The intergenerational transmission of liberal professions

By using university administrative and survey data on Italian graduates, we analyse the intergenerational transmission of liberal professions. We find that having a father who is a liberal professional has a positive and significant effect on the probability of a graduate of becoming a liberal professional. To assess the processes at work in this intergenerational transmission, we evaluate the effect of having a liberal professional father on the probabilities to undertake each of the compulsory steps required to become a liberal professional, which are choosing a university degree providing access to a liberal profession, completing a period of practice, passing a licensing exam and starting a liberal profession. Having a liberal professional father has a positive and statistically significant effect on the probability to complete a compulsory period of practice and to start a liberal profession; whereas there does not seem to be an effect on the type of degree chosen and on passing the licensing examination, at least after controlling for child’s and parental formal human capital.


Introduction
The focus of this paper is on explaining why children of liberal professional fathers have a larger probability to become liberal professionals. We consider liberal professionals who are self-employed workers providing public services which require them to hold a specic university degree, to obtain a professional license by passing an exam and to complete a compulsory period of practice, which has to be undertaken before the licensing exam. 1 By using university administrative data linked with post-graduation surveys covering the universe of graduates in 22 Italian Public Universities in 2002 and 2003, we nd that the probability of a graduate child to become a liberal professional increases of 9 (16) percentage points when the father is a graduate liberal professional rather than an entrepreneur (a blue collar). These are huge increases, given that only 13% of graduates become liberal professionals.
Similarly to the intergenerational transmission of income, the occupational transmission has been explained by inheritability of endowments and parents' investments in their child's human capital (see Tomes 1979, 1986). But, to justify a dierent degree of transmission for dierent occupations, it is necessary to recognise that there are two types of human capital investments: the indirect investment through formal education and the direct investment through the transmission of job-specic abilities and knowledge from fathers to children (see Laband andLentz 1983, 1992;Evans and Jovanovic 1989;Dunn and Holtz-Eakin 2000;Fairlie and Robb 2007;Fairlie and Krashinsky 2012). Liberal professions are a type of occupation where the intergenerational transmission of skills and knowledge is important and helps in lowering the entry barrier costs, e.g. shortening the time needed to set a portfolio of customers and increasing potential early prots.
If parental human capital investments were the only explanation for the occupational transmission from fathers to children, then there would be no reason for thinking that a high degree of occupational transmission is unfair. However, other possible mechanisms explaining the transmission of liberal professions are: the transfer of nancial resources, job preferences, family networking and the potential transmission of the family business. 2 Furthermore, an additional mechanism which can explain the large intergenerational association in liberal professions is nepotism, i.e. the fact that liberal professional fathers can help their children beyond their merits to be accepted and to complete a period of practice, to pass a licensing exam, or to undertake other steps required to become a liberal professional. 3 We are unable to evaluate the separate eect of nepotism; but, after controlling for variables which measure child's and parental formal human capital, and child's job preferences and family nancial resources, we can interpret the residual eect of having a liberal professional father on the probability of becoming a liberal professional as the combined eect of transmission of job-specic skills and knowhow, nepotism, family networking and potential inheritance of the family business. While we capture the formal human capital by controlling for a rich set of measures of educational choices and attainments in high school and university using administrative data, which are unlikely to suer of measurement errors; our measures of nancial resources and job preferences are proxy variables which might not fully control for the two related transmission mechanisms. Nevertheless, because we compute the eect of having a liberal professional father on the probability of becoming a liberal professional as the dierential eect with respect to having a father who is an entrepreneur and the transmission of nancial resources and job preferences is likely to be very similar between fathers who are entrepreneurs and liberal professionals, we expect the potential bias caused by these proxy variables to be small. The novelty of our paper is that we decompose for the rst time the probability of a graduate to become liberal professional in the product of four probabilities (processes) which represent four sequential steps that a child has to undertake to start a liberal profession, which are choosing degrees providing access to liberal professions which require practice period, completing a compulsory period of practice, obtaining a professional licensing and starting a liberal profession. This approach allows us to evaluate the eect of having a liberal professional father in each of these four specic processes and to explain how this eect is mediated by dierent mechanisms. In this way we can identify which process is the most important in explaining the intergenerational transmission of liberal professions, and therefore we can provide more precise policy recommendations to improve access to liberal professions.
Our approach is similar in spirit to Mare's educational transition model, which estimates the eect of parental background on the probability of progressing from one educational level to the next using a sequential binary model (see Mare 1979Mare , 1980Mare , 1981Mare , 2011. The main dierence is that, rather than evaluating the eect of family background on school transitions, we estimate the eect of parental occupation on sequential probability processes, which represent sequential steps that a child has to undertake to become a liberal professional.
More precisely, we consider the full sample of graduates and estimate the eect of having a father who is a liberal professional on each of four following probability processes: I.a the probability to choose university degrees that give access to liberal professions which require a compulsory period of practice, I.b the probability to complete a compulsory period of practice, I.c the probability of passing a professional licensing exam, I.d the probability to start a liberal profession.
Each of these probabilities is conditional on having undertaken the previous step, i.e. completing a period of practice is conditional on having a degree that gives access to liberal professions which require a compulsory period of practice, passing a professional licensing exam is conditional on having completed a period of compulsory practice, and starting a liberal profession is conditional on having obtained a license. Therefore, the probability to become a liberal professional for a graduate is given by the product of the above four conditional probabilities ([I.a], [I.b], [I.c] and [I.d]), which are sequential probabilities. 4 Our ndings suggest that the completion of a compulsory period of practice and the liberal profession initiation are the major processes at work in the transmission of liberal 4 In presence of omitted variables which aect all the above four probabilities, the computation of the probability to become a liberal professional is slightly more complicated, because it requires the estimation of a joint quadrivariate probability model that allows for correlation between the error components in the four probability processes. In the paper we show that the estimation results obtained using separate sequential probability models and the joint quadrivariate probability model are similar.
professions from fathers to children. On the contrary, the type of degree choice and the licensing examination do not play a major role in explaining the transmission of liberal professions.
When controlling for the eect of the observed mechanisms of transmission, i.e. for the transmission of nancial resources, formal human capital and job preferences, separately on the four dierent probability processes, we nd that the advantage of having a liberal professional father in the same eld of study, (i) on the probability to complete a compulsory period of practice (process I.b), is mainly explained by the transmission of formal human capital followed by family networking and/or nepotism, (ii) on the probability to pass a licensing exam (process I.c), is explained exclusively by formal human capital, (iii) on the probability to start a liberal profession (process I.d), is explained by the transmission of the family business and possibly nepotism.
The remainder of the paper is organised as follows. Section 2 summarises the literature related to our research. Section 3 provides some institutional details on the educational system and on the professional licensing in Italy. We then describe the data in Section 4 and provide descriptive measures of intergenerational mobility in liberal professions in Section 5. We assess the eects of having a liberal professional father and of dierent mediating mechanisms on the probability of becoming a liberal professional and on the four dierent sequential processes of intergenerational transmission in Sections 6 and 7, respectively. Finally, Section 8 concludes.
2 Related literature By assuming that the cost to acquire human capital related to a specic occupation is lower for children who follow their father's occupation and that fathers with a child who is a follower maximise their own earnings as well as their child's, Laband and Lentz (1983) develop an economic model which explains the mechanisms behind the intergenerational occupational transmission and the dierences in this transmission across occupations. Direct and indirect human capital transfers from fathers to children are assumed to be the mechanisms of intergenerational transmission at work, and the explanation given for why some types of occupations are more often transmitted than others is that they require job specic human capital that can be easily and cheaply transmitted from fathers to children. Laband and Lentz (1983) nd that for occupations where the direct transmission of job specic knowledge and abilities is more relevant, such as farmers and self-employed people, there is a higher percentage of children following their father's occupation. High levels of intergenerational transmission have been found also by Dunn and Holtz-Eakin (2000) and Srensen (2007) for self-employed people, by Lindquist et al. (2015) for entrepreneurs and by Pellizzari et al. (2011) for liberal professionals.
Beside the human capital transmission, another possible explanation for the strong intergenerational association is the presence of credit market imperfections, which may lead to a failure of meritocracy (see Evans and Jovanovic 1989;Dunn and Holtz-Eakin 2000;Caselli and Gennaioli 2005;and Fairlie and Kranshinsky 2012). Evans and Jovanovic (1989) propose an economic model for the decision to be self-employed, and they provide empirical evidence that wealthier people have higher probability of starting a self-employment activity. Dunn and Holtz-Eakin (2000) extend this model to allow for nancial capital transfers from fathers to children, so that the decision to become self-employed depends on the personal human and nancial capital as well as on the human and nancial capital transmitted from the father. There is also some empirical evidence that the probability of becoming a selfemployed worker or an entrepreneur is higher for children whose fathers are wealthier (see Holtz-Eakin et al. 1994;Parker and Van Praag 2006).
An additional potential explanation for the intergenerational occupational mobility, which has been mentioned but not formalised in a theoretical economic framework, is the transmission of preferences and attitudes from parents to children. For example, risk averse fathers are less likely to become entrepreneurs and probably transmit their risk aversion to their children, who in turn will be less likely to become entrepreneurs (see Dunn and Holtz-Eakin 2000;Fairlie 2002). Necker and Voskort (2014) provide some evidence on intergenerational transmission of risk attitudes looking at earnings risk. They nd that a child's earnings risk increases by 14% of a standard deviation for one standard deviation increase in father's earnings risk. This association is statistically signicant, but small in size.
A further mechanism of transmission is nepotism, which may aect the outcomes of school admission exams and licensing exams, and ultimately the probability of starting specic occupations. 5 It is generally dicult to distinguish the roles of nepotism and of human capital transfers in the intergenerational occupational transmission. This is because the intergenerational transmission of knowledge and the father's work network may increase intergenerational mobility without implying favouritism (see Magruder 2010; Ponzo and Scoppa 2011b; Kramarz and Skans 2014). It is perhaps easier to identify the contribution of nepotism when looking at exams for which the probability of success should be independent of the father's occupation once the child's ability is controlled for. An example of this is the licensing examination in Italy, which is a mandatory requirement to become a liberal professional.
Such licensing examination has been often accused of favouritism toward children of liberal professionals, but the empirical evidence is mostly anecdotal or based on statistical analysis that cannot adequately control for the intergenerational transmission of nancial resources, formal and informal human capital and preferences (see Basso and Labartino 2011). The most convincing evidence on the eect of fathers on children starting a liberal profession is given by Basso and Pellizzari (2010). 6 Using local administrative registers of professionals in Italy, they nd a negative relationship between the age when people start a legal profession and the frequency of their family name in the local register. Since the frequency of their surname is likely to indicate family connections, the negative relation might suggest a potential eect of nepotism on the probability of passing a license. The presence of nepotism is conrmed by a comparison of the relationship between starting age of a legal profession and frequency of the family names before and after the introduction of a reform aimed at reducing biases in the marking of licensing exams. The association between starting age and surname frequency decreases after such intervention, indicating a potential reduction in the nepotism eect.
A nal mechanism through which liberal professions get transmitted from parents to children is the potential inheritance of the family professional business which lower the entry barrier to the profession. Bennedsen et al. (2007) nd a causal signicant negative eect on 5 Previous papers that have studied the eect of nepotism include Lentz and Laband (1989) and Arulampalam et al. (2005), who look at school admission; P erez-Gonz alez (2006) and Bennedsen et al. (2007), who analyse the chief executive ocer (CEO) successions; Basso and Labartino (2011), who evaluate the eect of nepotism on the starting age of licensed professions; Ponzo and Scoppa (2011a), who study its eect on recruitment; and Scoppa (2009), who estimates the intergenerational mobility of public sector jobs. 6 The main results are also summarised in Basso and Labartino (2011). rms performance of the transmission of chief executive ocer (CEO) positions from parents to children, which seems to suggest that the decision to appoint a family member as CEO is not so meritocratic. Grossmann and Strulik (2010) consider the intergenerational transmission of ownership and control of a rm from parents to children. They develop a theoretical model to study whether preferential inheritance tax on family rms may lead to a cost for society because of the potential transmission of rms to heirs who do not necessarily have high entrepreneurial abilities. Calibrating the theoretical model using German data, they actually nd that preferential tax treatment of family rms worsen macroeconomic performance. Lindquist et al. (2015) focuses on the transmission of entrepreneurship from parents to children and, by using Swedish adoption data, they nd that the most relevant factors explaining such transmission are post-birth rather than pre-birth factors. This result suggests that there are not strong genetic mechanisms explaining the intergenerational transmission of entrepreneurship. Mocetti (2016) studies the intergenerational transmission of pharmacies in Italy. He nds that an increase in the cap imposed on the number of pharmacies per population (a decrease in rent) leads to a reduction in the intergenerational transmission of pharmacies, but has no eect on the career choices of children of non-pharmacists. This evidence suggests that high entry barriers provide a benet to children of pharmacists and this advantage may lead parents to favour their child beyond their merit.
To summarise, the main mechanisms at play in the intergenerational transmission of liberal professions are: (i) formal human capital; (ii) preferences for specic jobs, (iii) nancial resources, (iv) job specic human capital (informal human capital), (v) family network, (vi) nepotism, (vii) inheritance of the family business. Most of the above mechanisms of transmission of occupations have been emphasised also by sociologists, who stress that these occupational transmission mechanisms are relevant conduits for social reproduction (e.g. Our paper is also related to the literature on intergenerational mobility and especially to contributions that study the mechanisms explaining the transmission of occupations from parents to children. An approach often adopted to investigate these intergenerational mechanisms is the decomposition of intergenerational association in the part explained by mechanisms (such as education, cognitive and non-cognitive abilities, and nancial resources) and in the residual part which captures the intergenerational association net of these mediating mechanisms. This type of approach was introduced by sociologists in the 60's and 70's (see Blau and Duncan 1967;and Sewell and Hauser 1975) and was soon after adopted by economists (See Conslik 1974, 1977Atkinson 1980;and Atkinson and Jenkins 1984). 7 These studies have certainly helped in assessing the magnitude of some mechanisms in explaining intergenerational occupational mobility, but have left some more specic occupational transmission mechanisms unexplored.
To sum up, the contribution of existing literature has been to underline the role of dierent mechanisms in explaining the intergenerational transmission of occupations. Nevertheless, the empirical evidence on mechanisms is still fragmented as most of the studies focus only on few mechanisms and are unable to evaluate the role of each of them. Our paper provides some more comprehensive analyses on the mechanisms looking at their eects on the transmission of liberal professions from fathers to children as well as on the dierent underlying processes. In Italy all students with any type of high school diploma can enrol in a university degree. High school diplomas are upper secondary qualications, which are usually completed at age 18-19, and they can be academic (licei classici and licei scientici) or vocational (istituti tecnici and istituti professionali).
In the period considered in our empirical exercise most of the Italian Universities were public and, with the exceptions of few departments (e.g. Medical Schools and Architecture), there were no university admission exams. If students failed an exam or were unhappy with the mark obtained, they could re-sit the exam several times. Consequently, students usually took much longer than the minimum ocial period to complete their degree. Four-year degrees were usually completed in an average of 7.5 years, with only one in eight students completing within 4 years (ISTAT 2000).

Professional licensing in Italy
In Italy, as in many other countries, professional occupations are subject to a range of requirements to guarantee the acquisition of professional credentials (see Paterson et al. 2003;Catania and Monti 2011;and Pellizzari and Pica 2011). The main four prerequisites generally required by all types of liberal professions are: (i) to have a university degree in a eld of study relevant for the specic liberal profession; (ii) the acquisition of professional experience through a period of practice and/or specialised courses; (iii) passing a licensing exam; (iv) becoming a member of a relevant formal professional body. 8 Several liberal professions require a practice period spent under the supervision of a member of the relevant professional body and practitioners are not paid but may receive a fellowship. The length of the practice period is three years for accountants, two years for lawyers (but can be shortened to one year by attending a Law specialization school for two years), eighteen months for notaries, one year for psychologists, and six months for pharmacists and architects; while the practice period is not mandatory for engineers, geo-biologists, and agronomists.
The licensing exam is compulsory and consists of one or more written tests and an oral exam. Generally, the licensing exam takes place once per year in dierent provinces. There are no limits to the number of candidates admitted to the licensing exam and to the number of times an examination can be taken. Because the licensing exam includes an oral exam, it is impossible to guarantee the absence of interference with the examination committee's members to favour specic applicants.
Candidates who successfully pass the licensing exam have to become members of a formal professional body (Albo Professionale) before starting their liberal profession. Except for passing the licensing exam, there are no other relevant prerequisites for the enrolment in the professional body. The main requirement for the members of the professional body is to respect the code of conduct set by the body, which generally imposes rules and restrictions on pricing, advertising and business structure.

Data
We use data from AlmaLaurea, which is a consortium of Italian Universities whose aim is to provide employers with information on graduates. Graduates ll in a questionnaire at the completion of their degree (Prolo dei Laureati survey) and are followed and interviewed again after 1, 3 and 5 years from the degree (Condizione Occupazionale dei Laureati survey). These last three interviews are computer assisted telephone interviews administered by trained interviewers. Information from the four interviews is matched with students' details contained in the universities' administrative data registers, so that for each cohort of graduates AlmaLaurea is able to provide details on age, sex, area of residence, family background, educational choices and test scores pre and during university, labour market status during and after the university, occupational characteristics and wage after the degree.
The initial survey at the completion of the degree covers almost the whole population of new graduates from the Universities belonging to the AlmaLaurea consortium. The response rates in these initial surveys are usually well above 90% for each cohort of students. Looking at the interviews 5 years after the degree the respondents still represent more than 80% of the population of graduates who answered the initial interview. and Venezia Architecture. We do not consider students that are older than 40 at the completion of their degree and the few ones that were resident in a foreign country or with a foreign high school diploma before starting university.

Sample denition
Our nal sample of graduates includes 24,309 people, and we also consider the three following subsamples: 1. the subsample of graduates with degrees providing access to liberal professions which require compulsory period of practice to obtain a license (11,308 individuals), 10 2. the subsample of graduates with access to liberal professions who completed a compulsory period of practice (7,899 individuals), 3. the subsample of graduates who completed a compulsory period of practice and passed a licensing exam (5,601 individuals).
Because our analysis considers only liberal professions for which the university degree is mandatory, the probability of becoming a liberal professional without a degree is zero and when conditioning on having a degree we can focus on the sequential processes that occur from the choice of the type of degree to the entry into the labour market. In the Italian context the probability to get a university degree is much more related to parents' education than to parents' occupations (see Checchi et al. 2013); therefore, we do not expect any strong eect of having a liberal professional father on the probability of graduating and therefore omitting to consider the graduation probability process should not bias our results.  Table A1 reports some descriptive statistics and shows that 46.5% of graduates choose a degree that gives access to liberal professions for which the period of practice is mandatory, 40.7% obtain a professional license, and about 13.0% of graduates become a liberal professional within 5 years from graduation.

Explanatory Variables
To explain the probability to choose a degree with access to liberal professions requiring a compulsory practice, we use only child's characteristics observed at the start of the university, to explain the probability to complete a compulsory period of practice and to pass a licensing exam we consider also characteristics observed at the completion of the university degree, nally to explain the probability to start a liberal profession we consider additionally characteristics observed once the licensing exam has been passed.
The characteristics at the start of the university include a set of variables that measure the child's formal human capital, which are: age at the start of the university and its square term; high school nal mark, which ranges between 36 and 60; high school type, i.e. a dummy variable taking value 1 for vocational high schools (istituti tecnici and istituti professionali) and 0 for academic high schools (licei classici, scientici, linguistici and psico-pedagogici); area of residence in Southern Italy, which is given by a dummy variable taking value 1 for individuals living in the Southern regions and the two main Islands and 0 for individuals living in the Northern and Central regions 11 .
At the completion of the university we control for variables measuring nancial resources, job preferences, and human capital. We proxy the nancial resources by using two dummy variables for having worked during university and having received a university scholarship, which only students from low income families are eligible for. To measure the graduates' preferences for jobs with high degree of autonomy and independence and for jobs with high security, all graduates, at the completion of university, are asked the following two questions: \How important is high stability/security in the job you are looking for?" and \How important is independence/autonomy in the job you are looking for?" The answers are reported in a 5-point scale, where 1 means \not at all important" and 5 means \extremely important". We measure the preferences for job independence and security by considering the self-reported levels of job preferences and their square terms. The variables measuring human capital are: a dummy for having graduated from a South university; a set of dummy variables for the eld of study; the nal university grade standardised at department level by using all the observations available in the sample; 12 the interaction term between the dummy for a Southern university and the standardised university nal grade; 13 a set of dummy variables for 1, 2, 3, 4 and 5 or more years delayed graduation (no delay is the reference category), where the delay is computed as additional number of years spent to get a degree beyond the minimum period.
To explain the probability to start a liberal profession, we consider two extra explanatory variables which are two dummy variables for having passed the licensing exam between 13 and 36 months from graduation and between 37 and 60 months from graduation (having passed the exam within 12 months from graduation is the reference category). Conditional on the remaining variables, a delay in passing the licensing exam may be a signal of a lower human capital endowment.
The bottom panel of Table A1 summarises the above variables by reporting means and standard deviations using our sample of 24,309 graduates. The average high school nal grade is about 49 (out of 60 maximum points) and only one in three individuals has a vocational diploma. The average age at matriculation is 19, and only 4.7% of the individuals complete their degree within the minimum required period. 31.6% of the graduates were 12 The unstandardised nal degree ranges between 73 and 111 (i.e. 110 cum laude) and its mean and standard deviation are reported in Table A1. 13 The dummy for a Southern university and its interaction with the standardised university nal grade are included to capture dierences in the quality of the university in the South, but they can also capture potential dierences in the probability of passing a licensing exam and starting a liberal profession in Southern regions. resident in the South of Italy before starting the university, but only 24.8% obtain their degree in a university located in the South of Italy. 64.4% of people in our main sample have some work experience during university. On average the level of preference for job security and independence is about 4, which is just below the maximum level of preference which is 5.

Parents' occupation and education
To study the eect of parents' occupation and education on the probability to choose a degree with access to liberal professions requiring a period of compulsory practice, we consider a set of dummy variables to distinguish between fathers who are graduate liberal professionals, non-graduate liberal professionals, 14 managers, entrepreneurs, self-employed workers, non-manual workers and blue collars; having a graduate father who is not a liberal professional; and two dummy variables for mothers who are graduate and non-graduate liberal professionals. 15 Both self-employed workers and entrepreneurs work on their own account; but while entrepreneurs engage one or more employees on a regular basis, self-employed workers do not usually engage employees. Liberal professionals are self-employed workers who provide a public service which requires specic intellectual skills and an ocial license. Both blue collar and non-manual workers are employees; but while the former include unskilled and semiskilled manual workers, the latter include technicians, teachers, clerical workers and lower supervisors. Finally, managers are employees who have high managerial occupations such as directors, business executive, head teachers, university professors and chief physicians.
When modelling the probability to complete a compulsory period of practice, to obtain or to pass a licensing exam and to start a liberal profession, we consider dummy variables for having a graduate liberal professional father with the same degree, having a graduate liberal professional father with a dierent degree, having a liberal professional mother with the same degree, and having a liberal professional mother with a dierent degree or without a degree. Table A2 reports the mean of each of the dummy variables describing the fathers' and mothers' occupation and education in the sample of 24,309 graduates. More than 50% of the fathers are either blue collar or non-manual workers (19.1% and 31.5%, respectively), while 9.6% are liberal professionals, 4.6% are graduate, of this 1.3% with the same degree. Only 1.9% of the mothers are liberal professionals, whereof 0.1% with the same university degree.

Measures of intergenerational association
Let us denote the probability of a child of becoming a liberal professional within 5 years from graduation 16 conditioning on the father's occupation by P rY c 1SY f 1; ( 1) where Y c is a dummy variable taking value one if a child becomes a liberal professional and zero otherwise, and Y f is a dummy variable taking value 1 if his/her father's is a liberal professional and zero otherwise. We begin by reporting in Table 1 The odds ratio measures the so called intergenerational exchange mobility, which is unaffected by changes in the frequency of liberal professionals from the fathers to the children generation. It measures the association between becoming a liberal professional and having a liberal professional father, which takes values greater (lower) than 1 when the association is positive (negative).
This odds ratio is reported in the rst column in the top panel of Table 1, while in the second column we report the equivalent odds ratio when considering only children who become liberal professionals after a compulsory period of practice which are the type of liberal professions considered in our main analysis. In both cases, we nd that the odds to be a liberal professional if one's father is a liberal professional is about twice the corresponding odds than if one's father is not a liberal professional. We also compute the odds ratios when considering liberal professional fathers with and without a university degree and the transmission is much larger for graduate professional fathers (compare second and third row in Table 1).
To check whether there are any dierences in the degree of intergenerational transfer across liberal professions, we report the odds ratios computed by considering specic liberal professions in the bottom panel of Table 1. 17 The odds ratios increase when considering liberal professions for which there is a compulsory period of practice, especially if it is long (see column 2). The largest odds ratio is observed for pharmacists and this is likely caused by strict regulations which limit the number of new pharmacies and increase the likelihood that pharmacies be transmitted from fathers to children (see Mocetti 2016). For geo-biologists and agronomists, for whom there is no compulsory practice, the odds ratios are large but they are not signicantly dierent from 1. These results seem to suggest that high entry barriers to the profession increase the occupational transmission from fathers to children.
6 Intergenerational association: dierent mechanisms Let us consider the probability of a graduate of being a liberal professional conditioning on the father's occupation and education by P rY c 1SD f j ; ( 3) where j 1; :::; 7; Y c is a dummy variable taking value one if a graduate becomes a liberal professional and zero otherwise; 18 D f is a categorical variable denoting his/her father's occupation, which takes value 1 for graduate liberal professionals, 2 for non-graduate liberal professionals, 3 for managers, 4 for self-employed workers, 5 for non-manual workers, 6 for blue collar workers and 7 for entrepreneurs.
In column (1) of Table 2 we report the average marginal eects of having a father in a specic occupation relative to having a father who is an entrepreneur on the probability of 17 We do not report the odds ratio separately for psychologists because there are only ve fathers who are psychologists.
18 For children we consider only liberal professions for which there is a compulsory period of practice.
eoming lierl professionlD 19 whih re omputed using the following formul P rY c ISD f j P rY c ISD f U for j I; :::; T: @RA e hoose s referene tegory for the fther9s ouption the entrepreneurs euse their expeted inome is similr to the one of lierl professionls nd oth lierl professionls nd entrepreneurs work on their own ountD so tht fthers with these two types of ouptions re likely to trnsmit to their hildren similr jo preferenes @espeilly preferenes for jo independene nd riskA nd nnil resouresF 20 o understnd how the hoie of the referene tegory ets our resultsD we lso report in the eppendix e the orresponding results when onsidering lue ollrs s referene tegory @see eppendix e le eQAF he dierentil eet of hving lierl professionl fther inreses when onsidering lue ollrs @see le eQ olumn IA rther thn entrepreneurs @see le P olumn IAD it goes from VFP to IQFT perentge pointsD suggesting tht the trnsmission of nnil resoures nd jo preferenes from prents to hildren is more omprle etween lierl professionls nd entrepreneurs thn etween lierl professionls nd lue ollrsF o ssess the role of dierent mehnisms in explining the intergenertionl ssoition in lierl professionsD we lso ompute the verge mrginl eet of hving fther in dierent types of ouptions on the proility of hild of eoming lierl professionl when ontrolling for vetor of hrteristis X whih ptures fmily nnil resouresD jo preferenes nd forml humn pitlF e do this y estimting proit model for the proility to eome lierl professionl P rY c ISD f ; X ¨ 0 X 6 Q j 1 ID f j j ; @SA where¨denotes the umultive funtion of the stndrdised normlD X is row vetor of explntory vrilesD is the orresponding olumn vetor of oeientsD ID f j is n inditor funtion tking vlue one if the fther hs ouption j nd zero otherwiseD nd j is the orresponding oeient whih mesures the eet of hving fther with 19 These average marginal eects are computed considering a probit model for the probability to become a liberal professional and using the maximum likelihood estimates. 20 Using the Survey on Household Income and Wealth (SHIW) of the Bank of Italy over the period 1998-2010, we nd a very close value for the average net income of males who are liberal professionals and who are entrepreneurs, Euros 35,487 and 36,566 respectively. Using our main sample, we also nd a similar value for the average level of preference for job independence (security) between children of liberal professionals with the same degree and children of entrepreneurs, 4.016 and 3.951 (3.958 and 3.880) respectively. ouption j with respet to hving fther who is n entrepreneur @referene tegoryAF he verge mrginl eet of hving fther who is grdute lierl professionl with respet to fther who is n entrepreneur is omputed y onsidering the following dierene in proilities P rY c ISD f I; X P rY c ISD f U; X ¨ 0 X 1 ¨ 0 X; @TA repling the oeients with their mximum likelihood estimtes nd verging over the full smpleF he verge mrginl eets for fthers with other ouptions re omputed in similr wyF le P reports the verge mrginl eets of hving fther in spei ouptions on the proility to eome lierl professionl unonditionl on ovrites iFeF ontrolling forX nothing @olumn IAY nancial resources @olumn PAY job preferences @olumn QAY formal human capital @rgA t the strt of the university nd t the ompletion of the university @olumn RAY parental human capital @rgA @olumn SAY nd all variables together @olumn TAF he detiled list of vriles is reported t the ottom of le PF ih olumn reports the verge mrginl eets of hving fther with dierent types of ouption with respet to hving n entrepreneur fther ut using dierent set of vriles XF he eet of hving nonEgrdute lierl professionl fther is not signintly dierent from zeroY onverselyD the eet of hving grdute lierl professionl fther is HFHVP ut redues to HFHSS one ontrolled for ll oserved vriles @see le P olumns I nd TAF his residul ptures the eets of nepotism nd fmily networking ndD only for lierl professionl fthers with the sme degreeD the trnsmission of jo spei forml humn pitl nd fmily usinessF sn the following setion we etter identify nd explin the seprte ontriution of these residul mehnismsF 7 The eect of mechanisms on dierent processes sn this setion we deompose the proility of eoming lierl professionl in the produt of four sequentil proilitiesD whih re the proilities of @sFA hoosing degree with ess to lierl profession whih requires ompulsory period of prtieD @sFA ompleting period of ompulsory prtieD @sFA otining professionl liense nd @sFdA strting IV lierl professionF purthermoreD we llow eh of these proility proesses to e explined dierently y oserved hrteristisD whih re mesures of nnil resouresD jo preferE enesD hild9s forml humn pitlD prentl ouption nd edutionD y estimting the four following sequentil proit models @UA where Y c 1 D Y c 2 D Y c 3 nd Y c 4 D re dummy vriles whih tke vlue I respetively if the hild hooses degree with ess to lierl profession whih requires ompulsory period of prtieD ompletes ompulsory period of prtieD psses the liensing exm nd strts lierl professionY¨denotes the umultive funtion of the stndrdised normlY X C is vetor of ommon explntory vriles for ll four modelsD whih inludes onstnt nd the set of dummies for dierent fther9s ouptions with the usul referene tegory entrepreneur4Y Z s is vetor of extr explntory vrilesY nd s nd s re the vetors of oeients for X C nd Z s F he list of explntory vriles used for eh of the four models re desried in le QF e n express the proility of grdute of eoming lierl professionl s the produt of the ove four onditionl proilitiesD iFeF P rY c IX C ; Z P rY c 1 IX C ; Z 1 P rY c sn les RD RD R nd Rd we report the verge mrginl eets of hving fther in eh of the dierent ouptions with respet to hving n entrepreneur fther on the four proilities proessesD unonditionl on ovrites iFeF ontrolling forX nothing @olumn IAY nancial resources @olumn PAY job preferences @olumn QAY formal human capital @rgA @olumn RAY parental human capital @rgA @olumn SAY nd all variables together @olumn 6). 21 In Appendix B we also consider the same sequential model estimated using a joint quadrivariate probit model (see Table B1) and results are similar.
The choice of a degree which provides access to a liberal profession is taken before starting the university, therefore to explain the degree choice we consider only explanatory variables which are observed before or at the start of the university. Consequently, we do not control for the job preferences, which are reported after the completion of the degree, the dummies for having had a scholarship and having worked during the university, and the university nal grade. Nevertheless, because our reference category for the father's occupation is the entrepreneur and because the intergenerational transmission of job preferences, nancial resources and formal human capital is likely to be similar for entrepreneur and liberal professional fathers, we believe that our estimated eect of having a father liberal professional in column (6) is net of these three transmission mechanisms.
We nd that the average marginal eect of having a father who is a graduate liberal professional is not statistically signicantly dierent from having a father who is an entrepreneur. 22 On the contrary, the eect of having a graduate liberal professional father is statistically signicantly higher than having a father who is a blue collar (see Table A5a). These results suggest that after controlling for transmission of nancial resources, job preferences and formal human capital, which are likely to be similar for fathers who are entrepreneurs and who are graduate liberal professionals, the residual transmission mechanisms do not play a role in explaining the degree choice.
We nd a negative eect of having a father who is a non-graduate liberal professional with respect to having an entrepreneur father (see second row in Table 4a), which persists even after controlling of all explanatory variables observed before or at the start of the university. The dierential eect can be caused by the dierence in the transmission of human capital given that we now consider a liberal professional father who is not graduate. Conversely, we nd no eect of having a father who is a non-graduate liberal professional with respect to having a father who is a blue collar (see Table A5a). This seems to suggest that non-graduate liberal professionals transmit to their child a level of formal human capital similar to the blue-collars' one and lower than the entrepreneurs' one. We nd similar types of results also 21 The eects of the remaining explanatory variables for each of the probit models when controlling for all variables together are reported in Appendix A Table A4. 22 Henceforth when speaking about signicance we mean statistically signicance at 5% level.
when we consider the probability of choosing a degree providing access to liberal professions without restricting the professions to the ones requiring a compulsory period of practice. 23 Ultimately, our results suggest that children of liberal professional fathers are not more likely to choose degrees which provide access to liberal professions.
Looking at the probability to complete a period of practice without controlling for any variable (see Table 4b column (1)), we nd a large eect of having a liberal professional father, 26.1, 12.7 ad 9.1 percentage points for liberal professional fathers with the same degree, with a dierent degree and with no degree. This eect does not seem explained by the observed variables measuring job preferences and nancial resources (see columns (2) and (3)), but it is explained by the transmission of formal human capital. Once controlled for all covariates, the eects reduce of about 30%, 80% and 60% for liberal professional fathers with the same degree, with a dierent degree and without a degree, respectively. Findings are very similar when considering as reference category fathers who are blue collars rather than entrepreneurs (See Table A5b). These similarities in results reinforce our belief that it is not the transmission of nancial resources and job preferences (which are similar between liberal professionals and entrepreneurs but not between liberal professionals and blue collars) that explain the eect of having a liberal professional father on the probability to complete a compulsory period of practice.
Notice that most of the eect of liberal professional fathers without a degree or with a dierent degree on the probability of their child to complete a compulsory period of practice cancels out once controlled for all covariates. This suggests there are no other relevant mechanisms through which the intergenerational transmission aects the probability of completing a compulsory period of practice. On the contrary, the eect of liberal professional fathers with the same degree remains large even after controlling for the transmission of formal human capital, implying that there are other relevant mechanisms, in particular the nepotism and family networking and the transmission of job specic informal human capital and of family business. We try to net out the eect of transmission of family business by excluding all individuals who report that they are working in a family business 5 years after graduation irrelevant of their occupation, and we nd that the eect of having a liberal professional father with the same degree after controlling for all covariates is still very large 23 Results are available upon request to the authors.
(see Appendix A Table A6). This seems to suggest that the transmission of family business has probably a small role in explaining the probability to complete a period of compulsory practice.
Because all individuals who complete a compulsory period of practice do attempt to pass the licensing exam, we can interpret the estimated eect of having a liberal professional father on the probability of obtaining a license as the eect on the probability of passing a licensing exam. By comparing our probability of passing a licensing exam by type of liberal profession with the corresponding licensing passing rate published in \Il Sole 24 Ore" 24 , we nd indeed that our licensing success rates are comparable or even slightly higher. For this reason, we rename the probability of obtaining a license conditional on completing a practice period as the probability of passing the licensing exam.
Looking at the results for the probability of passing a licensing exam conditional on having completed a compulsory period of practice in Table 4c, we nd that the eect of having a liberal professional father is at most of 6 percentage points when omitting to control for any covariate and it is completely explained by the transmission of formal human capital. These results suggest that neither nepotism nor the transmission of job specic skills aect the probability to pass a licensing exam. Notice that family networking and the transmission of family business cannot aect the probability to pass a licensing exam because the only way they could have an eect is through nepotism. These results are conrmed when blue collar fathers are used as reference category (see Table A5c).
Finally, looking at the probability of starting a liberal profession without controlling for any covariate (see column (1) Table 4d), we nd an average marginal eect of 13.5 and 7 percentage points for liberal professional fathers with the same degree and with a dierent degree, and no statistically signicant eect for fathers who are non-graduate liberal professionals. Controlling for all covariates, the eect of liberal professional fathers with the same degree reduces to 8.4 percentage points and makes the eect of liberal professional fathers with a dierent degree statistically insignicant. Financial resources and job preferences do not seem to explain any of these eects; whereas variables measuring formal human capital such the standardised university degree and the dummy variables for a delayed graduation, have a statistically signicant average marginal eect on the probability to start a liberal profession but of opposite sign to the one expected (see Table A4). Because higher quality human capital decreases the probability to start a liberal professional, we infer that the selection into starting a liberal profession is not meritocratic. The lack of meritocracy makes us also think that it is not the transmission of job specic skills that provides an advantage to children of graduate liberal professionals with the same degree, but rather the transmission of the business or nepotism. To better disentangle these two residual mechanisms, we also estimate the average marginal eect of having a liberal professional father excluding all individuals who are working in a family business 5 years after graduation irrelevant of their occupation. We nd that the eect of having a liberal professional fathers with the same degree, after controlling for all covariates, becomes statistically insignicant (see Appendix A Table A7), which suggests that the inheritance of the family business plays a big role in explaining the probability to start a liberal profession.
In conclusion, our main ndings are the following: (i) the largest eect of having a liberal professional father is observed when a father has the same degree as his child, (ii) having a father liberal professional does not increase the probability to choose a degree with access to liberal professions requiring a compulsory practice; (iii) the transmission of human capital (probably both formal and informal) is the main mechanism explaining the probability to complete a compulsory period of practice followed by family networking and/or nepotism; (iv) the transmission of formal human capital is the main and only mechanism explaining the probability to pass a licensing exam after completed a compulsory period of practice; (v) the transmission of the family business and probably nepotism are the main mechanisms explaining the probability to start a liberal profession after completed a compulsory period of practice and passed a licensing exam.

Conclusions
In this paper we studied the mechanisms and processes of transmission of liberal professions from fathers to children. Using data on 22 Italian universities, we nd that there is a very strong intergenerational transmission. The odds of being a liberal professional for children of liberal professionals is twice the corresponding odds for children of non-professionals and it is especially large for liberal professions with high entry barriers, in particular accountants, lawyers, notaries, psychologists, pharmacists and architects for which a compulsory period of practice is required.
Our empirical results also suggest that nepotism does not play a role in explaining the probability of passing a licensing exam, but it might explain the probability of starting a liberal profession once a licensing exam is passed and as a matter of fact we nd a negative relationship between formal human capital and the probability to start a liberal profession. Furthermore, the transmission of the family business seems to play a substantial role in explaining the eect of having a father liberal professional with the same degree on the probability to start a liberal profession. The process of completing a compulsory period of practice is at least in part meritocratic, but it can also be partly explained by family networking which disproportionably advantages children of liberal professionals. This would suggest that high-ability children with no family members in the profession could be helped in starting a liberal profession by introducing (i) mentoring schemes where senior professionals get incentives to provide advice and help prospective professionals, (ii) programmes to help graduates in nding members of the relevant professional body available to supervise them for a period of practice, (iii) liberalisation reforms that increase competition and lower the entry barrier. Fairlie and Robb (2007) draw a similar type of conclusion from their study on the eect of having a father who is a business owner on the probability of children to become self-employed.
Our ndings are aligned with previous empirical evidence on liberal professions in Italy suggesting that one of the main reasons for the intergenerational transmission is that having a liberal professional father helps in lowering the entry barrier and this might lead to favouritism (see Mocetti 2016, for pharmacists, Pellizzari and Pica 2011 and Basso and Pellizzari 2010, for lawyers). Our study generalises previous studies to all types of liberal professions by providing evidence that part of the intergenerational transmission of liberal professions is explained by transmission of the family business, networking and potentially nepotism. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Notary and lawyer = liberal professional father with degree in Law. Accountant = liberal professional father with degree in Economics. Pharmacist = liberal professional father with degree in Pharmacy. Architect = liberal professional father with degree in Architecture. Engineer = liberal professional father with degree in Engineer. Geo-biologist = liberal professional father with degree in Geology or Biology. Agronomist = liberal professional father with degree in Agriculture.   Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother, non-graduate liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of all graduates.  Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (4) age at enrolment and its square term, vocational high school track, high school nal mark, living in Southern regions; (5) graduate liberal professional mother, non-graduate liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of all graduates. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree with access to liberal professions which require a compulsory period of practice. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree with access to liberal professions which require a compulsory period of practice and completed a compulsory period of practice. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay, having passed the licensing exam 3 years and 5 years after graduation; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree with access to liberal professions which require a compulsory period of practice, completed a compulsory practice period and passed a licensing exam.   Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother, non-graduate liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of all graduates. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. We also control for father's occupation and child's type of degree. Reference category: academic high school diploma, living in Central and Northern regions, university located in Central and Northern regions, graduation within the minimum period, no working experiences during university, no scholarship during university, licensing passed 1 year from graduation, mother who is not a liberal professional, liberal professional father. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (4) age at enrolment and its square term, vocational high school track, high school nal mark, living in Southern regions; (5) graduate liberal professional mother, non-graduate liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of all graduates.  308 11,308 11,308 11,308 11,308 11,308 Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree providing access to liberal professions requiring a compulsory practice period. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree with access to liberal professions which require a compulsory period of practice and completed a compulsory practice period. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay, having passed the licensing exam 3 years and 5 years after graduation; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree with access to liberal professions which require a compulsory period of practice, completed a compulsory practice period and passed a licensing exam. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree providing access to liberal professions requiring a compulsory practice period. Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. Control variables are: (2) having worked and having received a scholarship during university; (3) job stability and its square term, job independence and its square term; (4) age at enrolment and its square term, vocational high school track, high school nal mark, university in the South, eld of study, standardised university grade, interaction between South university and standardised university grade, dummies for graduation with delay, having passed the licensing exam 3 years and 5 years after graduation; (5) graduate liberal professional mother with the same degree, non-graduate or graduate with ad dierent degree liberal professional mother, non-graduate and non-liberal professional father; (6) all control variables. Sample of graduates who chose a degree with access to liberal professions which require a compulsory period of practice, completed a compulsory practice period and passed a licensing exam.
Appendix B: Joint sequential model In this Appendix we take account of the potential unobserved characteristics that aect the four dierent processes reported in Tables 4a, 4b, 4c and 4d by estimating a quadrivariate probit model which allows for correlation in the error terms in the four univariate probability models. Taking account of this correlation in unobserved explanatory variables is important because failing to do so may lead to an underestimation of the eect of having a liberal professional father especially on the later processes. Allowing for a non-zero correlation between errors in the four probit models is equivalent to consider for each model a composite error term given by the sum of a random eect, which is an individual random eect identically and independently normally distributed across individuals and entering each of the four models multiplied by a dierent coecient, and of an idiosyncratic error term, which is identically and independently normally distributed across individuals and across the four models but with a variance that can vary across models. By assuming, without loss of generality, that the individual random eect aects positively the probabilities of taking the four steps needed to become a liberal professional, students with a low level of the unobserved random component are more likely not to take these four steps; therefore the sub-sample of students who choose degrees providing access to liberal professions which require a compulsory practice period is a selected sample with relatively larger random eects and the sub-samples of students completing a period of compulsory practice and passing a licensing exam are even a more selected sub-samples with larger random eects. This selection process is known as \weeding out" or \sorting eect". 25 If having a liberal professional father has a positive eect on all the four probability processes, then children without a liberal professional father who took one or more compulsory steps are likely to have a larger unobserved random component than children with a liberal professional father. This implies that omitting this unobserved random component leads to an attenuation bias for the eect of having a liberal professional father.
In the following for simplicity we adopt the same notation used in Section 7. We assume that the four outcome dummy variables for individual i, Y c 1;i , Y c 2;i , Y c 3;i and Y c 4;i , which take value 1 respectively if a graduate chooses a degree that can lead to a liberal profession 25 See Cameron and Heckman (1998) and Van den Berg (2001) for more details on this selection process in sequential binary models for educational transitions and in the similar context of discrete duration models. whih requires ompulsory period of prtieD if heGshe ompletes ompulsory period of prtieD if heGshe otins liense nd if heGshe strts lierl professionD stem from four unoservle ltent vriles Y 1;i X C i 1 Z 1;i 1 " 1;i ; Y 2;i X C i 2 Z 2;i 2 " 2;i ; Y 3;i X C i 3 Z 2;i 3 " 3;i ; Y 4;i X C i 4 Z 3;i 4 " 4;i ; @WA where Y c s;i 1Y s;i e H for s I; P; Q; RY X C i is vetor of ommon explntory vriles for the four modelsD whih inludes onstnt nd set of dummies for dierent fther9s ouptionsY Z s;i is vetor of extr explntory vriles whih re used in eqution sY s nd s re the vetors of oeients for X C i nd Z s in eqution sY 26 " 1;i D " 2;i D " 3;i nd " 4;i re the error terms whih hve stndrdised qudrivrite norml distriution with ovrines @orreltionsA etween eh pir of error term " s;i nd " j;i given y sj F o llow for nonEzero orreltion etween errorsD we onsider the following joint likeliE hood L ª M i 1¨  Notes: Standard errors are reported in parenthesis. * p-value @ .10, ** p-value @ .05, *** p-value @ .01. 12 is the correlation between the error terms in the processes (1) and (2). 13 , 14 , 23 , 24 and 34 are similarly dened. Each process includes the set of control variables listed in Table 3.