Some references: \cite{Heckman_2001,ROY_1951a}

Estimation Strategies

Decission to move out

The evaluate the decision to move out we regress the decision to move out upon etc.... 

Dependent Variable

The main problem we were facing during our analysis was that there is no generated variable that could work as a proxy for our topic of interest in the SOEP.  Therefore we developed the following strategy to identify, if an individual had left his or her parental household during tertiary education,  based on the observation of the individual's household identifier.
We start by filtering all individual who obtained tertiary education from the bio-education data set provided in the SOEP core data.  In the next step we restrict the data set to individuals for who we know when they graduated from university. This reduces the number of individuals from 12877  to only  2511.  
Further we had to ensure that we observed individuals before they decided to leave their parental households. Not only because we want to integrate different covariates based on the parental characteristics but also to ensure it is possible to identify the year of leaving. We did this by restricting the sample again based on the $stell  variable that provides information about the relationship to the head of household.  We keep only individuals who we observe as children in their original household  before they graduated.  This leads to a additional decrease so that we remain with 1363 individuals.
Lastly we created  a dummy that indicates whether an individual left his or her parental household by comparing the original household number of the individual with the  wave specific household identifier (hhnrakt) in every year until his or her graduation./last year observed in tertiary education  We found that from the 1363 individuals 592 stated to left their parental household during their tertiary education.

Independent Variable

Birth cohorts
\cite{Holdsworth2000} points out that reason and destination of young people leaving home has shifted from leaving for marriage and then co-residing with the spouse, to an demand of young people expiriencing independent living, before building up an union with their future companion.  
Gender
Across all european countries, policy envoirements and social groups \cite{Billari2001} and \cite{Aassve2002} find that women leave earlier than men. Therefore we need to control for students in Germany as well.
Household income
It is very intuivly that the houshold income at the time of moving out, is a driving factor. On the other side has Germany student subsidy programs, which should provide a income independent decision of residency. \citep*{Laferrere2004} shows the househol income 's effect ambiguity on the decision of leaving home. While parent's higher income could result in a less constraint choice of a dwelling, it also can indicate better facilities, i.e. space in the parental home.
Migration Background
We control for a Migration background not only because \cite{Billari2001} and \citep{Aassve2002} find different patterns across European countries, but also \citep{Jeong_2013} show that immigrants in Canada keep the leaving age tendency of their home country for the first generations, before it disappears. 
Parent's educational background
We control for the influence by parental education with dummy variables for the achievement of the highest school diploma in Germany(Abitur). It is well documented in the literature, that  a higher parental education raises the probability of the children to go to college. \cite{Holdsworth2000} shows that in Britain as well as in Spain higher education of the father raises the probability of moving out to pursue higher education. For Britain she also proves the impact of the mother's education, while in Spain it doesn't have a significant effect.
The variables mentioned above were all subject to studies on the behavior of moving out before. In this paper we use a different approach to explain the decisions of a young adult to move out before college graduation. The approach allows to control for heterogeneity in personality as a driving factor for the decision.  We faced for all following Variables the Problem, that they were measured at different at points in time. For members of our treatment group, i.e. for the people moved out during college, we used the data justifiable to be valid at the time of decision taking. For individuals living at home at the end of their study we used data justifiable to be valid 3 years before ending their education. This rule to choose the adequate point of time was also applied for the household income.
Big Five
\citep*{Allport_1936}  started with  17,953  personality describing words and reduced them 4,505  personality adjectives. Using factor analysis they loaded these adjectives into five subordinate factors. By convention these are today  Openness to experience, Conscientiousness, Extraversion, Agreeableness and Neuroticism. 
 \citep{Caliendo2013} describe the personality traits as follows: 
Openness to new experience describes the ability for seeking new experiences and exploring novel ideas. Individuals with high scores should be creative, innovative and curious \cite{McCrae_1987}. It is also strongly correlated to cognitive skills, especially to intelligence related to originality and broad-mindedness \citep*{BARRICK_1991}
Conscientious individuals are described as achievement orientated on one side and on the other as hard workers, efficient and dutiful.
Persons with high scores in extraversion are predicted to be assertive, dominant, ambitious, energetic and seek leadership roles \citep{Judge_1999}.
Agreeableness focuses on interpersonal relationship. People with a high score are forgiving and have a trusting nature, though they are very cooperative. A low score would indicate a self-centered and hard bargaining individuals.
Neuroticism or as a opposite pole emotional stability as \citep{Caliendo2013} uses it. Neuroticism in his negative interpretation, so low scores, are individuals characterized as self-confident, relaxed and able to tolerance stress. Though they can manage performance pressure, remain optimistic and maintain relationships towards others.
These five factors are measured in the SOEP in a battery of 15 questions. We use the insights of the factor analysis in \citep*{schupp2007} to identify for each of the five the main three items and their algebraic sign on the trait. For the negative items we reverse the ranking and therefore generate each trait by adding the three items and z-normalize them. In \citep*{Cobb_Clark_2012}  and \citep{Elkins2017} show that for individuals in their adolescence groups a mean-level consistency for at least 4 years. Therefore we can include in the data set for determining the choice only individuals moving out after 2002 or finishing their studies later than 2006. 
\citep{Caliendo_2013} discuss the explanatory value of further non-cognitive traits, e.g. Locus of Control and Willingness to take Risk. Using a factor analysis they show their value to explain variety in human capital decisions. Therefore we include those two as well, as they are measured in a similar interval as the big five. 
Locus of Control
The idea of Locus of control was first introduced by \cite{Rotter_1966}. He uses a two dimensional concept describing the internal locus of control (What happens in my life depends on myself) and the external locus of control (What happens in my life depends on fate, luck and the actions of others).
\citep*{Berger_2016} use SOEP data to construct a one dimensional locus of control score using five items of the question battery, namely Question 1, 3, 5, 8  and 10. These items are chosen, because they represent a trade off between internal and external locus of control. They run a factor analysis to prove that there is one latent factor behind these five items and to approve the algebraic sign of them. All except the first are reversed and so a higher score indicates a higher internal and a lower external locus of control. They compare their concept to the ones of   \citep{Pinger_2016} or  \citep{Caliendo_2015} and find no significant differences. For more detailed analysis and arguments for choosing exactly these five and not more see the appendix of \citep*{Berger2016}. We again use the work of  \citep*{Cobb_Clark_2012}  and \citep{Elkins2017} to assume a consistency of 2 to 3 years.
Willingness to take Risk
The Willingness to take Risk is measured through a 0 to 10 scale in the SOEP.  \citep{Dohmen_2011} show that this measure has a high correlation with measures of risk in other contexts Therefore the hypothesis of a stable underlying risk preference is justifiable. \citep{Bonin_2007} show that Willingness to take Risk has an effect on labor outcome and can therefore be seen as factor contributing to human capital. As we try to explain the decision to move out as a result of the variety in individual human capital, we control on this facet as well.

Outcome of moving out

To calculate the impact of moving out we use a augmented Mincer equation: