Outline

• Key References

• WHy is housing relevant?

• Theoretical justification for imputing rents

• Different approaches to imput housing flow of service

• Distributional Impacts

Key References

Deaton, A., and S. Zaidi. 2002. "Guidelines for constructing consumption aggregates for welfare analysis." LSMS Working Paper No. 135,

Balcázar, C. F., Ceriani, L. , Olivieri, S. and Ranzani, M. (2017), Rent‐Imputation for Welfare Measurement: A Review of Methodologies and Empirical Findings. Review of Income and Wealth, 63: 881-898. doi:10.1111/roiw.12312

Key References

Deaton, A., and S. Zaidi. 2002. "Guidelines for constructing consumption aggregates for welfare analysis." LSMS Working Paper No. 135,

Balcázar, C. F., Ceriani, L. , Olivieri, S. and Ranzani, M. (2017), Rent‐Imputation for Welfare Measurement: A Review of Methodologies and Empirical Findings. Review of Income and Wealth, 63: 881-898. doi:10.1111/roiw.12312

Why is housing relevant?

The essence of the problem

In theory

• The utility is the value of the flow of services from occupying the dwelling rather than the expenditure for purchase it over the period of analysis

• If rental markets worked perfectly and all households rent their dwellings, the value of the flow of services is easily approximated by the value of the rent they pay.

However…

• Many households own their dwellings, So they also implicitly receive a flow of services that is equivalent to value of the utility that owning the property represents for them.

• In other cases, households receive housing free of charge or at subsidized rates by their employer, friends, relatives, government or other entities (non-market tenants).

Few housholds rent their dwelling

Theoretical justification for imputing rents

• Welfare measure (i.e., expenditure) must be consistent accross households in order to make comparisons among themselves

• Including the expenditure in rent by tenants and not the flow of service received by owners overestimate the welfare of tenants.

Different approaches to imput housing flow of service (i.e., imputing rent)

Self-assessment

Use the value reported by owners and non-market tenants when they answer "if you rented this dwelling, how much would you pay per month?"

Different approaches to imput housing flow of service (i.e., imputing rent)

Econometric and statistical methods

1. Find the best model for rents paid by tenants on the basis of observable dwelling characteristics

2. Apply the same model to home owners and non-market tenants

Different approaches to imput housing flow of service (i.e., imputing rent)

Capital market approach

• you could either;

  • Rent-to-value: Find the capitalization rate from rents and market value of the dwelling; or,
  • User cost: Collect information on the return rate for housing and operating costs

• then, apply the capitalization rate to the value of the owners occupied dwelling

Different approaches to imput housing flow of service (i.e., imputing rent)

Payment approach

• use information about the out-ot-pocket expenditure faced by households. For owners it would be the mortgage, interest payments, taxes, insurance, maintenance and repairs.

Different approaches to imput housing flow of service (i.e., imputing rent)

External sources

• Other household surveys, adminustrative register, newspaper or internet offer notices, multiple listing datasets, motgage transctions, key informat evaluations.

Different approaches to imput housing flow of service (i.e., imputing rent)

Self-assessment

• This approach is based on data collected about owners’ estimates of a fictitious market rent.

• Homeowners are asked to estimate how much they would pay if they were renting their home

• Assumption: owners can estimate rental equivalences

  • This should be less problematic in regions where rental market is active and well developed (Lanjouw, 2009)
  • But, owner-occupiers may over-estimate the true rental value of their dwelling given the affinity to their property or neighborhood (owner pride factor)

• Should be treated with caution and should be tested

Econometric models

• Hedonic model

  • Theory and generi form
  • Semi-log
  • Heckman Selection

• Stratification

Hedonic models - Theory

• Utility derives from attributes or characteristics of goods and not from goods per se (Lancaster, 1966)

• In equilibrium, economic agents observe the prices of differentiated products and specific amounts of characteristics associated with them. This reveals the implicit prices for the different characteristics (Rosen, 1974)

Hedonic models - Theory

Housing can be considered as a composite commodity:

$$R_h = R(\mathbf{L}_h, \mathbf{S}_h, \mathbf{N}_h) = \mathbf{R}(\mathbf{X}_h)$$

where,

• $\mathbf{L}_h$, Location of dwelling
• $\mathbf{S}_h$, Structural Characteristics
• $\mathbf{N}_h$, Neighborhood

However,

• No consensus about the specific explicit form the hedonic price function might take
• The relation between rent and characteristics should be non-linear

Hedonic models - Theory

• If we have $X_m$ observable attributes for a dwelling, with $m=1,2,...,M$, the most generic functional specification is, $$g(R_h) = \alpha_0 + \sum_{m=1}^{M}f_m(X_{hm})\beta_{hm}+ \sum_{m=1}^{M}\sum_{k=1}^{M}f_m(X_{hm})f_k(X_{kh})\gamma_{hmk} + \epsilon_h$$

  

  

Hedonic models - Theory

• If we have $X_m$ observable attributes for a dwelling, with $m=1,2,...,M$, the most generic functional specification is,

$$g(R_h) = \alpha_0 + \sum_{m=1}^{M}f_m(X_{hm})\beta_{hm}+ \sum_{m=1}^{M}\sum_{k=1}^{M}f_m(X_{hm})f_k(X_{kh})\gamma_{hmk} + \varepsilon_h$$

• In the literature, different specifications and estimation methods are found:
  • Linear, semi-log and higher order
  • Quantile regression, semi-parametric and non-parametric
  • Heckman selection model
  • Spatial Dependency

Hedonic models - Semi-log

$$\ln(R_h) = \alpha_0 + \sum_{m=1}^{M}f_m(X_{hm})\beta_{hm} + \varepsilon_h$$

• Pros:
  • The coefficients show approximately the percentage change in the imputed rent for a given unit-change in the covariate
  • It mitigates the heteroskedasticity problem
  • It is computationally simple
  • It allows the marginal rent-value to be a non-linear function of the size and quality of the dwelling
• Cons:
  • The unobserved quality of the dwelling chosen by renters can be different from that chosen by owners

Hedonic models - Heckman Selection

• IF the choice between owning or renting is not independent from the characteristics of the dwelling, the OLS estimators in the rental market might be inconsistent.

• A plausible solution is to implemente a Heckman two-stages selection model,

$$g(R_h) = alpha_0 + \sum_{m=1}^{M}f_m(X_{hm})\beta_{hm} + \varepsilon_h \text{ if }t_h = 1$$ where,

$$t_h = \begin{cases} 1 \text{ if } \sum_{m=1}^{M}f_m(X_{hm})\gamma_{hm} + \sum_{j=1}^{J}f_j(X_{hj})\delta_{hj} + \eta_h\\ 0 \text{ otherwise } \end{cases}$$

• $X_{hj}$ is a vector of explanatory variables which is assumed to determine the tenure status and to be independent of the rent value.
• Errors terms $\varepsilon_h \text{ and } \eta_h$ are jointly distributed as normal.

Hedonic models - Heckman Selection

• Pros:
  • Simple and fast to implement
  • We can apply the model fitted on tenants on the entire population and get an estimate of imputed rent for everybody
• Cons:
  • We risk to underestimate the prediction for those with higher flow of services from housing and to overestimate the prediction for those with lower
  • There is no way to test whether the prediction for owners and non market tenants is accurate
• consider:

  In some countries, housing and rental markets are not well enough developed to permit any serious estimate of rental value, and attempts to repair the deficiency using data from a small number of households are unlikely to be effective, however sophisticated the econometric technique

  (Deaton and Zaidi, 2002, p.38-39)

Stratification

• Define a set of relevant characteristics $(𝑋^𝐴, 𝑋^𝐵, 𝑋^𝐶, …)$

• Each characteristic have a set of possible realizations:

  • $X^A = \{x_1^A,x_2^A,x_3^A\}$ (e.g. Region1, Region2, Region3)
  • $X^B = \{x_1^B,x_2^B\}$ (e.g. Detached House, Flat)
  • $X^C = \{x_1^C,x_2^C,x_3^C,x_4^C\}$ (e.g. 1room, 2rooms, 3rooms, >3rooms)

• From which we can define strata of dwellings with homogeneous characteristics: $$(\underbrace{x_1^A,x_1^B, x_1^C}_\text{Stratum1}), (\underbrace{x_2^A,x_2^B, x_2^C}_\text{Stratum2}), (\underbrace{x_3^A,x_3^B, x_3^C}_\text{Stratum3})$$

• Take the average rent for each stratum and assign it to each owner-occupied or non-market tenant dwelling in the same stratum

Stratification

• Pros:

  • Dwellings in the same strata will be of a more homogeneous quality, leading to more precise estimates for owners and non-market tenants, since the model is defined on dwellings with similar characteristics

• Cons:

  • Increasing the number of strata reduces the average number of observations per stratum
  • Owners may belong to stratas that do not exist in the rent markets

• What we learn:

  • We may obtain better predictions for owners if we infer their rents using information from tenants with dwellings having similar characteristics

theoretical framework

• Population $N = [1, 2, ...,n]$ individuals, where $n \in \mathbb{N}$
• Distribution of welfare without rents: $x = [x_1, x_2, ..., x_n]$,
  • $x_i$ level of welfare aggregate individual $i$.
  • Assume $x_1 \leq x_2 \leq ...\leq x_n$

• Distribution of rents: $r = [r_1, r_2, ..., r_n]$,

• Three possible scenarios:

  $$\begin{align} A.& \quad r_i^A &= r \quad \forall i &\in N \\ B.& \quad r_i^B &= \rho x_i \quad \forall i &\in N, \rho \in (0,1) \\ C.& \quad r_i^C &= \rho_i x_i \quad \forall i &\in N, \rho_i \in (0,1) \end{align}$$ `

theoretical framework

$$y^j \equiv x = r^j = [x_1 + r_1^j,x_2 + r_2^j, ..., x_n + r_n^j] \quad j \in [A, B, C]$$

$$\mu(y^j)>\mu(x)$$

Distributional impact of Rent imputation

We are interested in

• Distribution

  • Shape

  • Inequality

  • Ranking

  • Shared prosperity

• Poverty

  • Levels

  • Profile

Different scenarios

Evidence from the literature

• In general, the literature finds that including rents reduces inequality
• Mainly developed countries
• Mostly income as welfare aggregate
• Some examples:
  • Guenardand S. Mesple-Somps (2010) for Madagascar and Cote D’Ivoire: the poor are more likely to own their homes
  • Gasparini and Escudero (2004) for the Greater Buenos Aires area: large proportion of house-owners at the bottom of income distribution, and income elasticity in housing expenditure <1
  • Törmälehto and Sauli (2010, 2013) for 29 EU-SILC countries: combined effect of the equalizing gap-effect and dis-equalizing re-ranking effect

Poverty indices

• Effects when poverty line is fixed

• Effects when poveryt lines is adjusted

Fixed poverty line

Fixed poverty line, by regions

Adjusted poverty lines

Poverty - Summary of results

• As expected, poverty decreases by keeping fixed the poverty line and adding imputed rents to the consumption aggregate
• Poverty changes very little when the poverty line is adjusted by adding imputed rent in the non-food component
• With an adjusted poverty line poverty tends to slightly decrease for tenants and to increase in rural areas (particularly in Iraq and Peru)
• The profile of the poor does not seem to change, both keeping fixed and varying the poverty line, according to the imputation method used