A Simple Model of Housing Rental and Ownership with Policy Simulations

Coleman, Andrew; Scobie, Grant M. Working Paper A Simple Model of Housing Rental and Ownership with Policy Simulations New Zealand Treasury Working Paper, No. 09/05 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Coleman, Andrew; Scobie, Grant M. (2009) : A Simple Model of Housing Rental and Ownership with Policy Simulations, New Zealand Treasury Working Paper, No. 09/05, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205602 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ A Simple Model of Housing Rental and Ownership with Policy Simulations Andrew Coleman and Grant M. Scobie N EW Z EALAND T REASURY W ORKING P APER 09/05 D ECEMBER 2009 ii NZ TREASURY WORKING PAPER 09/05 A simple model of housing rental and ownership with policy simulations MONTH / YEAR December 2009 AUTHORS Andrew Coleman Motu Economic and Public Policy Research PO Box 24390 Wellington New Zealand Email Telephone Fax [email protected] +64 4 939-4250 +64 4 939-4251 Grant M. Scobie The Treasury PO Box 3724 Wellington New Zealand Email Telephone Fax [email protected] +64 4 471-5005 +64 4 473-1151 ACKNOWLEDGEMENTS The initial version of this paper was developed when both authors were affiliated with the House Prices Unit in the Department of Prime Minister and Cabinet in 2007. The authors are indebted to their colleagues in that unit and to Duncan Maclennan for useful comments. Particular thanks are due to Professor John Creedy of the University of Melbourne who made extensive suggestions to improve the paper. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz DISCLAIMER The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government. The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS iii Abstract The housing market is both large and complex. This paper develops a simple model that captures the essential features of the supply and demand for housing, and which is used to evaluate the impact of a range of policy interventions. Increases in the stock of housing would reduce rents and house prices. A reduction in tax concessions for landlords would raise rents and moderate house prices. Additional subsidies for owner-occupancy would tend to reduce rents and raise house prices. Significant reductions in rents and house prices would follow a fall in the cost of housing, through, for example lower regulatory and consent costs. Falling real interest rates result in lower rents, higher house prices and lower owner-occupancy rates. Despite the widespread attention owner-occupancy rates have attracted, the paper concludes that they are not a particularly helpful guide to the state of the housing market. Typically they are quite insensitive to policy interventions, a result that follows from the integrated view of both the rental and ownership market, adopted in this study. JEL CLASSIFICATION R21 Housing Demand R31 Housing Supply and Markets R38 Government Policies KEYWORDS Housing markets; New Zealand; rental and owneroccupancy; elasticities; rents; house prices; policy simulations WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS iv Table of Contents Abstract ............................................................................................................................. iii 1 Introduction .............................................................................................................. 1 2 Existing studies ........................................................................................................ 3 3 A graphical representation ...................................................................................... 4 4 The Model .................................................................................................................. 8 4.1 Demand to rent houses .................................................................................................. 8 4.2 Demand to own houses .................................................................................................. 9 4.3 Total demand for houses ................................................................................................ 9 4.4 Supply of houses for rent ..............................................................................................10 4.5 Total supply of houses ..................................................................................................10 5 Parameter estimates .............................................................................................. 13 6 Results .................................................................................................................... 14 6.1 An increase in housing supply ......................................................................................16 6.2 An increase in the tax concession to landlords ............................................................17 6.3 An increase in subsidies to owner-occupancy .............................................................17 6.4 Increase in the cost of constructing a house ................................................................18 6.5 Increase in real interest rates .......................................................................................18 7 Sensitivity to changes in the underlying assumptions ...................................... 20 8 Conclusions ............................................................................................................ 23 References ....................................................................................................................... 26 Appendices ...................................................................................................................... 27 Appendix A: Signs of the elasticities .......................................................................................27 Appendix B: Derivation of the values of key elasticities..........................................................28 List of Tables Table 1: Values assigned to the basic parameters of the model .....................................................13 Table 2: Description of the changes in the policy simulations .........................................................14 Table 3: Estimated responses of rents, house prices and quantities ..............................................15 Table 4: The responses of prices and quantities in the housing market following a 10% increase in the tax concession to landlords under a range of values for the elasticity of demand for property with respect to the price of rents ...................................21 Table 5: The responses of prices and quantities in the housing market following a 10% increase in the tax concession to landlords under a range of values for the elasticity of supply of rental housing with respect to the return to landlords .....................22 List of Figures Figure 1: Prices and quantities in the housing market ........................................................................ 5 Figure 2: The effect of a policy change on the housing market .......................................................... 6 Figure 3: The effect of a policy change on the housing market (contd.) ............................................. 7 WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 1 A Simple Model of Housing Rental and Ownership with Policy Simulations 1 Introduction The housing market is large. In most countries it is a key component of investment and consumption expenditure. In New Zealand, residential houses are a significant part of total infrastructure and residential investment is typically over a quarter of capital formation. Rent paid to landlords is 5 to 6% of household expenditure, while imputed rent on owner occupied houses comprises 6 to 7% of household income.1 It is a complex market. Residential houses are long-lasting durable goods whose value is large compared to income. Their expense and durability means a house is not usually paid for in full at the time of purchase. Rather, houses are leased or paid off over long periods of time using sophisticated financial instruments. For this reason, private landlords have an unusually large role in the market: in New Zealand, approximately 30% of houses are rented. In addition, bank lending is dominated by advances against mortgages and housing features prominently in the retirement saving of many households. The market is further complicated because a set of wide-ranging government interventions influence the decisions of owner-occupiers and private landlords. In most countries governments play a major role through their investment in and ownership of public housing, their involvement in financial markets, and through significant interventions via the taxation system and welfare programmes. New Zealand is no exception. Furthermore, monetary policy is sometimes conducted with a conscious focus on outcomes in the housing market.2 The complexity of the market means it is difficult to analyse the effect of different policy interventions without a model. A model is needed because the long run responses to policy changes involve a number of feedback loops. For example, an increase in the 1 Between 2003 and 2007, residential housing comprised between 47 and 49 of the capital stock, and residential investment was 27-29 percent of gross capital formation. Imputed rent was 6-7 percent of total disposable income. 2 See for example Alan Bollard and Chris Hunt (2008) “Coping with shocks - A New Zealand perspective.” A background paper prepared for an address to the Canterbury Employers’ Chamber of Commerce, Christchurch, 25 January. http://www.rbnz.govt.nz/speeches/3208927.html WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 2 number of new dwellings will increase the total stock of housing and result in lower prices (everything else equal). Lower house prices will mean that some existing renters will be able to purchase a house, leading to an increase in the rate of owner occupied housing. However, potential investors in rental properties will also face lower house prices, and will find further investment profitable at existing rents. This will drive down rents, leading to a decrease in the owner-occupancy rate as new households form. The net effect on the owner-occupancy rate is ambiguous. In general, the overall effect on various housing market variables can only be assessed using a consistent analytical framework, incorporating estimates of the essential behavioural parameters. To date, models that simultaneously capture the incentives facing home-owners, landlords, and developers have been large and extremely complicated. The principal aim of this paper is to develop a simple model that, while abstracting from much of the complexity, captures the essential dual nature of housing as both a consumption good and an investment good. The model incorporates owner-occupiers, a rental sector, and a construction sector. The second aim of the paper is to analyse the effects of different policy options. Examples include policies that lower the marginal costs of housing (eg, through changes to regulation of land use, consent processes and building codes); policies that support the demand for housing (eg, housing related welfare payments); policies that influence the demand for home ownership through taxes and subsidies (eg, changes in the taxation of investment income from rental housing); and policies that change the cost of mortgage finance. The model is used to simulate how house prices, rents, and the quantity of rented and owner occupied houses are affected by these different policy interventions. In turn, these variables can be used to calculate the owner-occupancy rate.3 In each case the long run (equilibrium) state of the housing market is calculated. The model is silent on the dynamic adjustment path that house prices might take in moving from one state to another in response to a policy change. The analytical approach developed here can be used to guide policy formation in two ways. First, it indicates the scale of the change in a policy instrument that may be needed to achieve a given target level of an outcome variable in the housing market. For example, a policy analyst might wish to ask how much new dwelling construction would be needed to generate a rise of five percentage points in the owner-occupancy rate. Secondly, it can provide insights into the confidence that can be placed on these estimates by indicating how the answers depend on the various parameters in the model. To this end, we show how some results are indeed sensitive to a range of values for key parameters. The paper is structured as follows. In the following section we provide a brief synoptic view of a selected section of the literature on modelling the housing sector. Section 3 presents a graphical representation while Section 4 sets out the formal derivation of the model. This is followed by a discussion of the parameterisation (Section 5) and the policy simulations (Section 6). After a consideration of the robustness of the findings (Section 7), the paper concludes with a discussion and conclusions (Section 8). Additional details of the modelling are presented in two appendices. 3 We adhere to the term “owner occupied” rate rather than the more commonly used home ownership rate. The latter must, by definition, always be 100% as all homes must be owned. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 3 2 Existing studies There is a vast literature on the economics of housing, and a wide range of models of the housing sector have been developed. These can be broadly characterised as models which focus on a particular aspect of the market (eg, the demand for rental housing, tenure, or hedonic price measures), and large scale, relatively complex, simulation models. Examples of the first type abound. Recent work includes models of the tenure choice of young households (Haurin, Hendershott et al 1996); models that incorporate spatial effects (Glaeser and Gyourko 2007); models of spatial and temporal influences on house price formation (Hwang and Quigley 2008); models that measure demand responses (Khaled and Lattimore 2008); models of the impact of the taxation of landlords (Wood and Kemp 2003); and models of the effect of supply restrictions (Grimes and Aitken 2004, 2006). A number of large scale simulation models have been built. Notable among these are Meen and Andrew (2008) for the UK, and Wood, Watson et al (2003) for Australia. The UK model allows for population growth, different types of households, household formation, tenure choice, interregional migration, housing supply and earnings. The model can be used to simulate the effect of changes in policies such as an increase in the supply of land for new construction. The Australian Housing Market Microsimulation (AHMM) model captures the housing supply and demand decisions of consumers and investors and allows for the effect of taxation. Policies such as a grant to first home buyers or changes to the depreciation allowances for new construction can be assessed for their impact on tenure choice and home ownership rates. The model captures the effect of government interventions on incomes, costs and prices paid by decision makers on both the demand and supply side of the housing market. Like these large models, the model in this paper is designed to capture the fundamental economics of the housing market. By allowing for a range of feedback effects, it allows the analysis of the impact of policy changes or other externally imposed shocks on the long run level of prices and quantities. The model provides a more general and integrated view of the housing market than many other “single issue” models, while avoiding the very substantial resource costs of building and maintaining a large scale simulation model. The model is most closely related to small scale models of the housing sector that incorporate renters and owners. An example is the paper by Abelson and Joyeux (2007). They developed a model that specifically addressed the effect of taxes and subsidies in the housing market, recognising both an ownership and rental sector. However, their model does not allow for the full range of feedback effects from an initial exogenous shock. For example, they do not allow for shifts in the demand for owner occupied houses when they analyse the effect of a tax or subsidy to investors in rental property, nor do they permit the total supply of housing to vary. The model we develop here relaxes these restrictions and allows for a full range of feedback effects from any exogenous change in the housing market. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 4 3 A graphical representation In Figure 1 we provide a four quadrant graphical representation of the basic relationships. This particular form allows us to represent simultaneously the four key endogenous variables of interest: the price of houses, H P, rents R P, the quantity of rental houses, R Q, and the total quantity of houses, T Q. We assume all houses are identical so that there is a single price of housing and a single rental rate. Clearly this assumption is counterfactual. Nonetheless, it may not be as restrictive as it first seems. Many of the results derived using these assumptions can be interpreted as the demand for standardised housing units which have incorporated an adjustment for quality. Floor area would be one such simple adjustment. A convenient starting point is in the north-east quadrant where we depict the supply of rental housing () R S and the demand for rental housing () R D as functions of the rent. Both these relationships are drawn for an initial price of houses (denoted 0 H P). As we show subsequently, changes in the price of houses will result in shifts in the demand and supply of rental housing, as distinct from movements along the demand and supply curves. In addition, the supply function for rental housing has as arguments real interest rates ()r and taxes on income derived from rental property ()t. The demand function for rental property has as shifters the real interest rate ()r, real incomes ()Y and a variable to capture the effect of subsidies to owner-occupancy () τ , the total demand. The downward sloping rental demand curve () R D comes about through three distinct effects. In the first instance, a rise in rents will encourage renters to economise on rental space by having more individuals share a dwelling; this is an “intensification effect”. Second, higher rents will slow down the rate at which new households form and enter the rental market; this is a “formation effect”. Treating household formation as endogenous is critical to developing a full understanding of the effect of policy changes (Börsch-Supan 1986). Finally there is a “substitution effect”: as rents rise for a given price of houses, some existing renters will choose to become home owners. To satisfy the long run equilibrium market clearing condition in the rental market, the quantity of houses demanded for rental must be equal to the total quantity of rental housing supplied by investors. The intersection of the supply and demand curves for rental housing simultaneously sets the market clearing rent (denoted 0R P), and the quantity of rental housing () R Q. The demand curve T Din the north-east quadrant represents the total demand for housing. The curve traces out the demand for housing as rent varies, for a fixed level of house prices. The demand for housing is made up of the demand by renters and the demand by home owners. It is deliberately drawn steeper than the rental demand curve to reflect the way that substitution between renting and ownership is netted out at the level of total housing demand. The total demand for housing is also a function of the real interest rate ()r, real incomes ()Y, and subsidies to owner-occupancy () τ . The supply of housing is drawn as a function of house prices in the south-east quadrant, denoted () T SC, where C denotes costs of constructing additional housing units. For ease of illustration we will assume the supply of housing is initially fixed (ie, the supply curve is vertical at a given quantity). In the more general case, however, the supply of WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 11 Market clearing conditions There are two market clearing conditions. First, the supply of rental housing equals the demand for rental housing: 1(, ,,,,,) (, ,,,) (, ,,,)0 RH R R RRH RRH F P P trYG G S P P trY D P P Yr ττ =+ − = (6) Secondly, the total supply of housing equals the total demand for housing: 2(, ,,,,,) (,) (, ,,,)0 RH T T TH TRH FP P rYCG G S P C D P P Yr ττ =+ − = (7) In equilibrium, there is a pair of values of rent ( R P) and prices ( H P) that are consistent with equations (6) and (7). These values are functions of the sets of exogenous variables. We can write equations (6) and (7) as a system 1 2 (,) (,) 0 (,) FPx FPx FPx ⎡⎤ == ⎢⎥ ⎣⎦ (8) where R H P PP ⎡⎤ =⎢⎥ ⎣⎦ and x is a vector of the exogenous variables. The implicit function theorem can be used to derive the relationship between rents and prices and the exogenous variables: 1 1 2 RRRRRRHRH HTRTRTHTH F x Px SP DP SP DP F x Px SP DP SP DP −∂∂ ⎡⎤⎡ ⎤ ⎡ ⎤ ∂∂ ∂∂−∂∂ ∂∂−∂∂ =− ⎢⎥⎢ ⎥ ⎢ ⎥ ∂∂ ∂∂ ∂∂−∂∂ ∂∂−∂∂ ⎣ ⎦ ⎣⎦⎣ ⎦ (9) or 1[] x Px PFF − =− . Price effects of the exogenous variables Equation 10 describes the effect on prices and rents of changes in the level of government ownership ( R G and T G), taxes on landlords ()t, home-owner subsidies () τ , construction costs ()C, interest rates ()r, and income ()Y. [] 1100 010 RRRT R R R R R HRHT H H H H H RR RRR PTT T T PGPG PtP PCPrPY PGPG PtP PCPrPY St D SrDr DY FDSC Dr DY τ τ τ τ − ⎡⎤ ∂∂∂∂ ∂∂∂∂∂∂ ∂∂∂∂= ⎢⎥ ∂∂∂∂ ∂∂∂∂∂∂∂∂∂∂ ⎣⎦ ⎡⎤ ∂∂−∂ ∂ ∂∂−∂ ∂−∂ ∂ −⎢⎥ −∂ ∂ ∂ ∂ −∂ ∂ −∂ ∂ ⎣⎦ (10) Note that in the short run 0 T SC∂∂= . WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 12 These derivatives can be converted into elasticities. Noting that s x S Sx x ε ∂∂= , then () () () () () () () ( ) ()() () RR H TR T H R R R SR DR R H SR DR pr pr ph ph pT R DT T H ST DT pr ph ph SR DR SR DR QQ Ppr pr ph ph QP Q TH DT ST DT Ppr ph ph P QP QP FQP QP QP εε εε εεε εε εε εεε ⎡⎤ −− =⎢⎥ −− ⎢⎥ ⎣⎦ ⎡⎤ −− ⎢⎥ =⎢⎥ −− ⎣⎦ or (/)[] TH pp FQPE= (11) Let R T QQQ α = be the fraction of houses that are rented (approximately 0.3); H R PPP α =be the ratio of house prices to rents (approximately 20); and T T GGQ α =be the fraction of houses owned by the government (approximately 0.05). Then equation (10) can be converted into elasticities as follows: 100() 0 0 PR P PR P PR P PR P PR P PR P PR P GR GT t C r Y PH PH PH PH PH PH PH GR GT t C r Y Q SR Q DR Q SR DR Q DR GtrrY pGDTSTDTDT Cr Y E τ τ τ τ εαεαεαεαεαεαεα εεεεεεε αε αε α ε ε αε α αεεεε − ⎡⎤ = ⎢⎥ ⎣⎦ ⎡ ⎤ −−− ⎡⎤ − ⎢ ⎥ ⎣⎦ −−− ⎣ ⎦ (12) Appendix A sets out the predicted signs of the elasticities of rents () R P and house prices () H P with respect to the exogenous variables. The response of rents and house prices to changes in incomes, taxes, interest rates, subsidies, construction costs and the quantity of government owned houses can be calculated using equations (8) to (12). To do this, however, we must first establish values for the elasticities involved on the right hand side of these equations. Estimates are presented in the next section. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 13 5 Parameter estimates Table 1 displays the assumed values of the underlying elasticities. The first entry is for the elasticity of supply of rental housing with respect to the price of rents (denoted in equation (12) as SR pr ε ). It has been assigned a value of 1, implying that a 10% increase in the price of rents would induce a 10% increase in the supply of rental housing. The values in the table should be taken as reasonable “guesstimates” consistent with the literature on housing.7 In Section 7 we illustrate the extent to which our results are sensitive to changes in the values of these parameters. The elasticities of the total demand for housing with respect to rents and house prices are assumed to be small, -0.2 and –0.1 respectively. The latter value implies a 10% increase in house prices reduces total demand for housing by 1%. While these numbers are small, they appear broadly consistent with New Zealand macroeconomic data, for over the last four decades New Zealand has experienced large variations in real house prices but only very small changes in per capita housing stocks (see the discussion in Appendix B). These elasticities are smaller than estimates for New Zealand recently made by Khaled and Lattimore (2008) using household budget data. Their estimate of the own price elasticity of demand for housing is -0.44. It is not entirely clear how to reconcile these numbers. However, in our model there is no allowance for quality changes, whereas the actual data used by Khaled and Lattimore will capture how price changes lead to changes in the size of houses, or to improvements to existing houses. In contrast, our elasticity only refers to the number of houses. Table 1: Values assigned to the basic parameters of the model With respect to… Elasticity of… Supply of rental housing Demand for rental housing Total demand for housing Total supply of housing Rent 1.0 -2.0 -0.2 House price -1.0 1.0 -0.1 0 or 0.5 or ∞ Tax concession to landlords -1.0 Subsidy to ownership -1.0 0.1 Interest rate -1.0 1.0 -0.1 7 For a summary of empirical studies that estimate a range of elasticities for OECD countries see(Girouard, Kennedy et al 2006). WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 14 6 Results Using the baseline set of elasticity assumptions set out in Table 1, we calculate the response of rents, house prices, and the quantity of houses to five different policy changes or shocks to the housing market. In addition, we calculate the new owneroccupancy rate. (The owner-occupancy rate is always equal to 70% before the shock.) Table 2: Description of the changes in the policy simulations Exogenous variables changed in the policy simulations Description of the change A. A 0.5% change in the stock of housing A 0.5% increase in the total stock of housing is equivalent to a 10% increase in the stock of government owned housing, or 7,500 houses. B. A 10% change in the tax concession for landlords ( t) The subsidy to landlords is made up principally of the non-taxation of capital gains, estimated as 1.5% of the value of the house per annum. This is about 30% of the assumed total real return to landlords of 5.0%. A 10% increase would imply this rises by 0.15% from 1.5 to 1.65%. so total returns would increase to 5.15%, equivalent to a 3% increase in total returns.(a) C. A 10% change in the subsidies to owneroccupancy ( τ ) Total subsidies to home owners, comprising principally of the non-taxation of imputed rents, increase by 10%. This is computed as the product of the average owner’s equity share and the marginal rate of tax, giving an initial estimate of 16% of the cost of financing. A 10% increase in the subsidy implies a rise from 16.0 to 17.6%.(a) D. A 10% change in the cost of constructing houses ( C) The cost of building a house, including the land, increases by 10%. E. A 10% change in the mortgage interest rate (r) The mortgage interest rate increase by 10%; for example from 8.0 to 8.8%. (a) See Appendix B for further details Each shock represents a 10% change in one of the exogenous variables. The shocks are changes in (i) the stock of housing, (ii) the tax concession to landlords, (iii) the subsidies to owner-occupancy, (iv) the cost of constructing a house, and (v) the interest rate. The description of each of the changes is given in Table 2. The results, set out in Table 3, are calculated for three values of the housing supply elasticity that reflect three ways that the supply of housing could respond to an increase in house prices. In the first case, it is assumed that the elasticity equals zero, and total supply of housing is fixed. This corresponds to the short run (1 to 2 years), when it is assumed that there is no significant change in the total supply due to lags in the planning, consenting and building process. In the second case, the elasticity is 0.5. This corresponds to the medium term, when there is a supply response to a price increase. In the third case the elasticity is infinity. This corresponds to the long run, when any change in demand is met by sufficient additional supply to hold prices constant. In this case the price of houses is only determined by the cost of land and construction costs. The cases of inelastic supply (the very short run) and infinitely elastic supply (the very long run) can be regarded as the bounds on the responses of rents and house prices to economic shocks. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 15 Table 3: Estimated responses of rents, house prices and quantities Percentage change in a specified variable: Responsiveness of the total supply of housing to changes in house prices (The elasticity of total housing supply with respect to the price of houses) Short run (1-2 years) 0 (fixed supply) Medium term (3-5 years) 0.5 (intermediate case) Long run (>5 years) ∞ (infinitely elastic) A. The response to an increase in the stock of housing Rents -1.3 -0.4 0.0 House prices -2.3 -0.7 0.0 Quantity of rental units 0.3 0.1 0.0 Quantity of total housing 0.5 0.2 0.0 Resulting rate of owner-occupancy 70.05 70.02 70.00 B. The response to an increase in the tax concession to landlords Rents -0.3 -0.5 -0.6 House prices 0.6 0.2 0.0 Quantity of rental units 1.19 1.25 1.28 Quantity of total housing 0.00 0.09 0.13 Resulting rate of owner-occupancy 69.64 69.65 69.66 C. The response to an increase in the subsidy to owner-occupancy Rents 0.1 -0.5 -0.85 House prices 1.7 0.5 0.0 Quantity of rental units -0.55 -0.38 -0.30 Quantity of total housing 0.0 0.26 0.37 Resulting rate of owner-occupancy 70.17 70.19 70.20 D. The response to an increase in the cost of constructing a house Rents 0.0 4.0 5.7 House prices 0.0 7.1 10.0 Quantity of rental units 0.0 -1.04 -1.49 Quantity of total housing 0.0 -1.50 -2.15 Resulting rate of owner-occupancy 70.0 69.65 69.76 E. The response to an increase in real interest rates Rents 0.3 4.6 6.4 House prices -10.6 -3.2 0.0 Quantity of rental units -1.19 -2.29 -2.77 Quantity of total housing 0.0 -1.59 -2.28 Resulting rate of owner-occupancy 70.36 70.21 70.15 The three cases for the elasticity of supply do not imply a dynamic response in the sense that the market would evolve through these stages if a shock occurred. Rather, the model is based on comparative static positions. The results for the inelastic supply case give the equilibrium values of the endogenous variables (prices and quantities) that would occur in the long run if the supply were inelastic. The same equilibrium interpretation is appropriate for the other two cases we present. Provided this caveat is kept in mind it will be convenient to refer to the three cases as the short, medium and long run. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 16 The results are used to calculate the size of the policy change or shock that is necessary to increase the owner-occupancy rate by 1 percentage point in the medium term. In some cases, the results appear quite fanciful, because some policies have only tiny effects on the owner-occupancy rate even though they can have large effects on other aspects of the housing market such as the total quantity of housing. These results suggest that the owner-occupancy rate is, in many respects, a poor indicator of the welfare consequence of housing policies. 6.1 An increase in housing supply Section A of Table 3 shows the effects of the government increasing the total stock of housing by 0.5%, equivalent to about 7,500 additional houses, or 10% of the government stock. In the short run, the increased stock of houses would reduce rents and house prices by an estimated 1.3% and 2.3% respectively (see the top left hand cells of Table 3) thus improving affordability for both buyers and renters, other things constant. In contrast, in the long run case (with perfectly elastic supply) the government building programme has no effect on prices or quantities as the public investment merely crowds out private investment and the total supply of housing is unchanged (see the third column of Table 3). Only the relative proportions of public and privately constructed housing are altered. In the medium term, the increase in the stock of housing has very little effect on the owner-occupancy rate: it increases from 70 to 70.02%. The increase is tiny for two reasons. First, there is an offsetting reduction in private sector construction, so that the total stock of houses increases by less than the number of houses the government builds. Second, rents as well as house prices fall, so many of the new houses are occupied by tenants as the low rents induce new households to form. These figures suggest that to increase the owner-occupancy rate by 1% it would be necessary for the government to build houses equal to 25% of the initial stock (375,000 houses) - a clearly fanciful number. If it were to do this, rents would fall by 20%, house prices would fall by 35%, the number of rental units would increase by 5%, and the total stock of houses would increase by 10%. Put another way, a building programme of this size would have enormous effects on the housing market, but very little effect on the owner-occupancy rate. The owneroccupancy rate is the wrong way of measuring the impact of this policy, because it misses the extent to which the number of households increases to take advantage of the lower rents and house prices. A variant of this scenario is for the government to build the additional houses and then retain them as rental units.8 This would be equivalent to the case where the Housing New Zealand Corporation owned and managed an increased stock of social housing. The short run increase in the supply of rental housing would result in a fall in rents of 1.6% (in contrast to the initial case of 1.3%), and a fall in house prices of 1.6% (instead of 2.3%). In other words, the drop in house prices is moderated in the event these units are not put up for sale to the private sector. In the long run case there is still no effect on rents and prices but the additional rental properties owned by the government would, other things equal, lower the owner-occupancy rate. 8 These results, not reported in detail here, are available on request. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 17 6.2 An increase in the tax concession to landlords Under the existing tax regime, there are two principal concessions made to landlords. In the first instance, landlords typically do not pay tax on capital appreciation. If there is inflation, investors in leased residential property have a tax advantage over investors who simply invest in interest-bearing accounts, in which the inflation component of interest earnings is subject to tax. When the inflation rate is 3%, this tax advantage is worth 1.5% of the value of the property. This has the effect of making investment in rental property more attractive than would otherwise be the case. Furthermore, those who have some debt financing have the opportunity to reduce their tax liability by offsetting any interest payments associated with the rental property against other sources of income. A 10% increase in tax concessions to landlords is worth 0.15% of the value of the property (ie, 10% of 1.5%). If the total real return to property investors (rent plus capital appreciation) is assumed to be 5% in the long run, the increase in the tax concession increases the total yield by 3%, from 5 to 5.15%. In the short run, an increase in the tax concession received by landlords leads to a 1.2% increase in the quantity of properties for rent, lowering rents by 0.3% and increasing house prices by 0.6%. In the long run, the quantity of properties for rent increases by a similar amount, but house prices are unchanged and rents fall by 0.6%. In all cases the effect of increasing the tax concession is to shift the tenure mix towards a lower proportion of owner-occupancy and a higher proportion of renting. In the medium term scenario, the effect of the increase in the tax concession is to lower the owner-occupancy rate from 70 to 69.65%. These figures suggest that it would be necessary to reduce the size of the tax concession by 29% in order to increase the owner-occupancy rate by 1% in the medium term, that is from 1.5% of the value of the property to 1.1% of the value of the property, or by approximately $1,200 per year per property. A reduction of this size could be achieved by increasing the amount of tax paid by landlords or by lowering the inflation rate from 3% per annum to 2%. If the tax concession was reduced by this amount, rents would increase by 1.5%, house prices would decrease by 0.6%, the quantity of rented homes would decline by 3.6%, and the total quantity of houses would decline by 0.25%, equivalent to some 4,000 houses. The increase in owner-occupancy rates and the increase in the welfare of those who buy would therefore come at the expense of a decrease in the welfare of those who rent. The results in the long run case are similar except house prices do not decrease. 6.3 An increase in subsidies to owner-occupancy There is an extensive range of subsidies to home ownership, both indirect and explicit. Indirect subsidies are delivered by the tax system through the exemption of imputed rents from taxation (although the inability to deduct mortgage-interest payments has to be set against this). The government offers inducements to home ownership through such programmes as Welcome Home, a recently introduced shared equity scheme (essentially an interest-free second mortgage) and through the first home deposit subsidies for eligible households linked to KiwiSaver. We estimate these subsidies reduce the financing cost of owning a home (the real interest rate multiplied by the price of a house) by 16%, or approximately $2,500 per year.9 A 10% increase in the value of the subsidies (compared 9 At 5% real interest rates, the financing cost of owning a $300,000 home is $15,000 per year. $2,500 is 16% of this amount. The benefit disproportionately goes to those who own their own home outright. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 18 with no subsidies) therefore reduces the financing cost of owning a home by 17.6% (ie, 16% * 1.1). In the short run a 10% increase in the subsidy will increase the demand for housing, and house prices will be driven up, by 1.7%. In effect, a part of any subsidy is capitalised into house prices. The higher house prices lead to a modest increase in rents, by 0.1%, and a 0.55% decline in the quantity of rented housing. The net effect is to raise the rate of owner-occupancy from 70 to 70.17%. In the long run, there is no effect on house prices, as more houses are constructed in response to the higher demand. In this case, the ownership subsidies lead to a 0.85% reduction in rents (due to the lower demand), and a 0.13% increase in the total quantity of housing. The effect on the owner-occupancy rate is similar to the short run case. These figures imply that to increase the owner-occupancy rate by 1% in the medium term, it would be necessary to increase the subsidy to home-owners by 53%. This would be equivalent to approximately $1,250 per owner-occupier household per year. This would have the additional effect of lowering rents by 2.6%, increasing house prices by 2.6%, lowering the quantity of rental accommodation by 2%, and increasing the total quantity of houses by 1.4%. The results in the perfectly elastic case are similar, except there is no change in house prices and a larger increase in the housing stock. 6.4 Increase in the cost of constructing a house The cost of a house reflects three major components: the land, the materials and labour input, and the costs of the regulatory regime and consent process. Suppose there is a 10% increase in the cost of a house from any one (or combination) of these elements. In the short run, with an inelastic supply, there is no impact on the housing market. In the medium and longer terms however, house prices rise; in the extreme case they simply rise by the full 10% of the cost increase. Rents also rise, by up to 5.7%. The combined effect of an increase in building costs is to reduce the quantity of rented houses by more than 1% and the total quantity of houses by more than 1.5%. The owner-occupancy rate falls. This model suggests it would be necessary to reduce building costs by 29% in order to increase the owner-occupancy rate by 1% in the medium term. This would have the additional effects of lowering rents by 11%, reducing house prices by 22%, increasing the quantity of rental accommodation by 3%, and increasing the total quantity of houses by 4%. The results in the perfectly elastic case are qualitatively similar, except there is a larger change in house prices and a larger increase in the housing stock. This is the only policy that simultaneously reduces rents and house prices, increases the quantity of housing and raises owner-occupancy rates. 6.5 Increase in real interest rates The final case corresponds to a 10% increase in mortgage interest rates. This increases the financing costs of home purchase and reduces demand. In the short run house prices fall by 10.6% and rents increase marginally. This fall is moderated in the medium term, and in the case of an infinitely elastic supply of housing there is no price adjustment, but rents increase by 6%. The total quantity of housing declines by more than 1.5% but the owneroccupancy rate increases. Higher real interest rates then are typically associated with a combination of a fall in house prices, higher rents and a rise in owner-occupancy rates. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 19 These figures suggest that to increase the owner-occupancy rate by 1% in the medium term, real interest rates would need to increase by 48%. This would have the additional effects of increasing rents by 22%, reducing house prices by 15%, reducing the quantity of rental accommodation by 11%, and reducing the total quantity of houses by 8%. Thus an increase in interest rates will raise owner-occupancy rates, but at the expense of sharply reducing the quantity of housing. In this regard, it is instructive to recall the period from the late 1980s until 2005. Real interest rates fell from over 10% to under 5%; ie, a 50% reduction. The current model predicts that such a change would be accompanied by a substantial increase in real house prices, a construction boom, a fall in rents and a drop in home ownership rates. These outcomes were exactly those observed over this period. Table 3 indicates that the effect of interest rates on the housing market is very different in the short run and the long run. In the short run, a decline in interest rates leads to a large increase in house prices, and little change in rents, whereas in the medium term and long term there is only a small effect on house prices but a large expansion in the quantity of housing and a significant decline in rents. By most welfare metrics except the owneroccupancy rate, low interest rates are much better for the housing market than high interest rates. The transition from a high interest rate environment to a low interest rate environment can be difficult to manage, however, because of the tendency for house prices to overshoot in the short run (Coleman and Landon-Lane 2007). WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 20 7 Sensitivity to changes in the underlying assumptions To this point the results have been based on the basic set of parameters assumed in Table 1. Inevitably, one never has precise estimates of these parameters. It is therefore prudent to explore the extent to which the results are robust to changes in the underlying parameters. Models of the type developed here are more useful for policy analysis if the results hold broadly across a range of possible values for the key parameters. The sensitivity of the model’s results to a wide range of parameters was tested. In order to explore a substantial change, we varied five of the key parameters over a wide range, assigning four values to each. We then re-estimated the changes in each of the five endogenous variables to each of the five shocks. In each case we computed the responses for the three values of the supply elasticity of housing, corresponding to the short, medium and long run cases. The results in Section 6 remained remarkably consistent across this extensive range of alternative assumptions about the values of the underlying parameters.10 For example, consider Table 4, which shows the effect of varying the elasticity of the demand for housing with respect to rents (denoted D T pr ε ) when there is an increase in the tax concession to landlords. As this elasticity varied from -0.05 to -0.40, rents declined by between 0.48 and 0.59%; house prices rose by between 0.16 and 0.20%; and there was virtually no variation in the change in the number of houses in response to the increased tax concessions. However, in contrast to this robustness, a notable exception was the response to changes in the elasticity of supply of rental property with respect to the real rate of return to landlords. This term (denoted as SR φ ε ), describes how the quantity of rental property supplied by landlords responds to changes in the real rate of return.11 To illustrate: if the long run real return to investors were to increase from 4% to 5% (a 25% increase), and this were to result in a 12.5% increase in the supply of rental property, the value of this elasticity would be 0.5 (=12.5/25). Table 5 presents the changes in prices and quantities following a 10% increase in the tax concession to landlords (raising their overall yield from 5 to 5.15%). The results are given for four values of the elasticity of rental supply with respect to the real pre-tax return to investors: 0.25, 0.5, 1.0 and 2.0. The base case, used in Table 3, is 0.5. To illustrate, consider the first block in Table 5 which indicates the amount by which rents would fall given a 10% increase in the tax concession to investors.12 The top left hand cell contains the value -0.17. This means that if the elasticity of rental supply (denoted SR φ ε ) were 0.25, and if the pre-tax real return were to be raised by 10% as a result of an increase in the tax concessions, rents would fall in the short run by 0.17%.13 Looking 10 Results are available on request. 11 Full details of this key elasticity are developed in Appendix B. 12 Alternatively, these results can be read as the amount by which rents would rise if the tax concessions to landlords were to be curtailed such that their real pre-tax returns fell by 10%. This simply involves reversing the sign on the responses shown in the body of the table. 13 Alternatively, a reduction in the tax concessions would lead to a rise in rents of this amount (ie =0.17%). WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 27 Appendices Appendix A: Signs of the elasticities This appendix sets out the predicted signs of the elasticities of rents () R P and house prices () H P with respect to the five exogenous variables: income ()Y, taxes ()t, interest rate ()r, subsidies () τ and construction costs ()C. Consider the matrix () p Efrom equation (4). Given our assumptions, ()() () QP SR DR Q SR DR pr pr ph ph pPDT ST DT pr ph ph E αα ε ε α ε ε αε ε ε ⎡⎤ −− =⎢⎥ −− ⎢⎥ ⎣⎦ has signs +− ⎡ ⎤ ⎢ ⎥ ++ ⎣ ⎦and det( ) p E is positive. It follows that 1()() 1 () det( ) ST DT Q SR DR ph ph ph ph pPDT Q P SR DR ppr pr pr EE εε αεε αε αα ε ε −⎡⎤ −−− =⎢⎥ +− ⎢⎥ ⎣⎦ has signs ++ ⎡ ⎤ ⎢ ⎥ −+ ⎣ ⎦. The signs of the derivatives in equation 4: If QDR Y DT Y αε ε ⎡⎤ − ⎢⎥ − ⎣⎦ has signs ambiguous ⎡⎤ ⎢⎥ − ⎣⎦ then PR t PH t ambiguous ambiguous ε ε ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ (A1) If 0 QSR t αε ⎡⎤ ⎢⎥ ⎣⎦ has signs 0 − ⎡⎤ ⎢⎥ ⎣⎦ then 0 0 PR t PH t ε ε ⎡ ⎤ > ⎢ ⎥ < ⎣ ⎦ (A2) If () QSR DR rr DT r αε ε ε ⎡⎤ − ⎢⎥ − ⎣⎦ has signs − ⎡⎤ ⎢⎥ + ⎣⎦ then 0 PR r PH r ambiguous ε ε ⎡ ⎤ ⎢ ⎥ < ⎣ ⎦ (A3) If QDR DT τ τ αε ε ⎡⎤ − ⎢⎥ − ⎣⎦ has signs + ⎡⎤ ⎢⎥ − ⎣⎦ then 0 PR PH ambiguous τ τ ε ε ⎡ ⎤ ⎢ ⎥ > ⎣ ⎦ (A4) If 0 s T C ε ⎡⎤ ⎢⎥ ⎣⎦ has signs 0 ⎡⎤ ⎢⎥ + ⎣⎦ then 0 0 PR C PH C ε ε ⎡ ⎤ > ⎢ ⎥ > ⎣ ⎦ (A5) WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 28 Appendix B: Derivation of the values of key elasticities (1) The elasticity of supply of rental property (a) Preliminaries The first step in calculating the elasticity of supply of rental property with respect to rents, house prices, and taxes is to calculate how the supply of rental property varies with the pre-tax real rate of return. The pre-tax rate of return depends on the rent (after costs such as insurance and rates), the capital appreciation on a property, and the tax arrangements. We define a pre-tax-equivalent return for a particular after-tax return as the pre-tax return that would generate that after-tax return if income tax were paid on the full return. This is derived below. Let: H P = the price of a rental house; R P = the rent on a leased house; rRH p PP== rent as a fraction of the house price; π = the rate of property appreciation, which is untaxed; m = the income tax rate; t = the pre-tax value of the tax concession of not taxing property appreciation; Φ = annual pre-tax equivalent return from owning a rental property, in dollars; φ = annual pre-tax equivalent return from owning a rental property, in percentage terms. The after-tax return to a property investment is [(1 ) ] rH p mP π −+ Let (1 )tm m π =− be the pre-tax value of the tax concession that comes from not taxing the capital appreciation on property. Then [(1)] [ ](1) rHr H p mPp tmP ππ −+ = ++ − (B.1) Consequently the pre-tax equivalent return is : rH r p tP pt π φπ ⎡⎤ Φ= + + ⎣⎦ ⎡⎤ =++ ⎣⎦ (B.2) Currently in New Zealand, 0.035 r p≈ , 0.03 π ≈, 0.33m=, and 0.015t≈. Thus the total pre-tax nominal return is approximately 8% (0.035 0.03 0.015)++ and the pre-tax real return is approximately 5% (8 ) π −. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 29 Let SR φ ε be the elasticity of rental supply with respect to the real rate of return: . R SR R Q Q φ φ εφ ∂ =∂. This is the key elasticity from which the others are calculated. Our baseline assumption is that 0.5 SR φ ε =. This means, for example, that a one percentage point increase in the real rate of return from 5 to 6% increases the quantity of rentals by 10%. We judge that a reasonable range for this parameter is 0.25 1 SR φ ε ≤≤ , implying a one percentage point increase in the expected real rate of return raises the quantity of rentals by between 5 and 20%. (b) The elasticities of rental supply with respect to various prices (i) Elasticity of rental supply with respect to rent The elasticity with respect to the rent R P is calculated as follows: 1 ..... RR R R R R r SR SR pr RR RR H R QP Q P Q P p PQ PQ P Q φ φφ εε φφφφ ∂∂∂∂ == = = ∂∂∂∂ (B.3) In the above parameterization, 0.035 r p= and 0.05 φ =, so 0.7 SR sr pr φ εε ≈. (ii) Elasticity of rental supply with respect to tax The elasticity with respect to the tax concession t is calculated as follows: .... RR R SR SR tRRR Qt Q t Q tt tQ tQ Q φ φφ εε φφφφ ∂∂∂∂ == = = ∂∂∂∂ (B.4) In the above parameterization, 0.015t≈ and 0.05 φ =, so 0.3 SR SR t φ εε ≈. (iii) Elasticity of rental supply with respect to interest rates We assume that the elasticity with respect to interest rates is equal but opposite in sign to the elasticity with respect to the rate of return on property: SR SR r φ εε =− . (iv) Elasticity of rental supply with respect to house prices The elasticity of rental supply with respect to house prices is complicated. For a given rental income, an increase in house prices lowers the rate of return. However, if the property continues to appreciate at the inflation rate π, a 1% increase in house prices will not lead to a 1% decrease in the total rate of return. Rather, the total return will have only decreased by the ratio r p φ : ... RH R H r SR SR ph HR R H QP Q P p PQ Q P φ φφ εε φφφ ⎛⎞⎛⎞ ∂∂∂ == =− ⎜⎟⎜⎟ ∂∂∂ ⎝⎠⎝⎠ (B.5) as () RH PP t φπ =++and so 2 () H RH rH P PP pP φ ∂ ∂ =− =− . In the above parameterization, 0.035 r p= and 0.05 φ =, so 0.7 SR SR ph φ εε ≈− . WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 30 (2) The elasticity of demand to rent or own property for own use (a) Preliminaries We assume that the total demand for housing and the demand to live in rental housing depend on the rent charged and the after-subsidy cost of financing the purchase of a house, *h P. The latter can be thought of as the annual opportunity cost of purchasing a house at a price PH ; this is *(1 ) hH PrP τ =− . The demand functions can thus be written as * * (, ,) (, ,) DR R R h DT T R h QDPPX QDPPX = = (B.6) The key parameters to estimate that correspond to the first equation are the elasticity of the demand to rent housing with respect to the price of rent and the elasticity of the demand to rent housing with respect to the finance cost of housing. Denote the elasticity of the demand to rent with respect to the financing cost of housing *h Pas * D R ph ε . The elasticities with respect to τ , r, and H P are given by: ** * ** .. (1 ) RRhh D RDR ph Rh Rh DDPP QP QP τ τττ εε τττ ∂∂∂ − == = ∂∂∂ − (B.7) ** * ** .. RRhh D RDR rph Rh Rh Dr DPPr rQ P rQP εε ∂∂∂ == = ∂∂∂ (B.8) ** * ** .. Rh R hhh D RDR ph ph hR h hRh DP D PPP PQ P PQP εε ∂∂∂ == = ∂∂∂ (B.9) A similar derivation holds for the elasticities of the total demand for housing with respect to home-ownership subsidies, interest rates, and house prices. (b) Subsidies to home ownership The main subsidy or tax concession to home ownership in New Zealand occurs because imputed rent is not taxed, whereas interest and dividends from other sorts of capital are taxed. If one owns capital and is choosing whether to (a) rent a property and invest in interest and dividend earning assets or (b) purchase a property to live in, there is an incentive to purchase a property to live in because the imputed rent is not taxed. The subsidy in this case is the average tax rate on capital income. If one does not own capital and must borrow the purchase price, there is no advantage. The extent of the subsidy therefore depends on the extent to which property is owned outright. We use a value of 1/6 τ =. This is calculated by averaging the value of the subsidy across three groups: the third of households that own a house without a mortgage, the third of households that own a house with a mortgage, and the third of households that rent.14 In each case, we assume the average tax rate on capital income is 0.30. 14 Even though people who rent are not taking advantage of the subsidy, the subsidy affects their decision of whether to rent or buy. We include in this calculation the value of the subsidy to renters if they were to purchase. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 31 The first group is easiest to calculate, as they get the full tax concession. The tax concession for the other groups depends on the capital they have to contribute to the purchase of a house. We assume the average mortgage is half the value of the property for the group that has mortgages, and the average mortgage would be 90% of the value of the property for those that do not. This implies a value for 0.30*1/3(1+0.5+0.1) = 0.16 τ =. We round this to 1/6. We use the same parameter in the equation for the total demand for housing. (c) Demand elasticities with respect to rent and housing finance costs The data in Tables B.1 and B.2 summarise the evolution of property prices, rents, and the quantity of properties in New Zealand since 1991. The population figures and number of houses come from the census while the price and interest rate data are from the Reserve Bank of New Zealand. The interest rate is the average mortgage rate adjusted for the inflation rate.15 The data refer to the March quarter of each census year. The raw data are in Table B.1. In Table B.2, two adjustments are made to these data to aid comparability between years. First, the prices of houses and rents are deflated by the consumer price index. Second, the quantity of houses is adjusted for population. This is done by multiplying the number of houses in an earlier year t by the ratio of the 2006 population to the population in year t. Thus the table shows the number of houses that would have existed if the country had the 2006 population but same per capita ratios of houses. The data show that on a per capita basis the total number of houses increased by only 4% over the 15 year period. The number of rental units increased by 23%. Almost all of the latter increase took place between 1996 and 2001. During this period real house prices increased by 110%, while real mortgage rates declined by 60% . Thus the real financing cost of purchasing a house declined by 44% between 1991 and 2001 before increasing by 53% between 2001 and 2006. The fact that there was almost no change in the per capita quantity of houses demanded over the fifteen years despite these enormous variations in house prices and interest rates suggests that the elasticity of total housing demand with respect to the price of housing must be very small – probably less than 0.1. The data appear to be more informative about the effect of rents on the demand for rental property. Between 1996 and 2001 there was almost no change in real house prices, but a 9% decrease in real rents. Real mortgage rates declined from 8 to 5%, making home ownership somewhat more attractive. During this period the total number of houses (normalized for population) increased by 2%, while the number of rental houses increased 19%. If the main factor affecting the housing market was the 9% decrease in rents, the elasticity of rental houses with respect to rents would be 19/ ( 9) 2−≈− while the total elasticity with respect to rents would be 2/( 9) 0.2−≈− . Of course, as noted above, other things such as interest rates did change; however, they changed in a direction that would have made renting less attractive, suggesting these ballpark figures could underestimate the true elasticity. 15 The inflation rate is the average change in the CPI from the March quarter of the preceding year to the March quarter of the subsequent year. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 32 On the basis of the aggregate movements in house prices, rents, and housing quantities, it seems reasonable to postulate that 2 SR pr ε ≈− , 0.2 ST pr ε ≈− . The total demand elasticities are much more difficult to guess, given that the total quantity of houses per capita increased by about 1% every five years, despite a wide variation in house prices and interest rates. Nonetheless, these data are suggestive that the total demand elasticity with respect to house prices is small, perhaps -0.02 to -0.10. Table B.1: Number and price of houses in New Zealand, 1991-2006 Census Year Population Number of Houses CPI Rents House Prices (PH) Real interest rate (r) Rental Total ‘000 Index 1995=1000 % 1991 3,488 267 1177 924 808 812 11.7 1996 3,723 290 1268 1012 1069 1122 8.0 2001 3,876 359 1344 1091 1045 1212 5.2 2006 4,134 388 1454 1237 1173 2295 4.8 Source: Statistics New Zealand Census of Populations and Dwellings Table B.2: Number and price of houses in New Zealand, 1991-2006 (normalized) Census Year Number of Houses normalized to the population in 2006 Rent (r) House Prices (PH) rPH Rental ‘000 Total ‘000 Real indices 1995 =1000 1991 316 1395 874 878 1444 1996 322 1408 1056 1108 1249 2001 383 1433 958 1111 809 2006 388 1454 949 1855 1238 Source: Statistics New Zealand Census of Population and Dwellings; Reserve Bank of New Zealand (d) Trends in household formation and household size An important feature of the New Zealand housing market in the last forty years has been the declining size of the average household. The average number of people in each house declined steadily from 3.8 to 2.96 from 1966 to 1991, or by 1% per year. It declined a little further between 1991 and 2006 to 2.84. Several factors have been behind this trend. Amongst these has been a sharp decline in the average size of households with children, most notably a sharp decline in the number of families with three or more children. Between 1966 and 1991, the fraction of households with five or more people declined from 28 to 13%. Secondly, there has been a big increase in the number of households comprising a single person or a couple. Trends in the fraction of households of different size are shown in Table B.3. WP 09/05 A SIMPLE MODEL OF HOUSING RENTAL AND OWNERSHIP WITH POLICY SIMULATIONS 33 Table B.3: Distribution of households by size 1 person 2 people 1or 2 people 3-4 people 5+people 1966 12.5% 24.8% 37.3% 34.9% 27.8% 1971 14.1% 26.4% 40.5% 34.2% 25.3% 1976 15.6% 27.9% 43.5% 34.6% 21.9% 1981 18.4% 29.2% 47.7% 34.5% 17.8% 1986 19.4% 30.5% 50.0% 34.8% 15.2% 1991 20.2% 32.7% 52.9% 33.9% 13.2% 1996 20.8% 33.1% 54.0% 32.9% 13.1% 2001 22.9% 33.7% 56.6% 31.5% 12.0% Source: Statistics New Zealand Census of Population and Dwellings Changes in the average size of a household are a key aspect of the model, for total demand for housing changes in response to variation in rents and house prices only through changes in household formation. Excluding changes in the average size of a household that stem from a reduction in the average number of children, there are several ways that household formation might respond to prices: • older children change the time they leave their parents’ home; • the number of people living in households comprising unrelated people changes; in particular the number of people deciding to live by themselves as individuals or couples changes; • the number of families choosing to split up and form two households changes; • the number of families deciding to live in multiple family households changes; and • the number of older people choosing to move in with their children or into institutional housing changes. Aggregate census data suggest that the rising number of single households has been the most important factor since 1991. As Table B.4 indicates, there have only been small changes in the number of multiple family households and the number of “unrelated people” households. It is not clear why the total number of single family (including solo parent and couples) households has been declining, although the decline has been driven by falling numbers of households with four or more people. Table B.4 Distribution of households by type 1986 1991 1996 2001 Single 18.5% 20.2% 20.2% 22.9% 1 family 73.3% 72.2% 69.6% 67.6% 2-3 families 1.5% 1.7% 2.7% 2.1% unrelated people 5.9% 5.9% 5.2% 5.2% Total 1,078,005 1,166,568 1,268,094 1,344,267 Source: Statistics New Zealand Census of Population and Dwellings