policy seems to bethe Monetary aid, e.g., the distribution of a lower amount of aid directly to a largernumber of households (see figure 2).Given the endogenous amount of funding distributed towards the policies, it isup to the internal processes of the model how to foster the economy forward. Whenthe Monetary aid policy is introduced, more households are able to consume larger Please note that PS2 comes with a ’sensitivity’ run that automatically tests Boolean, quantitative param-eters, tax rules distribution, a run with all metropolitan regions and all policies. The code encloses built-inruns that provide output as comparative plots. +− (a) Empirical house prices data +− (b) Simulated house prices data Figure 1: Comparison between house prices for real empirical data and simulateddata for the case of Brasília, Brazil. Real data is drawn from public internet offers(2020). Simulated data follows standard run parameters and refer to the last month ofthe simulation (2020). No information from real estate is used on the simulated data.Only original composition and location in 2010 is used to initiate the households. Thesimulated data distribution consistently follow up with real data distribution up to themedian value. It performs worse in the upper half of the distribution. Simulated valuesalso follow more closely firms and jobs distribution when compared to real data.quantities at the goods and services market. The resulting sales and revenues allow forfirms to pay higher wages. This leads to an expected slight increase in prices. Eventhen, a smaller number of households fail to pay their rents or their mortgages or goa month without consuming goods and services. Overall, that leads to a much lowerinequality with a higher GDP achievement.The Rental voucher policy is a somewhat intermediate alternative with a muchsmaller number of households being supported. On average Monetary aid policyhelps 2,358.05 households monthly per municipality, compared to 47.5 for the Rentalvouchers and 12.37 for the Property acquisition program. Even then, Rental policyseem to achieve a nearly as lower inequality when compared to Monetary aid, althoughwith not as much an increase in GDP.Property acquisition seems to be the policy to perform worst. It lowers overall meanhousehold permanent income, compared to both other policies and to the No policybaseline. Further, it sharply increases inequality – as it provides an asset to a smallnumber of households. On the positive side, it seems to increase firms (constructionfirms) total assets in a more pronounced way than the other two policy alternatives aswell as it helps decrease house prices.The No policy baseline results are provided as a comparison of the performanceof the model. Consider that whereas the funding separated for the policy programsis reinvested in absolute terms, the investment when there is No policy is made infull via the linear transformation of the 𝜓 parameter. Conversely, among the policies’ That considers the standard run parameter of 1% of the population of the metropolitan region and thepolicy coefficient ( 𝛿 ) of .2 over the available funding for each municipality to apply on the policy. Alternativevalues for 𝛿 did not alter the results. a) Households Consumption (b) Households Permanent Income(c) GDP (d) Gini coefficient Figure 2: Results of policy experiment.
Red refers to the ’Property Acquisition’policy,
Blue to ’Rental Vouchers’,
Green to ’Monetary Aid’ and
Orange is the NoPolicy baseline. Monetary Aid is the policy application with a better performanceboth at the GDP level, but also with a reduced Gini coefficient indicator. PropertyAcquisition, however, seem to deteriorate inequality and contribute to GDP increase ina smaller proportion than the other policy tests, even worsening considerably householdspermanent income levels. Household consumption at the goods and services marketsignificantly increases with the Monetary Aid policy application.15lternatives, the exact same processes, procedures and parameters run each policyscenario. That makes the policy alternatives highly comparable among themselves.
We use an empirical, economic, spatial agent-based model that uses official data to gen-erate households, firms and municipalities that interact in the markets of labor, credit,real estate and goods and services to endogenously test alternative housing policy pro-grams. Poor households – those from the lowest fifth of the distribution – are registeredat their municipalities and organized according to their observed income levels. Mu-nicipalities collect funds via taxes on consumption, labor, firm profits, investments,property transactions and properties. Regularly they invest on a general improvementof quality of life. When applying policies, the municipal body alternately reserves afifth of its funds to (a) acquire and distribute properties for poorest households, (b)provide 24-month rental vouchers or (c) simply divide the monthly available resourceswith all of the registered households. Results hold for a number of different parameterintervals, rules and processes applied and metropolitan regions tested. Within the con-text of the model, the monetary aid performs better than the alternatives in nearly all ofthe indicators used. Mainly, monetary aid reduced inequality at the same time that itincreased overall economic output.PS2 benefits from a number of previous modeling works on macroeconomics,housing markets, transport and land-use change. We tried to incorporate most of thebenchmarks and procedures both in modeling and on communicating. The confidence inPS2 comes from the sustainable robustness it has shown on top of added mechanisms,data, parameters, markets. The confidence in the results come from the theoreticalcomparability among the alternative choices.The aim of the paper is not, however, to recommend an extinction of housingacquisition and distribution to poorest families. We believe PS2 only demonstrates thata given policy – however focused it might be – it might endogenously contribute moreto the economy when dispersing more the funds, rather than concentrate them in fewerhouseholds.Nevertheless, when facing an specific housing program with strict lack of shelter,rental vouchers might benefit a larger number of people and result in greater gains forthe society as a whole. Finally, we believe that the contributions of PS2 surpasses the policy analysis itself.We provide a comprehensive empirical, documented and robust agent-based model thatis open source and modular that might facilitate further research questions. The diffi-culties in working with PS2 and other ABMs is probably its flexibility and adaptation.We believe PS2 is nearly ready to study urban mobility – given location of workers andfirms, along with endogenous characteristics of both; social mobility – given the depen-dence of workers productivity on qualification and its current static nature; migrationand newly formed households; inheritance – for longer studies; a more detailed creditmechanism and authority ruling; urban zoning and regulation; amenities, neighborhood We also noticed that poor families recurrently – although slightly diminishing in numbers – accessed theRental program. As such, other structural policies might be needed.
Acknowledgements:
The author would like to thank LP, DF, VGN, AM for theircomments on an early presentation of this work.
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A Parameters
See table 1 for the parameter values used on the standard simulation run.21able 1: Parameters used on standard simulation run for the case of Brasília metropolitanregion, 2000-2010, minimum of 5 runs each.Parameters Code name Standard run values Tested intervalspop percentage of population .01 [.005, .03] 𝛼 productivity exponent .6 [0, 1] 𝛽 productivity magnitude divisor 10 [1, 36] 𝜄 labor market .75 [0, 1] 𝜂 percentage distance hiring .3 [0, 1] 𝜙 percentage entering real estate market .0045 [0, .05] 𝜎 hiring sample size 20 [1, 100] 𝜍 size market 5 [1, 20] 𝜌 + capped top value 1.3 [1, 1.5] 𝜌 − capped low value .7 [.5, 1] 𝜏 neighborhood effect 3 [0, 5] 𝛾 max offer discount – lower bound .6 [.5, 1] 𝜅 on market decay factor -.01 [0, -.05] 𝜋 markup .15 [0, .3] 𝜓 municipal management efficiency .00007 [.00001, .0001] 𝜈 max loan bank percentage .7 [0, 1] 𝜒 loan payment to permanent income .5 [0, 1] 𝑛 construction cash flow – number of months 24 [1, 36] 𝜐 lot cost .15 [.01, .3] 𝜁 sticky prices .7 [.1, .9] 𝛿 policy coefficient .2 [0, .3] 𝜃𝜃