6525.0 - Experimental Estimates of Imputed Rent, Australia, 2003-04 and 2005-06  
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APPENDIX 1 DETAILED METHODOLOGY


INTRODUCTION

This appendix provides greater technical detail of the methodology broadly summarised in Section 3 of the Information Paper.


The United Nations System of National Accounts 1993 recommends the market value approach as the method for imputing rent for owner-occupied dwellings. In the Australian System of National Accounts, the market value approach is used to produce estimates of the gross imputed rent for owner-occupied dwellings in the national household income account.


While the international standards for household income and expenditure statistics (ILO 2003) also recommend the same approach, there is no recommendation in relation to the specific imputation methods to be applied. In practice, a range of methods could be applied to household survey data to determine the equivalent gross market rental value of an owner-occupied dwelling. These include using a self-reporting method, applying a fixed rate of rental return, and/or statistical modelling.


The Statistical Office of the European Communities, Eurostat, has recommended a methodology that uses hedonic modelling of renters in the calculation of imputed rentals for dwelling services of owner-occupiers. Readers interested in the details of the Eurostat methodology may refer to Eurostat (2006).


In light of the availability of relevant ABS household survey data on the housing characteristics of households and the rent paid by tenants, this ABS study adopted the market value approach and used statistical modelling similar to that recommended by Eurostat to estimate the net imputed rent for owner-occupied dwellings. The Heckman method was also utilised in the modelling to account for the sample selection bias resulting from using modelled market rents from renters in the imputation process (see Heckman 1979).


Net imputed rent is calculated by subtracting housing costs from the estimated gross rents. Some components of housing costs were modelled using a stratification method.



BUILDING A MODEL FOR GROSS IMPUTED RENT BASED ON RENTERS

An imputation of the modelled market rents from the renter to the owner-occupier population is required as the market rent concept is only relevant to the renter population.


In the study outlined in this paper, hedonic regression was employed to explain the market rent for renters as a function of location and dwelling characteristics using SIH data. It decomposes the market rent for renters into its constituent characteristics (e.g. dwelling structure, location attributes or other characteristics), and estimates the value of each characteristic. These estimates were used in the calculation of the gross rent for the owner-occupier population. Readers interested in hedonics concepts and theories may refer to Rosen (1974).



Model specification

The dependent variable

For this study, a semi-log functional form was employed. This is common in many hedonic modelling studies in Australia and is sufficient in addressing the problems of multicollinearity and heteroscedasticity.


The explanatory variables

Ideally, all major characteristics which influence market rents should be represented in the models, but often data are not available. The variables available for this study were limited to location and dwelling characteristics plus some household characteristics that can be directly observed or derived from the SIH and Census results. These observed characteristics are considered important in market-determined rents paid by tenants in the private rental market.


In this study, the explanatory variables were divided into two types.


Type I variables

Type I variables describe the characteristics of the dwelling. The variables used were:

  • State - The state/territory where the dwelling is located
  • Section of state - The section of state as defined in SIH, that is, major urban, other urban, bounded locality and rural balance
  • Type of dwelling - Whether the dwelling was: a separate house; a semi-detached, row or terrace house, townhouse etc. with one storey; a semi-detached, row or terrace house, townhouse etc. with two or more storeys; a flat, unit or apartment in a 1 or 2 storey block; or a flat, unit or apartment in a 3 or more storey block
  • Dwelling size - In the absence of a measure of the total floor area of the dwelling, the total number of bedrooms was used as indicator of the dwelling size
  • Socio-Economic Index for Areas (SEIFA) 2001 - the Index of Relative Socio-Economic Advantage/Disadvantage was used to indicate the socio-economic condition of the area where the dwelling is located. A higher score indicates that an area has attributes such as a relatively high proportion of people with high incomes or a skilled workforce. For more information on the SEIFA, see ABS (2003). In this study, SEIFA quintiles were derived using the SEIFA Index scores for the corresponding Census 2001 Collection districts (CD). The corresponding SEIFA quintile for the dwelling was used as a dummy variable in the modelling. For the small proportion of CDs where SEIFA was not available, the SEIFA quintile was imputed using the most frequently occurring CD SEIFA quintile in the postal area where the CD was located
  • Rent by area deciles - Rent by area decile dummy variables were created using Census information for postcode areas to supplement the very broad locational attributes of 'State' and 'Section of state' used in the modelling. It can be considered as a proxy for a range of unaccounted characteristics associated with dwelling location, providing a finer geographic indicator of the variation of market rent throughout Australia. For 2003-04, the modelling used the 2001 Census results while the 2005-06 modelling utilised the more recent 2006 Census results. Each postcode in Australia was ranked by their median rent and then summarised as deciles, allowing small geographic areas to be assembled into homogeneous groups by their median rent. Each of the dwellings in the renter population was assigned the corresponding postcode decile.

Type II variables

Type II variables describe the characteristics of the households renting the dwellings. These variables are only included in the modelling of the market rent for renters to reduce the chance of model misspecification. The purpose of the modelling was to predict a rent that a property commands and not what the occupants can afford or the nature of their tenancy. The variables included:
  • Household income - Deciles of gross household income were used for this variable.
  • Landlord type - Information on whether the dwelling was rented through a real estate agent or from an unrelated person not living in the same household.

The Mills ratio

The Heckman procedure adjusted the hedonic model for any potential selection bias that could result from non-random selection from the renter population. It produced a statistical measure known as the Inverse Mills ratio which tests for the presence of selection bias. The Heckman procedure utilised logistic modelling in the calculation of the Inverse Mills ratio. More details about the Heckman procedure can be found in Heckman (1979) and Eurostat (2006).


The hedonic model

The basic model for the market renters was formulated as:


Equation: log rent(1)


where


Equation: ln_R_iis the natural logarithm of the weekly rent (i=1,2,3, ... , n, where n is the total number of renters),


Equation: X_jiis the jth type I variable,


Equation: Z_kiis the kth type II variable,


Equation: M_iis the estimated Inverse Mills ratio,


Equation: epsilon_iis the error term,


Equation: alpha_0is the model intercept, and


Equation: beta_j, Equation: delta_kand Equation: phiare the parameters which were estimated and used in the imputation of gross imputed rent for owner-occupiers.



Estimation and diagnostics

An Ordinary Least Squares (OLS) procedure was used to estimate the parameters of the above model. The goodness-of-fit of the estimated model was examined by looking at the estimated adjusted R-squared, which was found to be reasonably good for this cross-sectional analysis (i.e. 54 % for 2003-04 and 60 % for 2005-06).


The analysis of variance table was also examined for the overall significance of the model. Each of the estimated coefficients had the expected sign and statistical significance was checked. For both periods, the residuals plot displayed a random distribution of errors and the residuals were normally distributed. Presence of heteroscedastic variance and multicollinearity were also checked.



Explanatory notes

As mentioned previously, the effectiveness of hedonic modelling is critically dependent on the availability of data on rent-determining characteristics in the private rental market. Information available from SIH on the location and dwelling characteristics is limited.


Data were not available to further define location in terms of important attributes such as views or beach frontage and proximity to employment, transport and shops/services. Data were also not available on the market value of the rented dwelling (as a strong relationship between the house value and rent paid would be expected) nor on some important structural characteristics of the dwellings such as outer-wall construction, availability of garaged or off-street parking, size of block or number of bathrooms.


It was also not possible to account for any quality differences that might exist between owner-occupied and rented dwellings with similar characteristics. For example, owner-occupied dwellings may generally be fit-out with higher quality fittings or building materials, or maintained to a higher standard, although there were no data available to enable any differences to be quantified. This limitation applies to all estimates of imputed rent that were reviewed as part of this ABS project, whether compiled at the sectoral or household levels.


In addition to the locational and dwelling characteristics used in the hedonic model, logistic modelling to obtain the Inverse Mills ratio used the characteristics of the occupants including age of reference person, family composition and highest level of educational attainment of the reference person.


For both 2003-04 and 2005-06, the estimated coefficients for the Mills ratio were found not to be statistically significant. The Mills ratio variable was therefore dropped during the final estimation of the basic model. This indicates that there was no problem of selection bias in the renters data.



ESTIMATING GROSS IMPUTED RENT FOR OWNER-OCCUPIERS

The experimental estimates of the rental equivalence or gross imputed rent for owner-occupied and other dwellings were calculated using the estimated parameter coefficients (Equation: alpha'hat_0, Equation: beta'hat_j, Equation: delta'hat_k) from the basic renter model. Using the basic model specification above, excluding the Mills ratio, the rent was imputed for owner-occupied dwellings via regression model prediction.



Intercept adjustment

Firstly, the intercept was adjusted to control for the effect of type II variables used in the previous regression, as they do not have strong relevance to owner-occupied dwellings.


To do this, the intercept was adjusted to the mean for renters, that is:


Equation: intercept(2)


where


Equation: alpha'hat_0^adjis the adjusted intercept for imputation,


Equation: alpha'hat_0is the intercept estimate of the basic model,


Equation: delta'hat_kis the estimated coefficient for the kth type II variable, and


Equation: Z'bar_kis the mean of the kth type II variable.



Log adjustment

An adjustment was also required when taking the exponential of the log of rent to recover weekly rent values. An adjustment factor based on the estimated variance of the residual from the regression ensures the weekly rent values are centred around the mean (Eurostat 2006, p.25). Thus, the imputation equation with the log adjustment was formulated as:


Equation: rent ood(3)


where


Equation: R'hat^OOD_iis the estimated gross imputed rent for owner-occupied dwelling (i=1,2,3,...,n, where n is the total number of owner-occupiers),


Equation: alpha'hat_0^adjis the adjusted intercept calculated in equation (2),


Equation: beta'hat_jis the coefficient estimate for the jth type I variable in model (1),


Equation: X^OOD_jiis the owner's jth type I variable, and


Equation: sigma'hat^2is the estimated variance of the error term.


Note that it was assumed that Equation: epsilonfollowed a normal distribution with mean 0 and variance Equation: sigma^2.



Scaling factor

A final scaling factor was applied to preserve the relationship between the observed and modelled rent estimates for private market renters. The imputed rent distribution was repositioned to the original median rent observed from private market renters data.


The scaling factor was calculated as the difference between the weekly rent (R) and the estimated median gross imputed rent for private market renters (including the log adjustment). The median was used due to the skewness of the original market rent distribution. The scaling factor was found to be -$9.18 in 2003-04 and -$6.11 in 2005-06. A multiplicative scaling factor, i.e. the observed median rent as a ratio of the median imputed gross rent, was also considered, but its application resulted in unfavourable compression of the distribution and it was not applied.


The equation for the scaling factor is given by:


Scaling factor = median(Equation: R) - median(Equation: R'hat^renter) (4)


and the final imputation of gross imputed rent for owner-occupied dwellings is adjusted as:


Equation: R'hat^OOD^adjusted_i= Equation: R'hat^OOD_i+ (Scaling factor) (5)



Extrapolating imputed rent for high value owner-occupied dwellings

Data on the house value for owner-occupied dwellings is available from the SIH. Further investigation of the relationship between the estimated gross imputed rent and house value for owner-occupied dwellings revealed that for higher dwelling values the observed location and dwelling characteristics did not fully explain the variation in rent.


An extrapolation method using the relationship between gross rents and house value for the majority of owner-occupied dwellings, to adjust gross imputed rents for high value dwellings, was additionally worked into the study.


Setting the cut-offs for extrapolation

A visual inspection of the modelled results against the value of the dwelling suggested that $400 per week rent was the highest value of gross imputed rent that could be reasonably determined from the model, referred to in this paper as the 'ceiling rent'.


The dwelling value cut-off point for extrapolation was then determined by dividing the annual 'ceiling rent' by the model-estimated annual average rate of rental return for all owner-occupied dwellings, that is 3% in 2003-04 and 2.9% in 2005-06. The corresponding dwelling value cut-offs for extrapolation were $695,200 and $719,172. The proportion of owner-occupied dwellings that underwent extrapolation was 6.5% in 2003-04 and 7.5% in 2005-06.


Extrapolation via Regression Modelling

It was established from the owner-occupier data that the estimated rental rate of return has an inverse relationship with house value. Hence a quadratic inverse model for the rental rate of return was fitted and estimated using all observations below the respective cut-offs. The model is given by:


Equation: rate of rental return(6)


where


Equation: r_iis the rental rate of return for ith owner calculated as Equation: R'hat^OOD^adjusted_i/ Equation: p_i,


Equation: p_iis the ith house value,


Equation: theta's are the parameter coefficients for the inverse of price variables, and


Equation: nu_iis the error term of the model.


The gross imputed rents for those owner-occupiers with house values above the cut-off points were re-calculated using the estimated statistically significant coefficients in the above equation. The extrapolated gross imputed rent is given by:


Equation: R'hat^OOD^highvalue_j equation(7)


where


Equation: R'hat^OOD^highvalue_jis the adjusted gross imputed rent for the jth high value owner-occupied dwelling,


Equation: p_jis the jth house value, and


Equation: r'hat_jis the estimated rental rate of return.


Note that for 2005-06, the estimate for the third term in equation 6, Equation: theta'hat_2, was found not to be statistically significant. It was therefore excluded in the extrapolation for that period.



ESTIMATING HOUSING COSTS FOR OWNER-OCCUPIERS

The SIH collects information on all relevant housing cost items except house insurance, and repairs and maintenance. Expenditure information on these data items is only available for the HES subsample in 2003-04. A stratification method was used to estimate weekly expenditures on these items for the entire SIH sample, and to enable extrapolation in 2005-06, when these information were not collected.



Housing costs directly taken from SIH

Expenditures on body corporate payments, general and water rates, and the interest component of repayments of loans for the purposes of purchasing or building, were directly collected in SIH. All housing costs were net of refunds.



Estimating repair and maintenance costs

Repair and maintenance costs refer to the costs of maintaining the dwelling as it was first built. They include payments to contractors and the cost of materials for repainting, electrical work, plumbing, re-roofing, etc. These expenditure items are collected in the HES with a recall period of three months for payments to contractors and two weeks for expenditure on materials.


Given that expenditure on these items is likely to be at infrequent intervals and of significantly varying amounts, the raw data at the individual household level was too volatile to be used directly. The 2003-04 HES subsample of owner-occupiers was stratified by number of bedrooms, enabling the average cost of repairs and maintenance within each stratum to be obtained. The average cost in the stratum to which a dwelling belongs was then imputed to all owner-occupiers in SIH.


Since 2005-06 was a non-HES year, repair and maintenance expenditure was estimated by extrapolating the 2003-04 repairs and maintenance data using the published ABS consumer price index on 'House repairs and maintenance'.



Estimating insurance costs

Stratification by number of bedrooms was also applied to enable calculation of the average cost of house insurance and imputation of the average house insurance costs to all owner-occupiers in 2003-04. The ratio between expenditure on house building insurance and home contents insurance was applied to those households where these amounts were unable to be collected separately. For 2005-06, expenditure was estimated by extrapolating the 2003-04 data using the published consumer price index for 'Insurance services'.



ADJUSTING THE ESTIMATED NET IMPUTED RENT FOR TENANTS OF STATE/TERRITORY HOUSING AUTHORITIES

The net imputed rent for public tenants was benchmarked to the state mean weekly rental subsidies published in the CSHA National Data Reports for 2003-04 and 2005-06 using a multiplicative adjustment. This factor was equal to the ratio of the CSHA state mean weekly rental subsidy over the state mean weekly net imputed rent for public tenants. That is


Equation: SHA net imputed rent benchmarked final(8)


where


Equation: SHA net imputed rent benchis the benchmarked net imputed rent for the ith state housing authority (SHA) renter in the jth state,


Equation: SHA net imputed rentis the modelled net imputed rent for the ith SHA renter in the jth state,


Equation: mean rent of stateis the mean weekly rental subsidy for SHA tenants in the jth state, and


Equation: mean SHA weekly rental subsidyis the mean net imputed rent for SHA tenants in the jth state.



REFERENCES

ABS (Australian Bureau of Statistics) 2003, Information Paper: Census of Population and Housing: Socio-Economic Indexes for Areas, Australia, 2001, cat. no. 2039.0, ABS, Canberra.


AIHW (Australian Institute of Health and Welfare) 2005, Commonwealth-State Housing Agreement National Data Reports 2003-04, Public Rental Housing, Housing Assistance Data Development Series, AIHW cat. no. HOU114.


AIHW 2006, Public Rental Housing 2005-06: Commonwealth-State Housing Agreement National Data Reports, Housing Assistance Data Development Series, AIHW cat. no. HOU153.


Eurostat 2006, 'HBS and EU-SILC Imputed Rent', Meeting of the Working Group on Living Conditions, Luxembourg, 15-16 May 2006.


Heckman, J. 1979, 'Sample Selection Bias as a Specification Error', Econometrica, vol. 47, no. 1, pp. 153-161.


International Conference of Labour Statisticians 2003, Final Report of the 17th International Conference of Labour Statisticians, Geneva, 24 November to 3 December 2003.


Rosen, H. 1974, 'Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition', Journal of Political Economy, Vol. 82, pp.34-55.