Introduction

The relationship between a parent's career and a child's career choice has been the interest of researchers across several fields. In economics, Laband and Lentz have studied career following by children in a variety of industries. Not surprising, the reasons for following a parent into the same career vary. For example, Laband and Lentz (1983b) find that children of farmers who also become farmers tend to farm the same land as their parents, suggesting both human capital transfer in the form of knowledge of how to farm, and physical capital transfer in the form of the land and equipment required to farm. In the United States, nearly fifty percent of self-employed proprietors are second-generation business owners, suggesting that name brand loyalty, human-capital transfer, and physical-capital transfer might all influence the child's choice. Laband and Lentz (1990a) find that the sons of baseball players tend to play the same position as their fathers, suggesting human capital transfer either in the form of natural ability or knowledge of how to train and play at the highest level.

Laband and Lentz (1985) find that the children of politicians are more likely than the children of non-politicians to become politicians. Furthermore, the children of politicians do better than their parents in winning elections. The evidence suggests that politics is characterized by brand name loyalty and human capital transfer where parent politicians teach their children how to also be successful politicians.

Laband and Lentz (1992) find that the children of lawyers tend to do better in the early years of their own law practice than the children of non-lawyers. The evidence suggests that the practice of law can be characterized by human capital transfer, if parents teach their children how to be a successful lawyer, physical-capital transfer, if parents hand a successful practice to a child, and nepotism, if the children of lawyers are accepted to better law schools or provided with higher valued opportunities after law school simply because they are the children of lawyers. Nepotism appears to be an issue in medical school admissions in the United States; Laband and Lentz (1990b) find that the children of doctors have an advantage in medical school admission even if they have lower test scores or grades.

The question asked in this paper is whether there are benefits to family connections in Formula 1 (F1) racing. The question appears pertinent because family connections are important in other areas of auto racing. For instance, in 2005, 23 out of 76 National Association for Stock Car Auto Racing (NASCAR) drivers had a family connection. While Groothuis and Groothuis (2008) find no nepotism in NASCAR when it comes to career length, they do find evidence that the father of a current driver is more likely to exit the circuit in a given year. They suggest that fathers of drivers may retire early because the son is able to extend any brand name loyalty. In addition, Rotthoff, Depken, and Groothuis (2014) find that in NASCAR, sons of former racers are more likely to be on camera than their performance would indicate, which suggests brand loyalty transfer.

The F1 racing series provides an interesting case study because family connections occurred right from the start. For instance, in 1950, the first year of F1 racing, there were three sons of racing fathers in the series, including Alberto Ascari, whose father, Antonio Ascari, was a Grand Prix Champion. Also, in 1950 there were seven F1 racers who would be fathers of other racers and there were ten brothers of other racers. In 2017, the last year of our sample period, there were two brothers and six sons of other F1 racers, including Max Emilian Verstappen, the son of F1 racer Jos Verstappen. (1) Although the technology of F1 cars has changed and improved over time, family connections between drivers appear to have remained important over time, providing motivation to test for the various reasons for career following. (2)

Given these racing connections, we identify 58 Formula 1 drivers whose sons followed them into a racing career. In addition, we identify 31 sons who drove in Formula 1 who had a father in racing. We also identify 63 Formula 1 drivers who had brothers in auto racing. Our data set includes all racing connections; for instance, there are fathers identified in our data whose sons raced in other series such as Indy Car (or the Indy Racing League) or other Champ Car series. (3) We include all racing connections because there are only 9 Formula 1 fathers who had one or more sons follow them into F1 racing (a total of ten sons). We suggest that family connections in racing apply to all the different series of racing. To date, instances of career following in F1 have been exclusively male, therefore we use the designation of father, son, and brother. (4)

Using a panel of annual statistics for F1 drivers from 1950-2017, we investigate whether sons and brothers start their careers earlier and are better early in their career (human capital transfer), whether fathers are better drivers with longer careers than non-father drivers (brand name loyalty), and whether sons and brothers have longer careers than their productivity would suggest (nepotism). Our tests include both non-parametric and semi-parametric tests of career duration. To preview our results, it appears that F1 is characterized by a weak form of human capital transfer, with the potential for brand name loyalty transfer between fathers to sons, and that brothers (but not sons) may be subject to nepotism. (5)

Family Connections in Formula One Racing: Testable Hypotheses

Human-Capital Transfer

Formal education is one common way to acquire general human capital. In the United States, a high school education is expected to provide sufficient knowledge and skills to be successful in college or the work force (Kendall et al., 2007). However, firm specific human capital is often acquired through on-the-job training in what might be considered a shared investment between the firm and the employee (Becker, 1993). Furthermore, many occupational skills are learned informally on the job, such as learning by doing in farming, being a sole proprietor, or learning a corporate culture.

In sport, many of the skills required for success fall between formal and informal education; strategy and tactics might be something learned through study and practice, but innate ability might be augmented with physical training and nutrition. Still other sports skills can only be obtained by participating in the sport through learning by doing. In North America, baseball, hockey, basketball, and soccer use minor league teams to develop player talent, whereas American football develops skills in college athletics. In F1 racing, several lower series, such as Formula 3, GP2, and Formula 2 (formally Formula 3000), provide avenues for drivers to develop their skills.

Children from racing families have an advantage over children in non-racing families in that they grow up in the tradition of racing, can acquire skills and knowledge by being at the track and in the garage with their families, and by having family members who might have plans for intergenerational transfer of brand name loyalty or racing-specific capital recourses. For example, although Nico Rosburg was born after his father Keke Rosburg won the 1982 world championship, as Nico progressed through the developmental circuit he enjoyed the input of his F1 World Champion father. Laband and Lentz (1983a) suggest that occupation-specific human capital can be acquired as a by-product of growing up around elders with the same occupation-specific human capital, even proposing that some human capital is essentially free for career followers. (6) If this type of human-capital spillover is present in F1 racing, we expect to see sons and brothers entering the circuit at a younger age than drivers not related to previous F1 drivers. Furthermore, if human capital transfer is important in F1 racing, drivers with family connections should experience more success early in their careers than drivers without family connections.

This leads to two testable hypotheses:

H1: Sons and brothers of F1 drivers are no younger than other drivers at their debut;

H2: Sons and brothers of F1 drivers have no more success early in their careers than other drivers.

Brand Name Loyalty

In F1 racing, the details about sponsorship contracts are tightly held and are generally not publicly available. It is speculated that sponsorship revenue often comprises more than 50% of a team's income with the remainder coming from race prize money and shares in media revenues (Tierney & Fairlamb, 2002). Thus, team owners seek increasing sponsor dollars to provide more financial capital to finance team operations. Corporations sponsor teams to advertise their products and gain exposure for their corporate names. Drivers in many ways become a spokesperson for the corporations that sponsor their team. Thus, the driver's last name often becomes associated with a corporation and can become a brand of its own; for instance, four-time F1 World Champion, Lewis Hamilton, is known for his connection with the Mercedes AMG Petronas team (and likewise the team's sponsors). (7)

Laband and Lentz (1985) contend that occupational following may be an efficient mechanism for the transfer of rents across generations when the family name embodies goodwill. They argue this occurs in politics when several family members seem to run more on the family name than their inherent abilities as a politician. Examples in the United States might include family names such as Kennedy, Clinton, or Bush, and in the United Kingdom might include family names, such as Kinnock or Benn.

If a family name provides a marketing advantage in F1, then team owners may hire family-connected drivers of lower ability because of fan, consumer, or sponsor preferences. In some ways, brand name loyalty follows Becker's (1975) model of customer-based discrimination, where team owners hire less productive drivers to please sponsors. It appeals to sponsors because fan loyalty to a family name leads to more sales even if the driver is not as productive as other drivers. If family name loyalty is present in F1, we should find that only the most productive drivers have sons follow them into racing as these fathers have developed the greatest potential rents from their family name. (8) This leads to our third testable hypothesis:

H3: F1 drivers with sons who become drivers are no more productive than drivers without sons who become drivers.

Nepotism

Intuitively, nepotism is a form of Becker's employer-based discrimination (Becker, 1962). In Becker's original model, firm owners gain disutility in hiring members of a group. Nepotism, on the other hand, is the result of a firm owner gaining positive utility from hiring family-connected workers. Fathers might gain positive utility from hiring their child, even if more productive workers are available; hence, the popularity of the "and sons" (and increasingly of "and daughters") in firm names. In motorsports, nepotism would imply sons of F1 drivers having longer careers than their productivity would otherwise suggest. This leads to our fourth testable hypothesis:

H4: Sons and brothers of F1 drivers have careers no longer than non-family connected drivers.

To review, there are many not mutually exclusive reasons for children to follow a parent into a career in motorsports. Human-capital transfer contends that family-connected drivers enter racing at a younger age and might be more productive in the early years of their career. Brand name loyalty suggests that only the best drivers have sons follow them into racing. Finally, nepotism argues that family-connected drivers have longer careers than their productivity would suggest relative to drivers without family connections. The next section describes the data we use to test these various hypotheses in F1 racing.

The Data

To test our hypotheses, we use a panel describing all drivers in the F1 series from 1950 through 2017. This 67-year panel consists of 753 drivers and 2,797 observations. (9) Using various data sources, we identified drivers who are father-son relatives and drivers who are brother-brother relatives. Some drivers are brothers without being the sons of another driver, and some drivers are the father of another professional driver who did not compete in the F1 circuit. Table 1 reports those drivers identified as fathers, sons, and brothers in the F1 circuit.

Table 2 provides cross-tabulations of the brothers and sons, fathers and sons, and fathers and brothers. As can be seen, there are 10 drivers who are both a sons and a brother, for example, Michael and Mario Andretti, and 53 drivers who are a brother but not a son of an F1 driver. Five drivers are both the father and a son of another professional driver and 15 fathers are also a brother of another professional driver.

Table 3 reports the descriptive statistics of the entire sample and for each category of family connection. The data include age at time of competition, as well as performance data such as wins, podiums, laps led, races, and average finish. The average number of races per driver-year is approximately seven; per-season wins average 0.34; podium finishes average 1.03; and laps led per-season averages 22.48. (10) The average age in F1 is 31, with the youngest driver in our data being 17 and the oldest 56.

In Table 3, we report the means by family connection, comparing those with family connections to those with no family connections. We find that all performance variables are better in the sub-categories of family connections, compared to drivers without family connections. On average, fathers tend to do better than sons, while brothers do better than sons but worse than fathers. The average career length, as measured by all non-right censored observations, ranges from 3.6 years for drivers without family connections to 5.59 years for fathers. The careers of sons average 4.65 years and those of brothers average 5.21 years. Sons start their career at an average age of 24, brothers at an average age of 25, whereas fathers and drivers without family connections start their career at an average age of 28.

On the surface, the averages are consistent with nepotism, brand transfer, or human-capital transfer and all might cause career following in the F1 circuit. To further explore the importance of family relations and determine if nepotism exists in F1, we analyze the data using parametric, non-parametric, and semi-parametric techniques.

Human Capital Transfer and Brand Loyalty

Sons and brothers of drivers might have inherent advantages because they grow up in and around a racing environment. The human capital transfer from fathers to sons and from brother to brother might cause sons and brothers to be better drivers at a younger age, thereby increasing the odds that these individuals would be hired to drive for an F1 team at a younger age than non-family-tied drivers. To test this hypothesis, we test whether there is a statistically significant difference in starting age between sons and non-sons and brothers and non-brothers. The results of these tests are reported in Table 4a and show that both sons and brothers start their career in F1 at younger ages than non-sons and non-brothers. Among drivers who have three years of racing, sons start their career at an average age of 25.7 years of age whereas non-sons start their career at an average age of 30.7, and the difference is statistically significant. Brothers start their career at an average age of 28.8 whereas non-brothers start their career at an average age of 30.7 years, and the difference is statistically significant. Both differences suggest human capital transfer within F1 racing.

A second hypothesis about human capital transfer is that sons and brothers perform better early in their careers. To test this, we compare four common productivity measures between sons and non-sons and brothers and non-brothers after three years of racing in the F1 circuit: average finishing position, total wins, total podiums, and total laps led. The results are reported in Table 4a. While both sons and brothers have better finishing positions on average, the difference is only weakly significant for brothers. Brothers also have statistically significantly more wins, more podium finishes, and more total laps led, whereas sons have no statistically significant differences in these performance measures.

In the case of sons, there is no evidence that the four performance measures are jointly statistically different from non-son drivers. However, for brothers there is evidence that their production statistics are jointly statistically different from non-brother drivers. Therefore, while both sons and brothers exhibit human capital transfer by starting their careers earlier, it appears that brothers enjoy more productivity benefits from human capital transfer than sons.

A third hypothesis about family connections in F1 is that fathers who have sons in racing are themselves among the best drivers. This allows the driver fathers to capitalize on their brand (family) name through future generations of drivers, even if their son drives long after they retire. If a lower-quality driver has no brand loyalty, this would reduce the incentive to hire or encourage the next generation to enter the circuit. We aggregate each driver's career across all years and test whether fathers are statistically better than drivers without family connections in seven categories: age at end of career, total races, total laps, total wins, total podiums, average finishing position, and total laps led. The results for these tests are reported in Table 4b.

Fathers of drivers end their careers at an average age of 35.8 whereas non-fathers (who are also non-sons and non-brothers) end their career at an average age of 32.8 (the difference is statistically significant at the five percent level). Over the course of their careers, fathers complete 37 more races than their peers, complete 1,819 more laps on average, and finish 1.74 positions better on average. While having careers 3 years longer on average can contribute to more races and laps completed, fathers are also better drivers as reflected in averaging 4.5 more wins, 10 more podium finishes, and 285 more career laps led. We find that for fathers these productivity differences are jointly statistically different from zero. This is consistent with brand name recognition having value in F1 as it does in other areas.

Table 4b also reports the conditions for brand name loyalty for sons and brothers at the end of their careers. The evidence suggests that both sons and brothers have jointly significantly different productivity statistics at the end of their careers, compared to non-son and non-brother drivers. While brothers seem to outperform their peers early in their careers whereas sons do not, by the end of their careers both brothers and sons are outperforming their peers. This suggests that brothers might receive more human capital transfer compared to sons, as reflected in their performance early in their careers, but that brothers and sons end their careers with greater potential brand name loyalty, which they could pass along to the next generation of drivers.

Nepotism in Formula One: Evidence from Career Duration

The possibility of nepotism in F1 racing is the final hypothesis we test. We define nepotism as sons or brothers of F1 drivers having longer careers than non-son and non-brother drivers, holding quality constant. Estimating career lengths using standard OLS techniques has well-known problems. Therefore, we analyze the career lengths of F1 drivers via non-parametric and semi-parametric methods.

Non-parametric Estimation

To investigate career duration in F1 racing, we calculate yearly hazard rates as:

[h.sub.t] = [d.sub.t] /[n.sub.t], (1)

where [d.sub.t] is the number of drivers who end their career in year t and [n.sub.t] is the number of drivers at risk of ending their career in year t. The hazard rate can be interpreted as the percentage of drivers who exited F1 at the end of a given season, given their level of tenure at time t. We suspect that most exits were involuntary, particularly for drivers with short careers, although our data do not indicate whether exits were voluntary or not. (11)

In Table 5, we report the total hazard rate, the hazard rate for drivers with no family connections, and the hazard rate for those drivers with family connections of being a father, son, or brother for the first ten years of each driver's career. We find that family-connected drivers are less likely to exit early in their F1 career than non-family connected drivers. Drivers who become fathers of drivers have the lowest probability of exit at any given level of tenure. Brothers have a lower probability of exit compared to drivers without family connections at all levels of tenure less than ten years. Sons have a higher probability of exit than both brothers and fathers but generally a lower probability of exit than drivers without family connections.

While the non-parametric approach suggests there are differences in career length between family-connected and non-family-connected drivers, this methodology cannot determine if these differences are due to productivity differences or nepotism. We therefore move to semi-parametric techniques to control for differences in productivity.

Semi-Parametric Estimation

Methodology

To capture the overall length of a driver's career, our data contains only flow samples because 1950 is the first year of the series. As with most panels, our data are right-censored where many careers were ongoing when our sample ends in 2017. We, therefore, estimate semi-parametric hazard functions following Berger and Black (1998), Groothuis and Hill (2004), and Groothuis and Groothuis (2008). Because the data are reported at the season level we calculate the hazard rate as a discrete random variable. As with Groothuis and Hill (2004), we model the durations of a single spell and assume a homogeneous environment so that the length of a particular spell is uncorrelated with the calendar time at which the spell begins with the exception of a time trend. This assumption lets us treat all the drivers' tenure as the same regardless of when it occurred in the panel study. For instance, all fourth-year drivers are considered to have the same base line hazard regardless of calendar time, so a fourth-year driver in 2010 has the same baseline hazard as a fourth-year driver in 1960 with the exception of a time trend to capture the decrease in career length over time.

To understand how stock data influence a likelihood functions we follow the notation of Groothuis and Hill (2004). Suppose the probability mass function (pmf) of durations is defined as f(t,x,[beta]), where t is the duration of the career, x is a vector of performance and personal characteristics, and [beta] is a vector of parameters. Denote F(t,x-,[beta]) as the cumulative distribution function; the probability that a career lasts at least t[degrees] years is then 1 - F(t,x,[beta]). Defining the hazard function as h(t,x,[beta]) f(t,x,[beta]) / S(t,x,[beta]) and applying the definition of conditional probabilities, the pmf can be expressed as

f([t.sub.i],[x.sub.i],[beta]) = [??] [1-h(j,[x.sub.i],[beta])]h([t.sub.i],[x.sub.i],[beta]) (1)

If we have a sample of n observations, {[t.sub.1], [t.sub.2],..., [t.sub.n]}, the likelihood function of the sample is

L([beta]) = [??] f ([t.sub.i],[x.sub.i],[beta]) = [??]([??][1-h(j,[x.sub.i],[beta])] h([t.sub.i],[x.sub.i],[beta])) (2)

Often it is not possible to observe all careers until they end, hence careers are often right-censored. Let the set A be all observations where careers are completed during the sample period and the set B be all observations where careers are right censored. For the set B, all we know is that the actual length of the career is greater than [t.sub.i], the observed length of the career up through the last year. Because we know that the actual length of the career is longer than we observe, then the contribution of these observations to the likelihood function is just the survivor function,

S(t,x,[beta]) = [??][1-h(i,x,[beta])]

Following Groothuis and Groothuis (2008), we express the likelihood function as a function of the hazard functions. All that remains is to specify the form of a hazard function and estimate by means of maximum likelihood estimation. Using this methodology, the hazard rate is modeled as the conditional probability of exiting F1 series, given that the F1 career lasted until the previous season. Because the hazard function must have a range from zero to one, in principle any mapping with a range from zero to one can be used. Cox (1972) recommends

h(t,x,[beta])/1-h(t,x,[beta]) = [h.sub.t]/1-[h.sub.t] [e.sup.x[beta]] = exp([[gamma].sub.t]+[x.sub.[beta]]) (3)

which is simply a logit model with intercepts that differ by time periods. The term [h.sub.t] is a baseline hazard function, common to all observations; the [x.sub.[beta]] term, which reflects the driver's personal and productivity characteristics, shifts the baseline hazard function, but it affects the baseline hazard function in the same way each period. Berger and Black (1998) consider other hazard functions and find that the results are relatively robust across various specifications of the hazard function. We follow Cox and use the logit model.

The intuition behind equation (3), when using the logit model for the hazard function, is relatively simple. At the end of each year during the sample period during which a driver races in F1, the driver either comes back for another season or ends his career. If the driver's career ends, the dependent variable takes on a value of one, and zero otherwise. The driver remains in the panel until either the driver exits F1 or the panel ends. If the panel ends before the driver explicitly exists F1, the worker's spell is considered right-censored. Thus, a driver who begins his F1 career during the panel and races for six years will enter the sample six times. The value of his dependent variable will be zero for the first five years (tenure year one through year five) and be equal to one for the sixth year.

Because the drivers in the panel have varying career lengths we can identify the hazard function for both long and short careers. The disadvantage to this approach is that the vector [[gamma].sub.t] in equation (3) can be very large; here it would require 19 dummy variables. Another complication is that in F1 there are few drivers with very long careers, thereby making it difficult to precisely estimate the dummy variables in gt that correspond with the longest careers. To simplify the computation of the likelihood function and keep those few observations for drivers with long careers, we approximate the [[gamma].sub.t] vector with a 5th order polynomial in driver's tenure. This reduces the number of parameters to be estimated from 19 to five. The hazard function becomes

h(t,x,[beta])/1-h(t,x,[beta]) = [PHI](t)[e.sup.x[beta]] = exp([phi](t)+x[beta]) (4)

where [phi](t) is a 5th order polynomial in the driver's tenure. This method provides a very flexible specification of the baseline hazard but does impose more restrictions than Cox's model. (12)

Estimation Results

In Table 6 we report the estimates for two specifications of equation (2). In Model (1), reported in Column 1, we include only the dummy variables for family connections and continuous or nearly continuous positive performance measures; column 2 reports the marginal effects evaluated at the sample means (or discrete changes for indicator variables). In Model (2), reported in Column 3, we include the family dummy variables and negative performance measures; Column 4 reports the marginal effects evaluated at the sample means (or discrete changes for indicator variables).

In the first specification, we find that performance measures influence the likelihood of racing the next season. The more podiums, races completed, and laps completed in a season, the less likely a driver is of leaving F1 racing. Furthermore, the better the average finish of the driver during the season, the less likely they are to leave F1 racing that year. It appears that number of races won and laps led over the season are not significant influences on drivers leaving F1. The age of the driver is positively correlated with leaving F1 racing. The time trend is positively correlated with exit, suggesting that recent drivers are more likely to exit F1 racing each year, all else equal, than drivers in the past. This finding might suggest a greater level of competition among potential F1 drivers in recent years than in the past.

The coefficients on family connections provide interesting results. For ease of interpretation we convert the logit parameters to percentage changes as 100*[exp([beta])-1]. From Model (1), fathers are 53% less likely to exit, other factors held constant; being a son does not impact career exit in a statistically significant fashion; and being a brother lowers the likelihood of exit by approximately 35%. The results suggest some nepotism in F1 directed toward brothers (rather than sons); brothers have longer careers than non-brothers after controlling for quality.

Model (2) replaces the positive productivity measures of wins, podiums, laps led, total laps completed, and average finishing position, with negative productivity measures: indicator variables for having never led a lap during the season, never winning during the season, and never having a podium during the season. In this case, the results suggest that never leading a lap and never having a podium both contribute to increased probability of exiting F1 (6 percent and 7.5 percent, respectively). Fathers and brothers are still less likely to exit F1, all else equal, and sons do not seem to experience any different career length.

Overall, the evidence suggests that fathers have longer careers than non-fathers (who are also non-sons and non-brothers) perhaps because of the brand name recognition they develop over their career. The brand name recognition that the driver has developed can then be extended by a son who eventually enters professional racing, most often years after the father has retired. We define nepotism as extending the career of a family member beyond what their productivity would suggest. Only brothers seem to enjoy any impact of nepotism on their career length; sons do not experience any longer careers than drivers who are not sons (or fathers or brothers). (13)

Conclusions

This paper investigates the impact of family connections in F1 racing. Family connections have proven important in other industries, including law, acting, and sports (including other forms of motorsports). Children might follow their parents in a career because of human capital transfer between parents and children, brand-name recognition, or nepotism. We test all three of these possibilities in F1 using data describing drivers in that circuit from 1950 through 2017.

We find evidence that sons and brothers of F1 drivers both enter the circuit at a lower age, which is consistent with nepotism, innate ability, financial support, as well as human capital transfer, but only brothers seem to be more productive early in their careers. Sons of drivers are no better than non-son drivers in wins, podiums, or laps led during the first three years of their career; drivers who are brothers of other drivers are better than non-brother drivers in each of these categories. This suggests that while both sons and brothers gain some human capital transfer, it appears brothers gain more.

We test whether fathers are better drivers than drivers who do not have a son follow them into professional racing. We find that fathers tend to end their careers at an older age than non-fathers, and that fathers are better than non-fathers in terms of total wins, total podiums, total laps led, and average finishing position. This suggests that those drivers who have a son follow them into racing are from the best drivers. This supports the idea that fathers build brand-name recognition, which is transferred to their children, even if this occurs years after the father has retired from racing.

Finally, we test whether career length in years is impacted by productivity measures and family connections. We find that, holding productivity measures constant, drivers who become fathers of future professional racers are less likely to exit F1, supporting the previous intuition that such drivers seek to build brand-name recognition. Being the son of a driver does not influence the odds of exiting, suggesting that there is no nepotism for sons. On the other hand, being a brother of a driver reduces the odds of exit by approximately 6%, holding productivity constant. Thus, there appears to be nepotism directed toward brothers--their careers are longer than their productivity measures suggest. Therefore, it appears that family connections are important for certain drivers in F1, as they are in other industries.

Acknowledgements

We thank Trey Edgerton for research assistance and participants at the Eastern Economic Association Meetings, Western Economics Association Meetings, and Southern Economic Association Meetings.

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Craig A. Depken, II, (1) Peter A. Groothuis, (2) & Kurt W. Rotthoff (3)

(1) University of North Carolina - Charlotte

(2) Appalachian State University

(3) Seton Hall University

Craig Depken, PhD, is a professor of economics in the Belk College of Business at the University of North Carolina--Charlotte. His research areas are sports economics, applied public choice, real estate finance, and industrial organization.

Peter A. Groothuis, PhD, is a professor of economics in the Walker College of Business. His research interests are in labor market applications in sport economics, stadium finance, and stated preference methods.

Kurt W. Rotthoff, PhD, is an associate professor of economics and finance at Seton Hall University's Stillman School of Business. His research areas are applied microeconomics, financial economics, and industrial organization, with a special interest in sports economics and the economics of education.

(1) Max Verstappen is the youngest driver to compete in F1. He is also the youngest driver to lead a lap, set the fastest lap, score points, secure a podium, and win a race in F1 history.

(2) The one time that fathers are underrepresented is in the final years of our panel. This is because the fathers of tomorrow have not been identified since their children are too young to race at this time. Also, the variation in car technology has always been present in F1, as an example search for "six wheeled F1 car" and look at the differences across cars in the 1960s.

(3) Champ Car series was the name of the governing body of open-wheeled racing series in the United States when there was a split from Indy Car. They have since re-merged.

(4) Historically, male participants have dominated motorsports. However, there are female drivers in NASCAR, NHRA, Formula 3, ARCA, and rally circuits. Ashley Force Hood and Courtney Force, daughters of legendary drag racer John Force, both compete in NHRA events.

(5) As pointed out by a helpful referee, a child might follow a parent in career simply because the child seeks to mirror the parent. This desire might exist simultaneously with human capital, physical capital, name brand transfer, or nepotism but would be difficult to measure directly. Following a parent in the absence of any other intergenerational transfer might provide direct evidence of the desire to mirror.

(6) For a formal model of human capital transfer between generations, see Laband and Lentz (1983a). In their model they develop conditions when children acquire their education at home and when they acquire their education formally at school. Our hypothesis is that in racing, many skills can be transferred informally from fathers to sons.

(7) As of 2018, Lewis Hamilton had won the F1 World Championship in 2008, 2014, 2015, and 2017.

(8) There are published annual reports providing estimations of sponsorship volumes per team and driver by Christian Sylt, however, we do not include this variable in the analysis as there does not seem to be reliable data throughout the sample period.

(9) We removed drivers who died during a given season, including those who died in their first season of driving in Formula One. This removed Jerry Unser from the sample although he was both a father and a brother of another driver.

(10) A podium finish occurs when the driver finishes in the top three positions.

(11) As mentioned earlier, we drop observations that correspond to a driver who died in a given season.

(12) When higher order polynomials (the sixth and seventh power) are included, the results do not change. This suggests that a fifth order polynomial is flexible enough to capture the influence of the base line hazard.

(13) The online appendix, available at ssrn.com/abstract=3239602, provides additional models using various subsamples of the overall sample period. In general, the results are not sensitive to which period of Formula One's history is omitted from the models presented in Table 6.

Table 1. Family Connections in Formula One (1950-2017)

             FATHERS                             SONS
First        Last          First     Last        First      Last

Mario        Andretti      Niki      Lauda       Cliff      Allison
Michael      Andretti      Jan       Magnussen   Michael    Andretti
Julian       Bailey        Nigel     Mansell     Alberto    Ascari
Edgar        Barth         Satoru    Nakajima    Sebastien  Bourdais
Derek        Bell          Jonathan  Palmer      David      Brabham
Tony         Bettenhausen  Olivier   Panis       Jenson     Button
David        Brabham       Roger     Penske      Colin      Davis
Jack         Brabham       Paul      Pietsch     Christian  Fittipaldi
Martin       Brundle       Andre     Pilette     Gregor     Foitek
Ronnie       Bucknum       Nelson    Piquet      Brendon    Hartley
Adrian       Campos        Alain     Prost       Gene       Hartley
Duane        Carter        Bobby     Rahal       Alan       Jones
Erik         Comas         Keke      Rosberg     Kevin      Magnussen
Derek        Daly          Louis     Rosier      Pierluigi  Martini
Emilio       de Villota    Paul      Russo       Stirling   Moss
Jean-Denis   Deletraz      Bob       Said        Kazuki     Nakajima
Mark         Donohue       Ian       Scheckter   Joylon     Palmer
Guy          Edwards       Jody      Scheckter   Tim        Parnell
Teo          Fabi          Michael   Schumacher  Andre      Pilette
Juan Manuel  Fangio        Jo        Siffert     Teddy      Pilette
Wilson       Fittipaldi    Jackie    Stewart     Nelson     Piquet Jr.
Elmer        George        John      Surtees     Nico       Rosberg
Dan          Gurney        Piero     Taruffi     Carlos     Sainz, Jr.
Jim          Hall          Bobby     Unser       Harry      Schell
Graham       Hill          Jos       Verstappen  Mike       Taylor
Kazuyoshi    Hoshino       Gilles    Villeneuve  Michael    Thackwell
James        Hunt          Bill      Vukovich    Bobby      Unser
Jacky        Ickx          Manfred   Winkelhock  Max        Verstappen
Alan         Jones                               Rikky      von Opel
Jacques      Laffite                             Markus     Winkelhock
                                                 Alexander  Wurz

                                     BROTHERS
First        First     Last         First      Last

Mario        Michele   Alboreto     Pierluigi  Martini
Michael      Cliff     Allison      Tim        Mayer
Julian       Mario     Andretti     Stirling   Moss
Edgar        Michael   Andretti     Kazuki     Nakajima
Derek        Jean      Behra        Larry      Perkins
Tony         Stefan    Bellof       Nelson     Piquet Jr.
David        Lucien    Bianchi      Didier     Pironi
Jack         David     Brabham      Kimi       Raikkonen
Martin       Ernesto   Brambilla    Dick       Rathman
Ronnie       Vittorio  Brambilla    Jim        Rathman
Adrian       Martin    Brundle      Peter      Revson
Duane        Eddie     Cheever Jr.  Pedro      Rodriguez
Erik         Max       Chilton      Ricardo    Rodriguez
Derek        Patrick   DePailler    Troy       Ruttman
Emilio       Jose      Dolhem       Ian        Scheckter
Jean-Denis   Corrado   Fabi         Jody       Scheckter
Mark         Teo       Fabi         Harry      Schell
Guy          Luigi     Fagioli      Michael    Schumacher
Teo          Ralph     Firman       Ralf       Schumacher
Juan Manuel  Emerson   Fittipaldi   Jackie     Stewart
Wilson       Wilson    Fittipaldi   Jimmy      Stewart
Elmer        Marc      Gene         Maurice    Trintignant
Dan          Roberto   Guerrero     Bobby      Unser
Jim          Hubert    Hahne        Gijs       van Lennep
Graham       Lewis     Hamilton     Gilles     Villeneuve
Kazuyoshi    Nick      Heidfeld     Jacques    Villeneuve
James        Damon     Hill         Luigi      Villoresi
Jacky        James     Hunt         Derek      Warwick
Alan         Alan      Jones        Graham     Whitehead
Jacques      Jan       Lammers      Peter      Whitehead
             Chico     Landi        Justin     Wilson
             Nicola    Larini       Manfred    Winkelhock

Table 2. Cross Tabulations of Family Connections

               BROTHERS
SONS       NO            YES  TOTAL

NO        669            53   722
YES        21            10    31
TOTAL     690            63   753
               FATHERS
SONS       NO            YES  TOTAL
NO        669            53   722
YES        26             5    31
TOTAL     695            58   753
               FATHERS
BROTHERS   NO            YES  TOTAL
NO        647            43   690
YES        48            15    63
TOTAL     695            58   753

Table 3. Descriptive Statistics

                   Total      No Family   Father    Son       Brother
                   Sample

Exit                0.26       0.30        0.14      0.22      0.16
                   (0.44)     (0.46)      (0.35)    (0.42)    (0.36)
Age at Entry       29.95      30.21       28.80     25.65     28.80
                   (6.61)     (6.70)      (5.42)    (4.06)    (5.81)
Age                31.14      31.08       32.91     28.29     30.34
                   (6.07)     (6.00)      (6.05)    (5.22)    (5.73)
Tenure              4.05       3.58        5.59      4.65      5.21
                   (3.35)     (3.03)      (4.00)    (3.81)    (3.63)
Races               7.73       6.94        9.53     10.48     10.21
                   (6.64)     (6.58)      (5.79)    (7.17)    (6.28)
Wins                0.34       0.18        0.95      0.60      0.83
                   (1.21)     (0.82)      (1.95)    (1.52)    (2.03)
Podiums             1.03       0.70        2.08      1.38      2.01
                   (2.43)     (1.96)      (3.23)    (3.09)    (3.40)
Laps Led           22.48      12.76       59.50     38.55     50.03
                  (74.99)    (54.24)    (118.63)   (94.17)  (116.62)
Laps Completed    375.04     335.26      458.06    523.84    494.62
                 (331.05)   (323.06)    (295.09)  (382.45)  (332.70)
Average Finish     13.29      13.84       11.73     12.21     11.86
                   (5.71)     (5.77)      (5.24)    (4.76)    (5.23)
Never Led           0.76       0.82        0.61      0.66      0.63
                   (0.42)     (0.38)      (0.49)    (0.47)    (0.48)
Never Won           0.87       0.92        0.69      0.80      0.75
                   (0.34)     (0.27)      (0.46)    (0.39)    (0.43)
Never Podium        0.72       0.78        0.54      0.68      0.55
                   (0.44)     (0.41)      (0.50)    (0.47)    (0.49)
Sample Size     2,835      2,057         403       135       406

Notes: Standard deviations reported in parentheses.

Table 4a. Human Capital Transfer to Sons and Brothers

Human Capital Transfer                 Sons         Brothers

H1: Age at Debut                       -4.67 (***)  -1.97 (***)
                                       (2.95)       (1.99)
H2: Productivity in First Three Years
Average Finishing Position             -1.65        -1.22 (*)
                                       (1.56)       (1.85)
Total Wins                              0.37         0.95 (***)
                                       (1.09)       (4.55)
Total Podiums                           0.10         2.74 (***)
                                       (0.11)       (4.92)
Total Laps Led                         12.77        54.51 (***)
                                       (0.54)       (3.83)
Joint Test of Significance (F4,1338)    1.76         7.24 (***)

Notes: Sample describes productivity for 349 Formula One drivers who
had a career at least three years long. Differences reported between
sons/brothers against non-sons/non-brothers. Absolute values of
t-statistics reported in parentheses. (***) p < 0.05, (**) p < 0.10.

Table 4b. Conditions for Brand Name Loyalty at End of Career

Productivity Measure      Fathers vs.    Sons vs.       Brothers vs.
                          Non-Father     Non-Son        Non-Brother
                          Peers          Peers          Peers

Age at Career End          3.07 (***)    -5.06 (***)     0.14
                          (1.04)         (1.47)         (1.05)
Total Races               37.65 (***)    24.06 (***)    37.62 (***)
                          (7.24)        (10.23)         (7.31)
Total Laps              1819.26 (***)  1368.91 (***)  1885.92 (***)
                        (353.97)       (504.85)       (359.93)
Total Wins                 4.52 (***)     2.13           3.11 (***)
                          (0.66)         (0.78)         (0.66)
Total Podiums             10.02 (***)     4.58 (***)     8.94 (***)
                          (1.70)         (2.19)         (1.71)
Average Finishing       -174 (***)        0.22          -2.02 (***)
Position
                          (0.77)         (1.09)         (0.76)
Total Laps Led           284.57 (***)   129.18 (***)   171.62 (***)
                         (43.23)        (53.18)        (42.28)
Test for Joint             9.64 (***)     5.45 (***)     6.96 (***)
Significance (F7,4669)

Notes: Coefficients reflect differences at end of career. Standard
errors reported in parentheses. (***) p < 0.05, (**) p < 0.10.

Table 5. Career Exit Hazard Rates First Ten Years of Career

Tenure      No Family    Father    Son       Brother
            Connections

 1           0.35         0.08      0.26      0.11
 2           0.26         0.13      0.27      0.17
 3           0.21         0.09      0.31      0.04
 4           0.28         0.10      0.09      0.14
 5           0.23         0.09      0.10      0.14
 6           0.26         0.16      0.22      0.06
 7           0.29         0.12      0.00      0.10
 8           0.24         0.13      0.14      0.16
 9           0.16         0.15      0.17      0.19
10           0.32         0.13      0.20      0.18
Max Tenure  19 years     19 years  18 years  19 years

Table 6. Determinants of Career End in Formula One

                          Model (1)              Model (2)
VARIABLES        Exit (1=Yes)  dPr(Exit)/dX   Exit (1=Yes)

FATHER           -0.754 (***)  -0.107 (***)   -0.740 (***)
                 (0.147)       (0.018)        (0.149)
SON               0.231         0.038          0.246
                 (0.270)       (0.045)        (0.277)
BROTHER          -0.438 (***)  -0.065 (***)   -0.421 (***)
                 (0.155)       (0.022)        (0.159)
YEAR              0.044 (***)   0.007 (***)    0.042 (***)
                 (0.004)       (0.001)        (0.004)
AGE               0.085 (***)   0.013 (***)    0.083 (***)
                 (0.010)       (0.001)        (0.010)
RACES            -0.130 (***)  -0.021 (***)   -0.138 (***)
                 (0.028)       (0.004)        (0.014)
WIN               0.416 (**)    0.066 (**)
                 (0.208)       (0.033)
PODIUM           -0.250 (***)  -0.039 (***)
                 (0.079)       (0.012)
LAPSLED          -0.284        -0.045
                 (0.277)       (0.044)
LAPS             -0.033        -0.005
                 (0.059)       (0.009)
AVE FINISH        0.021 (***)   0.003 (***)
                 (0.009)       (0.001)
NEVERLED                                       0.723 (***)
                                              (0.215)
NEVERWIN                                      -0.248
                                              (0.309)
NEVERPODIUM                                    0.730 (***)
                                              (0.190)
CONSTANT        -90.707 (***)                -87.522 (***)
                 (8.800)                      (8.870)
Pct. Correctly   76.33                        76.62
Classified

                Model (2)
VARIABLES       dPr(Exit)/dX

FATHER          -0.105 (***)
                (0.018)
SON              0.040
                (0.047)
BROTHER         -0.063 (***)
                (0.022)
YEAR             0.007 (***)
                (0.001)
AGE              0.013 (***)
                (0.001)
RACES           -0.022 (***)
                (0.002)
WIN
PODIUM
LAPSLED
LAPS
AVE FINISH
NEVERLED         0.105 (***)
                (0.028)
NEVERWIN        -0.040
                (0.051)
NEVERPODIUM      0.107 (***)
                (0.025)
CONSTANT
Pct. Correctly
Classified

All models include 2,797 observations for F1 drivers from 1950-2017.
Both models estimated using logit specification. Standard errors
clustered by driver reported in parentheses. Marginal effects evaluated
at the sample means for continuous variables; evaluated using discrete
changes for indicator variables. (***) p < 0.01, (**) p < 0.05, (*) p
< 0.1. Each model includes a fifth order polynomial in driver tenure
(in years) which is jointly significant at the 99% confidence level.