Renting versus Owning and the Role of Human Capital: Evidence from Germany

Abstract

In a world with complete markets, the decision whether to rent or buy a home is not influenced by risks related to human capital. If markets are incomplete and have frictions, however, this may change. Renting should become more likely the more mobile a household has to be and the more income risk can be diversified. Using household panel data from Germany, we test both predictions. We find that mobility requirements have a positive effect on the probability of renting. This effect is robust even after controlling for state dependence, unobserved heterogeneity and other factors known to influence the tenure mode choice. Our data, however, does not support the hypothesis that the potential to diversify net income risk when renting affects the tenure mode choice.

Appendix

Cluster Analysis

Our cluster analysis uses the observed transitions between occupation-industry groups to delineate professions. Let i denote a occupation-industry group and $p_{ij}$ the probability of an individual belonging to this group conditional on being a member of group j in the previous period. The transition probability is

$$ p_{ij} = \frac{\sum_{t\in T} N_{i,t|j,t-1}}{\sum_{t\in T} N_{i,t}}\;, $$

(14)

where $N_{i,t|j,t-1}$ is the number of individuals in group i in period t conditional on being in group j in period $t-1$. $N_{i,t}$ denotes the total number of individuals in group i in period t.

To estimate transition probabilities between occupation-industry groups, we use information on individuals in the full sample that are in employment and have been in the GSOEP for at least two years. Each individual falls into one of 9 ISCO-88 1-digit occupations and one of 14 NACE Rev.1 1-digit industries. This leads to 126 occupation-industry groups, of which two have no observations in our sample. The estimated transition probabilities provide the data with which we select professions. We use a K-Medians cluster algorithm that starts from a given partition of the groups and proceeds by exchanging groups between clusters so that all groups within a cluster are closest to the cluster’s centroid. The algorithm converges when occupation-industry groups are no longer exchanged between profession groups. We run the cluster analysis with different initial profession groupings found by a first step agglomerative cluster algorithm. In most cases, the cluster analysis leads to 14 profession groups.

Table 7 presents the estimated transition matrix for the 14 professions. The professions are fairly stable. The diagonal elements of the matrix shows the transition probabilities within professions. The lowest within transition probability is 79 percent, the highest 94 percent. The off-diagonal elements, which are the transition probabilities between professions, are almost always lower than 3 percent. The lowest between transition probability is 0 percent and the highest about 10 percent.

Table 7 Transition matrix for the 14 profession cluster

Survival Analysis

We estimate the coefficients in Eq. 4 using a linear regression for censored data

$$ \ln (\tau_{h}) = \mathbf{x}(\tau_{h})\boldsymbol{\beta} + \varepsilon_{h}\;, $$

(15)

where $\tau _{h}$ is the time since household h moved into the current dwelling. A spell is completed if the household moves to a new residence or disbands. Disbandment is the result of emigration or death. Incomplete spells are defined to be right-censored. The vector $\mathbf {x}(\tau _{h})$ collects, possibly time-varying, household characteristics at time $\tau _{h}$, as well as a full set of profession, region, and time dummies. The latter take the value one if household's residence spell begins in the respective year. The idiosyncratic error term is distributed with $\varepsilon _{h} \sim N\left (0,\sigma ^{2}\right )$.

Equation 15 is estimated with ML, using a flow sample of residence spells from the GSOEP. In particular, a household enters the sample if it moves to a new residence or is newly formed between 1985–2003. We allow for multiple spells of the same household and adjust standard errors in the estimation accordingly. In total, we have 6,842 residence spells, of which 3,407 are completed. The remaining spells are right-censored.

Table 8 reports summary statistics of household characteristics in the spell sample. With respect to most of their socioeconomic characteristics households in this sample are quite similar to recent movers as summarized in column (2) of Table 1. This is attributable to the fact that the GSOEP, on average, follows newly moved households for only 5 years.

Table 8 Summary statistics for residence spells, 1985–2004

Income Series

We derive the profession-specific constant-quality income series from the hedonic repeat-measures regression

$$ y_{i,t} = \alpha_{0} + \mathbf{x}_{i,t}\boldsymbol{\beta} + \gamma_{p0} D_{p,i,0} + \gamma_{pt} D_{p,i,t} + c_{i} + \varepsilon_{i,t}\;, $$

(16)

where $y_{i,t}$ is the log of the employment income of individual i in period t $(t=1984, \ldots , 2004)$. The vector $\mathbf {x}_{i,t}$ contains time-varying individual characteristics, as well as a full set of region dummies. The binary indicator $D_{p,i,0}$ is set to one if individual i is employed in profession p in the base period $t=1995$. The binary indicator $D_{p,i,t}$ is set to one if individual i is employed in profession p in period $t \neq 1995$. The profession dummies for the base period, $D_{p,i,0}$, control for the income change of individuals who switch professions between periods. Observed and unobserved time-constant characteristics are captured by the individual specific effect $c_{i}$. $\varepsilon _{i,t}$ is an idiosyncratic error term.

Estimating Eq. 16 directly would lead to a biased estimator, because unobserved characteristics captured in $c_{i}$ are omitted. We therefore use a fixed effects estimator, which subtracts the individual-specific average from each observed variable. This removes the observed and unobserved time-constant characteristics, $c_{i}$, from the regression equation. Estimating this modified regression with OLS leads to an unbiased estimator for the coefficients in Eq. 16.

We use an unbalanced panel sample of the relevant 15,701 employed individuals in the GSOEP to estimate the coefficients. Following the literature on Mincer wage equations, we include education in years, labor force experience in years, and labor force experience squared in $\mathbf {x}_{i,t}$. Further controls comprise age, work hours, and duration of current employment. These variables are suggested by Shiller and Schneider (1998) to ensure that the income index captures only the income trend of fully employed individuals in a given profession. As economic theory does not suggest a particular functional form for the age and work hours variable, we use the Box-Cox type transformation suggested in Bunke et al. (1999). These functions capture non-linearities, such as the common hump-shaped age profile of income. Table 9 presents these fixed effects estimates. The fit of the regression is reasonably good as measured by the $R^{2}$. Moreover, the estimated coefficients of the control variables have reasonable signs and are statistically significant.

Table 9 Hedonic repeat-measures income regression

We obtain profession-specific income series in two steps. First, we compute constant-quality index series $I_{p,t} = \exp \{\widehat {\gamma }_{p,t}-0.5\widehat {\sigma }^{2}_{\gamma _{p,t}}\}$. $\widehat {\gamma }_{p,t}$ is the estimated time dummy coefficient from Eq. 16 for profession p in period t. $\widehat {\sigma }^{2}_{\gamma _{p,t}}$ is the estimated variance of the coefficient estimator, which corrects for small-sample bias. The index series are normalized to one in the base period 1995. Second, we convert the series into series in levels, thereby taking account for unemployment

$$ Y_{pr,t} = (1-u_{p,t})I_{p,t} \bar{Y}_{pr} + u_{p,t} B_{t} I_{p,t}\bar{Y}_{pr}\;. $$

(17)

The median employment income $\bar {Y}_{pr}$ is for profession-region cell $(pr)$ in year 1995. The unemployment rate $u_{p,t}$ is estimated from the GSOEP. $B_{t}$ is the OECD summary measure of unemployment benefits, which is the ratio of gross benefit entitlements and gross earnings (Martin 1996). $B_{t}$ is published only on a biannual basis and we interpolate values for non-covered years linearly. The full-employment income $I_{p,t} Y_{pr,1995}$ and the unemployment benefit $I_{p,t}B_{t}Y_{pr,1995}$ are weighted by the profession-specific unemployment rate in the respective period. After deflating with the consumer price index, we obtain the final constant-quality real income series.

Rent Series

We derive the region-specific rent series from the hedonic repeat-measures regression

$$ y_{i,t} = \alpha_{0} + \mathbf{x}_{i,t}\boldsymbol{\beta} + \gamma_{r,t} D_{r,i,t} + c_{i} + \varepsilon_{i,t}\;, $$

(18)

where $y_{i,t}$ is the log rent of dwelling i in period t $(t=1984, \ldots , 2004)$. The vector $\mathbf {x}_{i,t}$ collects time-varying characteristics of the dwelling. These include variables related to modernization (indicators if a bathroom and central heating are present), as well as variables related to the landlord-tenant relationship (indicators for subsidized rental housing and different lengths of tenancy). The binary indicator $D_{r,i,t}$ is set to one if the dwelling is observed in region r and period t. Unobserved and observed time-constant characteristics, such as size of the dwelling, type of building, and type of urban area are captured by the dwelling-specific effect $c_{i}$. $\varepsilon _{i,t}$ is an idiosyncratic error term.

We estimate the coefficients in Eq. 18 using an unbalanced panel sample of 9,852 rental dwellings in the GSOEP. As before, we use a fixed effects estimator, which removes the time-constant observed and unobserved characteristics, $c_{i}$, from the regression. Table 10 reports the coefficient estimates. The fit of the regression measured with the $R^{2}$ is reasonably good. Moreover, the estimated coefficients for the included time-varying variables have reasonable signs and are statistically significant at the usual significance levels.

Table 10 Hedonic repeat- measures rent regression

We compute region-specific constant-quality rent series in two steps. First, we compute constant-quality index series from the estimated time dummy coefficients in Eq. 18 with $I_{r,t} = \exp \{\widehat {\gamma }_{r,t}-0.5\widehat {\sigma }^{2}_{\gamma _{r,t}}\}$, where $\widehat {\gamma }_{r,t}$ is the estimated time dummy coefficient for region r in period t. $\widehat {\sigma }_{\gamma _{r,t}}$ is the corresponding estimated standard error of the coefficient estimator. This second term corrects for small sample bias. The index series are normalized to one for our base period 1995. We then, second, convert the index series into level series $R_{r,t} = \widehat {I}_{r,t} \bar {R}_{r,1995}$, where $\bar {R}_{r,1995}$ represents the median rent level in region r for the year 1995. After deflating with the consumer price index, we obtain the final constant-quality real rent series.