The IRPUD Model: Private Construction Submodel



The Private Construction Submodel considers investment and location decisions by private developers, i.e. by enterprises which erect new industrial or commercial buildings, and by residential developers who build flats or houses for sale or rent or for their own use. Thus the submodel is a model of the regional land and construction market.


Industrial Location

The industrial location submodel makes no distinction between basic and non-basic industries, i.e. all industries are located or relocated endogenously subject to sectoral employment projections for the whole region. The model locates industrial or commercial floorspace suitable as workplaces in the 40 industries considered in the model. However, as the amount of floorspace occupied by worker is not constant over time and certain types of floorspace can be used by several industries, the model actually locates workplaces or employment, which are subsequently converted to floorspace. The location of workplaces of all industries may also be controlled exogenously by the user in the Public Programmes Submodel in order to reflect major events such as the location or closure of large plants in particular zones.

Change of zonal employment occurs in the model in four different submodels:

(1)
 

Decline of zonal employment due to sectoral decline, lack of building space and intraregional relocation of firms is modelled in the Ageing Submodel.
 

(2)
 

Changes of zonal employment due to the location or removal of large plants exogenously specified by the user are executed in the Public Programmes Submodel.
 

(3)
 

Changes of zonal employment due to new jobs in vacant industrial or commercial buildings, in newly built industrial or commercial buildings or converted residential buildings are modelled in this submodel.


New workplaces are either located in existing vacant industrial or commercial buildings, in newly constructed industrial or commercial buildings or in converted residential buildings.

Before starting the location process, industries are sorted by decreasing floorspace productivity, or rent paying ability, and processed in that order.

The total demand for new workplaces of industry s in the region is

(1)

where DEsli(t,t+1) are net changes in employment of industry s on land use category l in zone i modelled in previous submodels resulting from sectoral decline, lack of building space and intraregional relocation of firms as well as from exogenously specified public programmes.


a) New Jobs in Vacant Buildings

Declining industries or relocating firms leave buildings vacant that may be used by other industries. For this purpose, the forty industries have been divided into groups with similar space requirements.

If this demand is less than the total supply of suitable floorspace, it is allocated to vacant floorspace with the following allocation function:

(2)

where Kslj is the capacity of existing buildings on land-use category l in zone j for workplaces in industry s.Vslj is the number of jobs accommodated.


b) New Jobs in New Buildings

For any remaining demand, new industrial or commercial buildings have to be provided. This demand is allocated to vacant industrial or commercial land with the allocation function

(3)

where Cslj are new workplaces in industry s built on land-use category l in zone j between t and t+1. Lslj is the current capacity of land of land-use category l for such workplaces in zone i; since it is continuously reduced during the simulation period, it bears no time label.

The utility uslj(t) used in Equations 2 and 3 is the attractiveness of land-use category l in zone j for industry s and has three components:

(4)

where usj'(t) is the attractiveness of zone j as a location for industry s, usl(t) is the attractiveness of land-use category l for industry s, and us(clj )(t) is the attractiveness of the land price of land-use category l in zone j in relation to the expected profit of economic activity s. The vs, ws, and 1–vsws are multiplicative importance weights adding up to unity. The three component utilities are constructed similarly to the components of the housing utility uhki(t) (see Housing Market Submodel). Like all utilities in the model, the uslj(t) remain unchanged during the simulation period as calculated at time t. The price or rent of industrial or commercial buildings is not represented in the model.

The land capacity Lslj is normally taken as being fixed as specified in the zoning plan. If a piece of land was formerly in a built-up area, its development implies the demolition of existing buildings. In addition, under certain restrictions in zones of high demand, the capacity Lslj may be extended by demolition of existing buildings with less profitable building uses to represent displacement processes going on within existing neighbourhoods. As Lslj is updated after the location of each industry, it bears no time label. All workplaces or dwellings displaced by demolition during a simulation period are replaced in the same period by iterating the industrial and residential submodels several times.


c) Conversion of Existing Dwellings

In the case of service workplaces, the capacity of a zone may also be extended by conversion of existing dwellings into offices where the demand for office space is high in relation to supply in order to represent the displacement of dwellings by offices observed within or near the CBD. All dwellings converted to offices during a simulation period are replaced in the same period by iterating the industrial and residential location submodels several times.


Retail Location

Retailing is treated like any other industry in the model except that the zonal attractiveness usj(t) (see Equation 4) for retailing includes an attribute n

(5)

where tq2ijm(t) are shopping trips (g = 2) of households of income group q from residential zone i to shopping zone j using mode m, yhi(t) are retail expenses of households of income group q in zone i at time t, Ers(t) is retail employment in zone j at time t, Er(t) total regional retail employment, and vn(.) the value function mapping attribute n to utility. This attribute indicates retail sales per retail employee in zone j expressed in units of average turnover per retail employee in the whole region.


Housing Supply

Housing is represented in the model as a distribution of dwellings classified by (see Housing Market Submodel:
- type of building (single-family, multi-family)
- tenure (owner-occupied, rented, public)
- quality (very low, low, medium, high)
- size (1, 2, 3, 4, 5+ rooms)

This housing distribution is collapsed to up to thirty more aggregate housing types for use in the occupancy matrix, which links dwellings with households (see Housing Market Submodel). Changes to the housing stock in the zones occurs in three submodels:

(1)

Ageing of residential buildings, i.e. filtering down the quality scale, is modelled in the Public Programmes Submodel.
 

(2)

Public housing programmes specified exogenously by the user are executed in the Public Programmes Submodel.
 

(3)

Maintenance/Upgrading and new housing construction are modelled in this submodel.



a) Maintenance/Upgrading

Landlords are assumed to invest in their housing stock if by doing so they can expect to raise their profits. The proportion of dwellings upgraded in each period is calculated for each dwelling type in each zone as a function of the expected rent increase in that submarket after improvement. As the eventual rent increase is not known at this point in time, the landlords employ a simple rent expectation model based on vacancy rates at the beginning of the simulation period:

(6)

where Uki(t,t+1) is the number of dwellings of housing type k in zone i to be upgraded if a sufficient number of dwellings of the same housing characteristics (size and building type) but lesser quality exits in the zone, Dki(t) is the number of dwellings of this type in the zone and Vki(t) is the number of vacant dwellings of this type. The exogenous elasticity curve f(.) controlling landlord investment behaviour specifies that landlords upgrade their stock if the number of vacancies is low.

Filtering and maintenance/upgrading work in opposite directions. Their net effect may result in an overall deterioration or improvement of the housing quality in a zone.


b) New Housing Construction

The submarkets of the housing construction submodel are the housing types of the aggregate (30-type) housing classification, or rather a subset of them, as only good quality housing is assumed to be built.

Before starting the location process, housing types are sorted by decreasing price or rent per square metre and processed in that order.

The demand for new housing of type k to be built during the period from t to t+1, Dkli, is estimated by the model using a similar rent expectation model as in the maintenance/upgrading submodel:

(7)

where Ck(t,t+1) is the number of dwellings of housing type k to be built between times t and t+1. The difference to Equation 9 is that the estimated demand is totalled over all zones, as the location of new housing has yet to be determined.

The housing demand thus estimated is allocated to vacant residential land by a multinomial logit model:

(8)

where Ckli(t,t+1) are new dwellings of type k built on land-use category l in zone i between t and t+1 and Lkli is the capacity of that vacant land for dwellings of type k. Lkli bears no time label as it is successively reduced during the simulation period by land uses with similar land requirements. The utility ukli(t) expresses the attractiveness of land-use category l in zone i for dwellings of housing type k:

(9)

where uki(t) is the attractiveness of zone i as a location for housing type k, ukl(t) is the attractiveness of land use-category l for housing type k, and u(ckli)(t) is the attractiveness of the land price of land-use category l in zone i in relation to the expected rent or price of the dwelling. The vk, wk and 1–vkwk are multiplicative weights adding up to unity. The component utilities are constructed similarly to the components of the housing utility uhki(t) (see Housing Market Submodel). Like all utilities used in the model, the ukli(t) remain unchanged during the simulation period as calculated at time t.

Dwellings built during a simulation period utilise land immediately, but become available to the housing market only in the subsequent period.


Price Adjustment

At the end of each simulation period housing prices and rents are adjusted to reflect changes in the composition of housing stock. Upgraded and new dwellings are more expensive than existing ones, so dwellings of a certain housing type become more expensive in zones with much building activity than in zones with little new housing construction.

Changes of housing prices and rents due to changes in demand are dealt with in the Housing Market Submodel, price increases through inflation in the Ageing Submodel. Prices or rents of industrial and commercial floorspace are not considered in the model.

Zonal land prices by land use category are adjusted as a function of the demand for land of that land use category in the zone in the period just completed, i.e. by the proportion of newly developed land of that category in the zone:

(10)

where plj(t) is land price per square metre of land use category l in zone j at time t, llj(t,t+1) is the amount of land of category j newly developed in zone l, and Llj(t) is the amount of developable land of that land use category in zone j at time t. The function f(.) is an S-shaped elasticity curve entered exogenously resulting in a reduction of land prices if no development took place in the period and a price increase if the rate of development was high. In built-up inner-city zones with little or no developable land a similar function of the proportion of redevelopment is used. No attempt is made to determine equilibrium land prices. The price adjustment model reflects price adjustment behaviour by land owners. If they decrease or increase prices too much, this will become apparent and be corrected in the subsequent simulation period.




© 1998 Michael Wegener, IRPUD