Understanding Housing Rent Imputation for Statistical Purposes

Guidance note on Housing Rent Imputation 12thMeeting of the Pacific Statistics Methods Board (PSMB) 2ndOctober 2023 Noumea, New Caledonia Dr. Jean-Paul ZOYEM (SPC consultant Welfare Economist) PACSTAT project (P169122): Statistical Innovation and Capacity Building in the Pacific Island Countries

Rational of housing contribution to the well-being The commonly shared opinions on housing The use of a house contributes to the well-being of the household members, Dwelling standing is a mirror of the well-being that is provided to household members Based on these opinions we can easily agree to account for the use of housing in the consumption aggregate The challenge is: How to value the use of the dwelling? Some households are paying a rent as renters of their dwelling, Some others are not paying for the dwelling (non-renters) as they are either: Homeowners, Users for free of dwelling provided by relative, employers, government, etc

Data for Housing Rent Vocabulary Actual rent is the rent that a household has actually paid. Self-reported imputed rent is the amount of money the households would have to pay (receive), if they were to rent on the market the dwelling they are currently occupying. Imputed rent is the value allocated to the rental service in the computation of consumption aggregate.

Data for Housing Rent Data source It is common for consumption and expenditure surveys (HIES) to collect rent data on: Actual rent for renters and Self-reported imputed rent for the non-renters. The imputed rent is derived from either actual rent or self-reported imputed rent using imputation methods. Different approaches of rent imputation exist in the literature; the most commonly used being: Self-reporting rent approach (or self-assessment) ; Hedonic rent imputation model

Self-reporting rent approach Imputed rent is calculated based on self-reported information Actual rent for renters and Self-reported imputed rent for the non-renters. Limitations of the Self-reporting rent approach This approach assumes that respondents are both informed and objective: about the value of their dwelling, and about the rent they would pay (receive) for a home with similar quality and location attributes. This assumption may hardly hold: Reliability of Self-reported imputed rent is questionnable for different reasons. Poor knowledge of rental market by non-renters; Lack of objectivity of the non-renters

Self-reporting rent approach: limitations Poor knowledge of the rental market Repondents may not be informed enough to come up with realistic estimate of the rent: Acountry where the rental market is thin with few transactions, Acountry where the rental market doesn t exist (Some rural areas with no exchange on actual rent) An example from Maldives reports that: A self-reported imputed rents from a household income and expenditure survey were found to be unreasonably high; Analysts thought that the respondents based their answers on the rate they would expected to receive if renting out their property as a guesthouse; In fact, in the Maldives virtually all dwellings outside the capital are owner-occupied; therefore there is no rental market for residents in their surroundings. Lack of objectivity on the Self-reported imputed rent For example due to the so-called owner pride effect: This is the tendency for owners to place above market values on special features of their dwellings, especially if they created those themselves .

Hedonic rent imputation model Hedonic rent model bases the rent imputation on the dwelling features Main idea is that a household rent is a function of its dwelling features. Main features of the dwellings (data collected in HIES): type of construction (separated houses, building, etc) number of rooms attached kitchen building materials of roof, wall, floor, etc, age of the building, type of toilet, water connection, electricity grid connection, neighborhood characteristics, location characteristics (province, urban/rural), Etc Regression model Dependent variable (actual rent) / Independent variables (dwelling features).

Hedonic rent imputation model Model specification The simplest and mostly used specification of the model is the standard linear regression that is actually the log-linear model specified as follows ln???? = X + = 0+ 1X1 + 2X2 +.. ?X? + , where ln???? is the logarithm of actual rent paid by household h, X is a vector of k characteristics of household h s dwelling (X1being the first regressor, all the way to the k-th regressor, X?), and is the error term. The model is estimated on the renter population, Regression coefficients are used to predict rent out of sample, i.e., for homeowners and other non renters. Before they can be added to the consumption aggregate the predicted value should be transformed back from logarithmic to currency unit.

Hedonic rent imputation model Transforming logarithmic back to currency unit Step 1: the na v transformation: ???? = exp( X ) The na ve transformation is not correct since it would systematicaly underestimate the rent. The correct transformation is an adjustment of the na ve transformation. Step 2: adjustment of the na v transformation Different methods of adjustment In practice, it is advised to use the Duan s estimator as follows : 1 ? =1 ? exp(? ) where ? are the regression residuals. Duancoef = ????????= ???? *Duancoef

Hedonic rent model and data constraints In some cases it may be problematic to compute the hedonic model on actual rent The sample of renters is small in size, It is generally accepted that a minimum of 15 - 25% households should participate in a rental market to develop a reliable model. In the PICTs it is frequent to see this proportion below 5%. The sample of renters is highly segregated: that is, if the characteristics of rented dwellings are widely different to those of homeowners Example: renters are mainly in appartment while homeowners mainly use one-family houses The information on which regression predictions are based may be too poor for out-of- sample rent imputation to be reliable. For example: important features are missing (building year, type of floor, etc)

Hedonic rent model and data constraints (continue) Hedonic model using the Self-reported imputed rent When data on actual rent is not reliable a frequent practice is to base the hedonic model on self-reported imputed rent. The self-reported rent may not be the correct estimate of the housing use service; but it is believed that this information is consistent with the ranking of well-being. Therefore, it is relevant to use it since the objective of poverty analysis is the ranking of well-being. Hedonic model strategy: 3 options for dependent variable Actual rent, Self-reported imputed rent, Combination of actual rent (for renters) and self-reported imputed rent (non-renters) Selection among the 3 options It is recommended to conduct preliminary statistics analysis to assess the reliability of self-reported imputed rent.

Hedonic rent model and data constraints (continue) Assessment of the reliability of self-reported imputed rent Analysis should adress the following issues: Is the distribution of self-reported values reasonable, given the context? What can we learn from basic summary statistics on actual and self-reported rents computed by population subgroups (e.g., urban and rural) ? Key concern: Is there Evidence of systematic differences between actual and self-reported rent indicating that non-renters regularly over-estimate (or under-estimate) the market value of their dwelling? Which Strategy of allocating rental value to households (imputed rent): Based on the results of the reliability assessement

Hedonic rent model and data constraints (continue) Strategy of allocating rental value to households (imputed rent) Select the dependent variable for hedonic model: Actual rent Self-reported imputed rent Combination of actual rent (for renters) and self-reported imputed rent (non-renters) Allocation of imputed rent Actual rent to renters and Estimated rent to non-renters, Estimated rent to both renters and non-renters,

Rent imputation: adjustment for maintenance costs Maintenance costs The maintenance cost refers to any cost incurred by the household to keep its dwelling in good conditions, among which: Electrical maintenance Fence and property enclosures Painting maintenance Plumbing maintenance Roofing maintenance Maintenance cost can be seen as a regrettable necessity rather than welfare enhancing It is recommended to adjust the imputed rent by deducting maintenance cost. Identify outliers and properly correct them before using for adjustment of imputed rent

Process of rent imputation From housing markets to hedonic model on self-reported imputed rent Process chart of rent imputation Are there different rental markets in different parts of the country? Yes. Divide the data into individual markets and proceed with each set of calculations individually No. Proceed with the full dataset Are there enough data to develop a reliable model? Yes. Proceed the model on actual rent from renters. Impute the actual rent to renters and the estimated rent to non-renters. No. Incorporate the self-reported rental value from the non- renters. Do the rental values differ significantly from the self-reported values? No. Pool actual rent with self- reported rent. proceed the model on the combined variable (actual and self-reported rent). Impute the actual rent to renters and the model estimated rent to non- renters. Yes. Drop actual rent. proceed the model on self-reported rent. Impute the estimated rent to renters and non-renters.

Rent imputation: PSMB recommendations PSMB to provide feedback on the main guidance points of substance: 1. Rent imputation should be conducted in respect of the process chart defined in the Guidance note "Monetary poverty measurement". 2. A solid statistical analysis should be conducted to ascertain the reliability of "actual rent" and "self-reported imputed rent" to choose the best option for rent imputation. 3. Rent imputation should be based on the hedonic regression model. 4. The transformation of the logarithm of the rent to currency rent should be performed according to the Duan method. 5. The imputed rent should be adjusted for the maintenance cost, which in turn should be previously corrected for outliers to avoid lumpy expenses