IMPUTED RENT IN HOUSEHOLD BUDGET

SURVEY

Inga Masiulaitytė, August 24-28, Ventspils, Latvia 2006

Content

Definition of the imputed rent

Methods

Results

Conclusion and proposals

Imputed rent

The imputed rent refers to the value that shall be imputed for all households that do not report paying full rent, either because they are owner-occupiers or they live in accommodation rented at a lower price than the market price, or because the accommodation is provided rent free.

Methods

• Self – assessment method

• Homogeneity groups method

• Heckman method

• Log-linear method

Self assessment method

Self – assessment method is based on the owner-occupiers answers about potential rent for their dwellings. This method is subjective method, and can not show real situation in the rental market.

Homogeneity groups method

The dwelling are disjointed in quantity groups so that the rental value of dwelling within each group is a homogenous as possible. Data on actual rents paid within each group are obtained. The average rent paid in the group to which dwelling belongs is imputed to the owner-occupier.

Heckman method 1The sample selection model consists of two equations The first equation indicates if target variable is observed, i.e. if there is a response or a nonresponse:

kkkr z*

here zk is a value of a vector of auxiliary variables, is a vector of parameters, k is the error term, a random component.We only observe whether it exceeds a certain threshold, say 0, because that results in the response or nonresponse:

kz

.0,0

,0,1*

*

k

k

krif

rifr

Heckman method 2The second equation assumes a linear relationship between the target variable y and a vector of auxiliary variables ),...,( 1 Jxxx

kkk uy x*

here is a random component, is a vector of parameters that have to be estimated using the sample data. is also a latent variable. The study variable y is defined by:

ku *ky

.0,

,1,*

k

kk

krif

rifyy

.

Log-linear regressionLets us introduce a variable l with the values:

Then the log-linear model can be defined as:

Nkyl kk ,...,1,ln

kkkl x

here – is vector of coefficients, – are values of known auxiliary variables, – are random errors.

kx

k

Population and sample design

 Nr. Strata Population Sample

1 Vilnius 1997 206

2 Kaunas 1854 191

3 Klaipėda 764 79

4 Šiauliai 625 64

5 Panevėžys 628 65

6 Other cities 6262 645

7 Rural areas 7000 750

  Total 19130 2000

Stratified random sample is used. Replication number is 1000.

Auxiliary variablesLocation of dwelling (strata)Type of dwellingNumber of roomsWaterHot waterElectricityHeatingGasKitchenKabel TVGarageSeweragePhone

Results 1Empirical average of estimates of mean rent using different imputation methods by strata (5 per cent of tenants)

50

150

250

350

450

1 2 3 4 5 6 7

Strata

Litas True rent Heckman Homogeneity Log-linear Self assess

Results 2Empirical average of estimates of mean rent using different imputation methods by number of rooms (5 per cent of tenants)

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8+

Number of rooms

LitasTrue rent Heckman Homogeneity Log-linear Self assess

Results 3Empirical average of estimates of mean rent using different imputation methods by strata (10 per cent of tenants)

0

100

200

300

400

500

1 2 3 4 5 6 7

Strata

Litas True rent Heckman Homogeneity Log-linear Self assess

Results 4 Empirical average of estimates of mean rent using different imputation methods by number of rooms (10 per cent of tenants)

0

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8+

Number of rooms

Litas

True rent Heckman Homogeneity Log-linear Self assess

Results 5Empirical average of estimates of mean rent using different imputation methods by strata (30 per cent of tenants)

50

150

250

350

450

1 2 3 4 5 6 7

Strata

LitasTrue rent Heckman Homogeneity Log-linear Self assess

Results 6Empirical average of estimates of mean rent using different imputation methods by number of rooms (30 per cent of tenants)

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8+

Number of rooms

Lit

as

True rent Heckman Homogeneity Log-linear Self assess

Results 7Empirical average of estimates of coefficient of variation of rent using different imputation methods

Coefficient of variation, %

0,0

0,5

1,0

1,5

2,0

2,5

3,0

True coef f icientof variation

Heckman Homogeneity Log-linear Self assess

%

ConclusionThe imputed rest estimated by Self-assessment method is better to use when we have 5 per cent of tenants.

The imputed rent estimated by Homogeneity groups method has a smaller bias than estimated by Heckman or Log-linear methods.

Proposals

Test these methods on EU-SILC data.

Test influence of new auxiliary variables on the estimation of rent.

ReferenceJeroen Smits, (2003) Estimating the Heckman two-step procedure to control for selection bias with SPSS. http://home.planet.nl/~smits.jeroen/selbias/Heckman-SPSS.doc .

WEN Hai-zhen, JIA Sheng-hua. GUO Xiao-yu, (2004) Hedonic price analysis of urban housing: An empirical research on Hangzhou, China, Journal of Zhejiang University SCIENCE, 6A(8), p. 907-914.EU–SILC DOC TFMC-12/06. Third Meeting of the EU-SOLC task force on methodological issues. Imputed rent.. Eurostat-Luxembourg, April 2006, EU-SILC DOC TFMC-12/06.

DOC HBS/161/2006/EN, DOC EU-SILC/162/06/EN. Meeting of the working group on living conditions (HBS, EU-SILC and IPSE). HBS and EU-SILC Imputed rent.. Eurostat-Luxembourg, May 2006.

Bethlehem J., Cobben F., Schouten B., May 2006, Nonreponse in Household Surveys. Version 1, Statistics Netherlands, Methods and Informatics Department, p. 141-142.

Bradley C. Martin, Rahuk Ganguly, SAS program for Heckman 2-stage estimation. University of Georgia, College of Pharmacy, Athens, GA 30602, http://www.rx.uga.edu/main/home/cas/faculty/heckman.pdf Eurostat Phare MultiCountry Programme, Organise by ICON-Institute GmbH/Germany of behalf of Eurostat. Report on the Methodological Study: “Possible data sourses and methods to calculate the target variable “imputed rent” for Lithuania”. Action code: 1138-ILC-SerCon-Lithuania-1

THANK YOU FOR YOUR ATTENTION!