Housing and labor decisions of households

Abstract

In this paper, we analyze the relationship between the demand for housing and the family employment. To do so, we develop an economic model and use a sample of Spanish households to analyze the housing tenure choice (ownership or rental of the house) and the demand for housing in relation to family labor decisions. We have gone beyond previous studies by incorporating the discrete decisions of tenure choice and the participation of women in the labor market, proving that these decisions are interrelated and broadening the scope of our findings and conclusions. We obtained an important description of the effect of economic factors on housing and labor decisions and demonstrated that a change in a family’s employment decisions affects housing decisions and vice versa. In addition, we determined to what extent housing and labor decisions are affected by changes in the wife’s educational level and changes in family composition. Our findings show that the labor decisions have more sensitivity than housing decisions to these changes.

Appendices

Appendix 1: Sample selection variables from the bivariate probit model

The expressions for the λ terms calculated from the bivariate probit (determined from the user manual and the help file of LIMDEP) associated with each alternative scenario are as follows:

for the sample with two wage earners

$$ {{\uplambda}}_{\text{T}} = \frac{{\phi \left( {{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} } \right){{\Upphi}}\left( {\frac{{{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} - {\hat{\rho}}{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }}} \right)}}{{{{\Upphi}}_{\text{b}} \left( {\frac{{{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} - {\hat{\rho}}{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }},\frac{{{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} - {\hat{\rho}}{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }} / {\hat{\rho}}} \right)}} $$

$$ {{\uplambda}}_{\text{P}} = \frac{{\phi \left( {{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} } \right){{\Upphi}}\left( {\frac{{{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} - {\hat{\rho}}{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }}} \right)}}{{{{\Upphi}}_{\text{b}} \left( {\frac{{{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} - {\hat{\rho}}{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }},\frac{{{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} - {\hat{\rho}}{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }} / {\hat{\rho}}} \right)}} $$

for the sample with one wage earner

$$ {{\uplambda}}_{\text{T}} = \frac{{\phi \left( {{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} } \right){{\Upphi}}\left( {\frac{{{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} - {\hat{\rho}}{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }}} \right)}}{{{{\Upphi}}_{\text{b}} \left( {\frac{{ - {\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} - {\hat{\rho}}{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }},\frac{{{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} - {\hat{\rho}}{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }} /- {\hat{\rho}}} \right)}} $$

$$ {{\uplambda}}_{\text{P}} = \frac{{\phi \left( {{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} } \right){{\Upphi}}\left( {\frac{{{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} - {\hat{\rho}}{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }}} \right)}}{{{{\Upphi}}_{\text{b}} \left( {\frac{{ - {\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} - {\hat{\rho}}{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }},\frac{{{\mathbf{Z}}_{\text{T}}^{\prime } {\hat{\delta}}_{\text{T}} - {\hat{\rho}}{\mathbf{Z}}_{\text{P}}^{\prime } {\hat{\delta}}_{\text{P}} }}{{\sqrt {1 - {\hat{\rho}}^{2} } }} /- {\hat{\rho}}} \right)}} $$

In these expressions, ϕ and Φ are the density function and the cumulative probability function with a normal distribution, and Φ_b refers to the bivariate normal distribution; ${\hat{\delta}}_{\text{T}}$ and ${\hat{\delta}}_{\text{P}}$ are the estimated coefficients of bivariate probit model, defined by equations (1) and (2); and $\hat{\rho }$ is the estimated correlation coefficient between the random terms of these equations.

Appendix 2: Estimation of hedonic housing prices

Following the approach of Goodman (2002) and Barrios and Rodríguez (2007), we obtained the regional housing prices by estimating the following hedonic price equations for each of the 17 Spanish regions (Comunidades Autónomas in Spain):

$$ \ln p_{{{\text{O}}i}} = {\varvec{\delta}}_{\text{O}}^{\prime } {\mathbf{X}}_{{{\text{O}}i}} + u_{{{\text{O}}i}} \quad {\text{for owner}} - {\text{occupiers}}\quad i = 1, \ldots ,n_{\text{O}} $$

(8)

$$ \ln p_{{{\text{R}}j}} = {\varvec{\delta}}_{\text{R}}^{\prime } {\mathbf{X}}_{{{\text{R}}j}} + u_{{{\text{R}}j}} \quad {\text{for tenants}}\quad j = 1, \ldots ,n_{R} $$

(9)

where p _Oi and p _Rj are the monthly imputed rent self-reported by owner-occupiers and the current rent paid by tenants, respectively; X _Oi and X _Rj are vectors for the characteristics of housing and the environment for owner-occupiers and renters, respectively; u _Oi and u _Rj are the corresponding random disturbances; and n _O and n _R are the number of owner-occupiers and renters, respectively.

To calculate the regional housing prices, we defined a standard dwelling based on the average of the explanatory variables using the total sample. Table 10 defines the explanatory variables, their descriptive statistics, and the standard dwelling resulting from these values. For each Spanish region, we calculated the purchase housing price and the rental housing price for this standard dwelling according to the corresponding estimated Eqs. (8) and (9), respectively. Table 11 summarizes these regional housing prices.

Table 10 Descriptive statistics of housing characteristics

Table 11 Hedonic price indices by regions within Spain (in logarithm)

Appendix 3: Estimation of hourly wages

In this study, we defined the hourly wage as the ratio of the monthly income that the individual received from work to the monthly hours worked. The ECPH offers the “current monthly labor income” variable and the “hours worked during the last week” variable. Thus, we constructed the monthly hours worked as the product of the weekly hours worked and the number of weeks in a month. Given this approach, the “hourly wage” variable may be endogenous to the decisions related to the labor supply.

To solve this problem of endogeneity, we estimated the hourly wage of an individual as a function of their observable characteristics following the method of Fernández-Val (2003). We performed this estimation separately for men and women. We considered all individuals who were members of a couple and who were of working age (i.e., younger than 65 years based on the Spanish definition). The estimation procedure followed is the Heckman’s two-stage procedure (Heckman 1979), which corrects for the selection bias associated with the participation of the individual in the labor market.

In the regression used to calculate wages (second stage of the procedure), the dependent variable was the log-transformed hourly wage and the explanatory variables considered were the age and the educational level attained by the individual and whether they were employed in the public sector (sector = 1) or the private sector (sector = 0), and a series of dummy variables that represented the size of the town and the region in which the individual resides to account for regional economic inequalities. The estimates of participation and hourly wage for men and women using this approach are summarized in Tables 12 and 13. We estimated these wages for individuals who were working as employees, rather than for self-employed individuals, as is the usual practice in the labor market literature.

Table 12 Estimates of participation and the hourly wage equations for men

Table 13 Estimates of participation and the hourly wage equations for women

Most of the independent variables were statistically significant and produced the expected results in both wage equations. The variable that accounted for the selection bias due to participation or not in the labor market, λ, was significant for women but not for men.

From these estimated wage coefficients, we calculated the potential hourly wage associated with each individual according to their characteristics, both for individuals who work as employed and for self-employed individuals.

Appendix 4: Marginal effects of bivariate probit model

Although the marginal effects of the bivariate probit model can be calculated at different levels (Greene 1996; Christofides et al. 1997), we agree with Greene (1996) that a natural step is to consider the marginal effects of the covariates on conditional probabilities. Table 14 shows these conditional marginal effects.

Table 14 Marginal effects for conditionated probabilities (provided by LIMDEP 8.0)