1
How do social networks affect the accuracy of income
expectations?
Master Thesis EconomicsB.J.L. Alberts 5747082
B.J.L.Alberts@student.uva.nl
Thesis Supervisor: J. Hartog MSc Eco
2 Statement of Originality
This document is written by Student Bob Joseph Lionel Alberts who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
3 1. Introduction
In economics, the decision to pursue an education is seen as an investment decision. An investment in education is expected to pay off in the form of a higher income. This approach to education can be slightly problematic, when one considers that future incomes are
uncertain at the time the decision to pursue a particular education is made. To solve this problem, a number of relatively recent studies have started to study how well the expectations of income describe the observed later returns to education.
The manner in which income expectations are formed is, therefore, extremely relevant to the field of economics and the study of returns to education. In recent studies concerning the formation of expectations, however, there has not been an attempt to systematically look at the way that social networks, which can be operationalised by indicators like parental educational attainment, the location of the parent’s income in the national income ranking or the density of a student’s hometown, influence the way expectations are formed or how they affect the accuracy of income expectations. The research question of this paper is therefore:
“How do social networks affect the accuracy of income expectations”
To answer this research question, we will first discuss a theoretical framework based on search theory and social network theory. Search theory shows us that decisions are not made on perfect information, but that there are costs connected to the acquisition of information. Social networks are expected to have the ability to decrease the search costs of information, resulting in more accurate estimations. Secondly, we will review the recent literature on income expectations. Thirdly, we will discuss our empirical strategy and our two datasets; one dataset contains UvA economics students’ income expectations, the other information on the incomes of recent graduates. To answer our research question we will apply a number of different methods. In the first method, we will compare the expected and observed wage structures. In the second method, we will estimate the effect of social networks on a measure of the forecasting gap that is based on individual respondents’ income expectations minus a personalized median income. In the third method, we will estimate accuracy as smaller group variations in income expectations. In the fourth method, we will examine the effect of social networks on income uncertainty expressed as probability estimates. In the last method, we will examine the effect of social networks on levels of optimism. Finally, we will discuss our results.
4 2.1. Theoretical Framework
In the field of human capital, education is seen as an investment. A person can either choose to find employment and accept the wage that comes with his initial level of education, or he can choose to forgo several years of employment in order to receive a certain level of education which will grant him a (potentially) higher income. The difference between the initial level of income and this higher level of income is usually referred to as the returns to education (Hartog & Oosterbeek, 2007).
However, future returns to education are unknown at the time at which the decision whether to continue education is made. To solve this dilemma, the literature has turned to the study of expectations of income to describe how decisions to continue education are made. It is, therefore, important to determine the accuracy of expected incomes and how variations in this accuracy can be explained.
In our understanding of the accuracy of expectations, Search theory can be a guide. It teaches us that the search for information bears costs, usually in the form of time. Individuals are unlikely to pursue completeness in information because that is costly. Accordingly, individuals will only continue acquiring information up to the moment that the marginal costs of search equal the expected marginal benefits. Decisions are, therefore, not made on the basis of perfect information (Stigler, 1961).
Informational search costs are not homogenous. Each individual faces his own search costs. For individuals with a high hourly income the opportunity costs of searching for an additional hour is higher than for individuals with a low hourly income. Furthermore, the access to information differs between individuals. Estimates may be based on information individuals found by chance. Lastly, accuracy of estimates is also determined by the amount of information that was collected to verify earlier information. That is, accuracy does not only refer to the expectation being close to the realized value, but also to the variance of the
5 Blackwell et al. (2001) tell us that there are two processes that are used in an
informational search. The first process is an internal search process. This comes down to a memory scan of all of the information that might have been randomly absorbed by a searcher, for example a student, from all sorts of different sources in the past, but which may still be useful to answer the question the searcher is trying to answer. For example, a student who is trying to determine what economists earn might remember a television program he watched three years earlier. The second is an external search process. This means that the searcher will consult external information sources which can help them answer their question. Direct access to these external sources of information might be restricted in many ways. Therefore, an external search process usually involves several forms of search channels. Search channels structure information in a way to make it accessible.
To help us understand how search channels create variation in search costs, social network theory can be useful; it evaluates social structures by mapping out the number of individuals within a social structure and the way that they are linked (Wasserman & Faust, 1999). It can explain differences in search cost by differences in social networks. Large communities have many members. Individual members tend to have more connections. People in these communities might be linked through intermediaries. Small communities have few members. Individual members tend to have fewer connections. The amount of
information available through intermediaries is limited. Subsequently, the likelihood that people will therefore be randomly exposed to information that is useful for them is lower in smaller communities.
Van Rijnsoever et al. (2009) describe how search channels can affect both types of search processes. Amongst other types of search channels, they discuss social networks as search channels. The type of social network can affect both the information that you randomly happen to absorb and it can function as an important search channel. They confirm that
interpersonal search is more effective in larger than in smaller communities. Secondly, they indicate that wealthy and highly educated parents often encourage a more inquisitive attitude in their children, which increases the “involvement” of these children in their search. This involvement is presented as the reason why social networks which include a lot of higher educated and wealthy people are more effective in transmitting information. This
6 2.2. Literature Review
In this section we will review the literature that will help us answer the research question. The literature on income expectations is scarce. Most of the literature below discusses the income expectations. The accuracy of income expectations is an important aspect of that research. This paper is particular in the fact that it focuses on social network effects.
Mansky (1993) criticizes the standard theories about the way that wage expectations are supposed to be formed. These standard theories tend to view the way expectations are formed as homogenous over all students. He indicates that there are many ways in which individuals form their expectations and states that models need to account for this
heterogeneity. Not accounting for this leaves two problems. Firstly, educational choices cannot be accounted for if the perceptions of returns of schooling are not known. The second problem is that one cannot infer objective returns to education from realized incomes if the process of educational choices is unknown. In other words, using realized incomes in economic models is unwarranted if there is no evidence that students actually base their expectations on realized incomes.
This paper is not directly important for answering the research question, mostly because it is a conceptual rather than an empirical paper. It does, however, confirm the theoretical assumptions made in the theoretical framework that different students face different search costs. They apply different methods of obtaining information about future incomes.
Betts (1996) held a broad survey of 1269 Berkeley students of all years and
disciplines. It asked them for their perceptions on salaries for different types of education. Betts finds that estimated incomes are close to actual mean incomes. It also showed that students focus their attention on gaining more precise information about earnings in their chosen subfield. Fourth year students had a better understanding than first year students. Students with highly educated parents make more accurate estimates. Gender, ethnicity and academic achievements are not significantly related to expectations.
This paper is quite relevant for answering our research question, because it establishes the ability of students to accurately estimate actual mean incomes. Secondly, it confirms that there may be a social network effect in the form of higher parental educational attainment. Lastly, it establishes a framework in which students actively seek out information about their
7 chosen subfield which increases accuracy. In that way, it is congruent with the search cost framework that we established in the theoretical framework.
Webbink and Hartog (2004) study the expected wage of students in tertiary education. They use the dataset from the panel “verder studeren” which has 3945 respondents from both universities and vocational tertiary education. It has about 56% retention. The panel asked students about the expectations of income at several years during their education and about realized earning after graduation. This research is interesting because it does not compare expectations to the mean income at the time of measurement of the expectations, but to the actual realized income. The study finds that students can quite accurately predict their future income, not only as a group but also as individuals.
This paper is relevant because it firstly confirms the ability of students to correctly estimate wages on an individual level. Secondly, it does not find evidence for the social network effect of parental educational attainment. This indicates that there can be a discussion about the existence of this social network effect.
Dominitz and Manski (1996) held a computer administered personal interview (Capi) with 110 respondents from both Madison High School and the University of Wisconsin-Madison. This is a rather small sample. The Capi had inbuilt feedback to correct for errors. What is remarkable about this study is that the authors do not measure a point estimation, but ask for income ranges dependent on levels of education. They find that the expectations of income vary significantly among students. Students tend to overestimate the range of income. There is a general belief that the returns to education are positive. Incomes are expected to rise between the ages of 30 and 40. Students show considerable uncertainty about their own earning. That uncertainty is not reflected in estimations of median income.
This paper does not necessarily help us answer the research question. However, it does indicate that there can be uncertainty about incomes among students who correctly estimate a median income. We will exploit this fact in one of our methods for determining accuracy. Wolters (2000) studies the wage expectations of students in two high schools; a business college and a university of applied sciences in Switzerland. He uses an interactive, computer-assisted questionnaire. He had a total of 137 respondents. The survey was set up in a way to be comparable with the US survey by Dominitz and Mansky (1994). This facilitates comparisons between the two studies. The questionnaire asked wage expectations in four categories: medium wage at 30 with a low level of education, at 40 with low level of
8 education, at 30 with a high level of education and at 40 with a high level of education.
Wolters did not follow the income ranges approach we find in Dominitz and Mansky (1994). Estimated wages were not found to be significantly different from real wages, as measured by national labour force surveys. Controls for a number of personal characteristics are mostly not significant. Furthermore, comparison with the US results shows that students overestimate the characteristics of their type of labour market. US students overestimate the inequality in wages, while Swiss students underestimate the inequality in wages in their country.
Because this paper is comparable to Dominitz and Mansky, it is relevant in a similar manner. It also has its independent relevance in the fact that it signals the presence of an internal information search process. This can be deduced from the difference between Wolters’ study using Swiss students and that by Dominitz and Mansky using American students. Students have apparently absorbed information about the characteristics of the type of labour market that they are exposed to and they use this information in their estimates. Zafar (2011) collected panel data at Northwestern University that contains subjective expectations about major-specific outcomes. It keeps track of the wage expectations of undergraduates for their own and other majors. Of the 161 respondents, 117 continued up to the last survey. Analyzing students who revise their educational decisions (by switching majors) helps to build understanding on how students form their expectations of income. It finds that predictions for income related to their major become more accurate the more time students pursue the same major, but remain as accurate as initial estimates for other majors. This paper is not relevant for answering our research question. It does, however, confirm our search theory framework in the formation of income expectations.
Botelho and Costa Pinta (2004) conducted a controlled experiment which involved 273 Portuguese business and economics students. In this experiment, students were divided in four groups, one of the four groups received financial incentives for accuracy the other three did not. The incentivized students were asked to estimate average earnings, the other three groups were divided into a group that would estimate average earnings, a group that would estimate their own earnings and a group that would estimate both. This study confirms that students expect a college premium, regardless of a financial incentive. They find that female students overestimate the gender gap. They also find that students tend to self-enhance. They expect their own returns to education to be higher than the average. Finally they find that students who are about to enter the labour market have more realistic expectations than
9 beginning students.
This paper is not directly relevant for answering our research question. However, the observation that students tend to self-enhance is a fact that we will use in one of the methods to answer our research question
Brunello, Lucifora and Winter-Ebmer (2004) study expected earnings and expected returns to education. They conducted a questionnaire on three thousand students in twenty-six business and economics faculties across ten European countries. The students are asked about starting expected earnings, with university education and without university education. They find a positive college premium. They also find that female students expect lower future earnings and worse job prospects. Family background plays a significant part in expected earnings and job prospects. This indicated that social networks are still relevant in modern European labour markets. Dispersion in the expected earnings does not correlate with actual labour market dispersion, but is correlated with students’ collection of information about future earnings. This means that expected earnings are not an echo of the current level of earnings, but that information about potential changes in the level of earnings is also included in expectations
This study is important for answering our research question because it confirms a social network effect for parental income.
Nicholson and Souleles (2001) use data from a survey of medical students of the Jefferson University over 25 years. This allowed them to compare expected income with realized income. They found that expected incomes and realized incomes are strongly related. Expected incomes are, however, not based on static realized incomes. Sharp increases or decreases are also represented in expectations. Another find is that female students expect to earn less than male students. They thirdly find that test scores increase earnings expectations. Finally they show that subjective income expectations are more useful in predicting specialty choice than the more commonly used adaptive expectations. The reluctance that many economists feel towards using expectations is thus ungrounded.
This study is only relevant in the fact that it confirms the ability of students to
accurately estimate incomes. It does not discuss social network effects and therefore does not help us answer the research question.
10 What we thus learned from the literature is that students have the ability to estimate incomes accurately. The literature presents us with mixed evidence for the existence of social network effects in the form of parental educational attainment and parental income rank. Finally, it confirms a theoretical framework in which expectations become more accurate the more invested students are in knowing future incomes of a specific educational track.
Unfortunately, none of the literature directly ties social network effects to the theoretical framework on search costs. None of the papers above specifically look at the effects social networks can have on the height of search costs and how that height influences the accuracy of expectations. That question is the focus of this study.
11 3. Empirical Strategy
In this section we will discuss the datasets that will be used and the methods that will be employed in order to answer our research question: “How do social networks affect the accuracy of income expectations”.
Social networks will be indicated by variables for population density, parental educational attainment and parental income rank. Of course, there are more forms of social networks, but these three types of networks overlap with the social, financial and human (educational) capital that is present in certain social networks. Traditionally, areas with a higher population density are associated with a higher level of social capital in their inhabitants. Higher levels of educational attainment indicate higher human capital. Higher incomes indicate higher financial capital. All of these forms of capital are expected to
improve an individual’s chances in life. In this study, however, we are mostly interested in the question of whether social networks with low levels of a certain type of capital are less
conducive to transmitting information and therefore in helping respondents formulate accurate income expectations.
Our assumptions are that social networks decrease information costs. The population density of a respondent’s hometown functions as an indicator for a larger social network. Such larger social networks contain more individuals and the chance is therefore larger that there is an individual in that social network who has the information that can help in
establishing accurate expectations. This information can either be acquired actively (by
contacting the person who has the information) or passively (the information is something that just happened to come up in a conversation). If population density is positively correlated with average wages, it might be the case that respondents from higher population density cities estimate wages higher. We do not expect that there is such a correlation; there are high income villages and low income villages, just like there are both people with low and high incomes in large cities. Secondly, we expect that respondents with high parental educational attainment have access to social networks filled with people with academic degrees. In these networks, the probability is higher that a respondent can actively or passively acquire
information about the height of incomes related to a master in economics. It might be the case that respondents with high parental educational attainment expect higher incomes on average. This expectation, however, is based on the college premium that parents enjoy. Because we are interested in the expectations of respondents who are pursuing a master in economics, we do not find the expectation of a higher average wage problematic. Thirdly, we expect that
12 parental income rank is an indicator for social networks filled with people with a high income rank. Usually, high incomes are related to high ranking professional jobs. Employees with a master in economics often end up in those kinds of jobs. Respondents with access to those social networks have access to people who know what incomes in those kinds of jobs actually look like. Respondents with parents who earn a lot of money might underestimate the
likelihood of earning such amount of money and might therefore overestimate their own incomes. In other words, they might have a warped view of the distribution of incomes. The fact that most of these social networks might also have an effect that might increase the value of an estimate does not necessarily mean that such an estimate is inaccurate. Only if a variable affects the height of the expectations but not the height of the observed incomes can an expectation be said to be inaccurate.
Accuracy of income expectations shall be analysed in a number of ways. Firstly, we will compare the expected and observed wage structures. Secondly, we will measure the forecasting gap, the difference between an individual respondent’s income expectations minus a personalized median income. Thirdly we will look at the distribution of expectations on a group and on an individual level. Lastly, we will examine accuracy as optimism.
3.1. The data.
In this paper, we will use two data sets. The first dataset is the 2008 SEO Elsevier labour market dataset called “Studie en Werk”. This dataset is based on a survey that has been held annually since 1997 among graduates who have just finished their higher education and have started their first jobs in the Netherlands. Graduates are grouped in 70 HBO (university of applied sciences) bachelor clusters and 50 University master clusters. The survey contains questions on the process of acquiring a job, features of that job, graduates’ features of their time as a student, graduates’ demographic features and the like. This paper focuses on the 2008 version of the survey to obtain a number of objective features of the labour market. It contains 80255 general observations, which include 195 respondents with a master in economics. These 195 respondents are most useful for our research.
The second dataset was collected by the University of Amsterdam, faculty of
economics, section human capital, among business economics or economics students in 2012. We will call this Dataset “UvA Human Capital”. The survey contains students’ expectations on future income, students’ demographic features and students’ features of their time used as a student. It contains 402 observations.
13 3.2. Cleaning up the “UvA Human Capital” dataset.
Working with two datasets can prove problematic. We will therefore adapt the “UvA Human Capital” dataset so it can be used in comparison with the “Studie en Werk” dataset. This “clean up” of the datasets constitutes of removing problematic observations and defining variables in a way that is different from their definition in the original datasets.
To start, some students plan to find employment outside of the Netherlands. The income we will establish from the “Study en Werk” dataset will only represent incomes within the Netherlands. Because incomes vary widely over different countries, the median and mean income expectation will not be a forecast for just the Netherlands. To make both of these variables comparable, we will have to remove respondents who wish to seek employment outside of the Netherlands from the dataset. This way, the reported income expectations become income expectations for economics graduates in the Netherlands. As a result 101 observations are dropped and we are left with only 301 observations to work with. Secondly, this paper will analyse social networks and their ability to distribute
information. Typically, foreign students do not have access to Dutch social networks, before coming to the Netherlands, and should therefore be excluded from the benefits that such social networks would bring. We will therefore remove the students who answered yes to the variable “foreign” from the dataset. As a result, another 91 observations are dropped and we are left with only 210 observations. These 91 observations will be kept aside for later tests.
Thirdly, a number of variables need to be adjusted in such a way that the definition in “Uva Human Capital” is in accordance with the definition of “Studie en Werk”. To facilitate the use of ordinal variables in regressions, we will redefine a number of ordinal variables into separate dummy variables. Three variables we are particular interested in are those that concern social networks. The first of these is the variable Urban which indicates the population density of a student’s hometown. This ordinal variable will be transformed into three separate dummy variables for respectively high urban density “HighUrb”, Medium urban density “MidUrb” and rural town density “Rural”. This transformation is necessary because the original ordinal scale did not involve a gradual increase in population density, but indicated a respondent’s self-reported perception of population density. By transforming it into dummies, we test the effect of categories, rather than imprecise measured scales. The second set of network variables concern the educational achievement of the
14 student’s parents. In the UvA Human Capital dataset, these are described by the variables “FathEduc” and “MothEduc”, respectively indicating paternal educational achievement and maternal educational attainment. They will be transformed into dummy variables “Fathhigh”, “Fathmid” and “Fathlow” and “Mothhigh”, “Mothmid” and “Mothlow”. The Fath-variables refer to the father’s (paternal) level of education. The Moth-variables refer to the mother’s (maternal) level of education – high-variables refer to a parent that has at least a University bachelor degree, mid-variables refer to a parent that has at least an MBO-degree and at most a HBO-degree and low-variables refer to a parent which has at most a high school diploma. The third network variable concerns the place of parents on the national income spectrum. This is indicated by the variable “Income”, which indicates the place of a student’s parents’ income in the national income distribution and will be redefined as five dummy variables “Inc20”, “inc40”, “inc60”, “inc80” and “inc100”. These respectively represent the first, second, third, fourth and fifth 20 percentiles of the income spectrum.
Finally, we will adjust the dummy for gender. In this dataset, the variable indicates female gender; in the “Studie en Werk” dataset it indicates a male gender. We will redefine the variable in this dataset to also indicate male gender (for a complete list of the definition of variables, see Table A.2 in the appendix).
3.3. Cleaning up the “Studie en Werk” dataset.
The Studie en Werk dataset will also need to be adjusted in order to make it comparable with the “UvA Human Capital” dataset. Firstly, we will restrict the observations to people who have a master degree in economics. We will do this by dropping all of the observations for which the value of the variable isat does not correspond to the isat value of a master in economics (for these isat values, see Table A.1. in the appendix).
Just as in the adjustments in “UvA Human Capital”, we will need to redefine the variables for social networks. There is no variable for urban density in this dataset; we are, therefore, unable to redefine that variable into several dummy variables. Parental educational attainment is indicated by “Oplpa” for the paternal (father’s) educational attainment, and “Oplma” for the maternal (mother’s) educational achievement. They will be redefined in the same six dummy variables as the “UvA Human Capital” dataset: “Fathhigh”, “Fathmid” and “Fathlow” and “Mothhigh”, “Mothmid” and “Mothlow”. Herein paternal educational
15 moth-variables. High-variables refer to a parent that has at least a University bachelor degree, mid-variables refer to a parent that has at least an MBO-degree and at most a HBO-degree and low-variables refer to a parent which has at most a high school diploma. The variable which concerns the place of a respondent’s parents’ income on the national income spectrum, the parental income rank, is called “ouderink” and will be redefined in the same five dummy variables as the “UvA Human Capital” dataset: “Inc20”, “inc40”, “inc60”, “inc80” and “inc100”. These respectively represent the first, second, third, fourth and fifth 20 percentiles of the income spectrum
(for a complete list of the definition of variables, see Table A.3. in the appendix).
3.4. Are the datasets adequate?
The datasets that we use are not ideal. Firstly, both datasets have a limited number of observations. The “UvA Human Capital” dataset has only 210 observations that we will use for most of our analysis. The “Studie en Werk” dataset has only 195 observations that we will use for most of our analysis. While both datasets posses enough observations for statistical research, it would have been preferable if we could base our research on a larger number of observations.
Secondly, these two datasets originally contained variables which might have been defined in different terms. To solve this problem, we have redefined a number of variables, as described in sections 3.2 and 3.3, this redefinition is not always optimal. In the case of
paternal (and maternal) education attainment, Medium paternal educational attainment is defined as having a father with at least and MBO-degree and at most a HBO-degree. This is a rather broad definition that in the case of the “UvA human capital” dataset involves more than 50% of the observations in paternal educational attainment. This definition is, however, necessary to create similar definitions in both datasets. In the same vein, we are facing the problem that the observed income is defined as an individual income, while the expected income is defined as a median. This creates conceptual problems in analyses that compare the two. Similarly, the two datasets only facilitate the comparison between the variables “grvak” and “tentgem” for university academic achievement. This is problematic because “grvak” indicates the grade of one course, while “tentgem” indicates an average over several courses. This also creates conceptual problems.
A third inconvenience is that many variables, such as parental income rank and high school grades, are self-reported. This means that we are not measuring effects directly, but
16 measuring them indirectly. The perception of the respondent is involved. A respondent might falsely believe that their high school grades, the population density of their hometown or parental income ranks are higher than they actually are. If there is a connection between falsely self-reported variables and the accuracy of income expectations, this might warp our findings.
A fourth inconvenience is that there is a time gap between the observed incomes and the expected incomes. On its own, this gap poses a numerical problem, but when we take into account the exact timing of the gap, we are facing a more profound problem. The observed incomes were taken in 2008, this means that, in all likelihood, most of the respondents found employment before the financial crisis of 2008. The expected incomes were reported in 2012, at least four years after that financial crisis. It is therefore doubtful if the observed incomes represent the same economic fundamentals as the ones on which the expectations are based. A final inconvenience is that the variables that indicate social networks only indirectly represent social networks and the manner in which information is distributed through them. Rather than building extensive computer models for the social networks for each individual respondent and test how well each type of social network transmits information, we use variables that indicate (self-reported) characteristics of social networks and test how they influence post-facto accuracy of expectations. In so doing, we make the assumptions that: 1. Post-facto accuracy of expectations is based on the quality of information received. 2. Social networks themselves are used as informational channels. 3. Other methods of forming accurate forecasts are not related to the characteristics that indicate a specific social network. The fact that our datasets are not ideal does not mean that they are not adequate. We have been able to redefine variables in a manner that makes them comparable to each other. The number of observations in both datasets are more than minimum sample size that the central limit theorem demands. Both datasets concern highly educated people in the same country, in which many economic fundamentals are still exactly the same. Lastly, the results that we find by measuring social networks indirectly on the post-facto accuracy of expectations may still be meaningful and can be studied more elaborately in later studies.
17 3. 5. Median Income comparison.
Our first test will be to determine if the expectations of the median income, which we get from the “UvA Human Capital” dataset, differ significantly from the observed median
income, which we get from the “Studie en Werk” dataset. The former will be indicated by the variable “incmsc”, the latter can be indicated by either the variable “firstInc”, for annual salary of the first job, or “currentInc”, for the annual salary of the current job. This study will work with the variable “currentInc”. Using this variable allows us to base our analysis on more observations. Furthermore, the variable “firstInc” may be polluted by internships which are reported as first jobs. “CurrentInc” is still a legitimate variable to use because the “Studie en Werk” dataset focuses on recent graduates.
To test this, we will perform a z-test (McClave and Sincich, 2002, pp 493) on the zerohypothesis that these values are not equal. We will test two-sided and we will use a level of significance of 0.05, so the critical value (CV) will be 1.96.
Equation 3.1
The literature on expectations suggests that the medians will be equal. However, as stated in section 3.1, the datasets are four years apart. Four years of salary growth might therefore generate a significant gap between expected and observed median incomes. It might also be the case that the UvA human capital sample differs from the samples in other studies. For these reasons it is useful to test whether the expected and observed median incomes are statistically equal. Because of the four year time-gap, this would constitute a rather statistical test of only light weight.
When we observed statistical equality, it indicated that the majority of respondents can estimate incomes accurately. This means that the contrast between those respondents who estimate accurately and those who estimate inaccurately will be more apparent. When the expectations and the observed median incomes differ, the contrast is less pronounced and it will be harder to determine whether networks decrease the accuracy of estimates.
18 3.6 Comparing the Wage Structure
In this test we will compare the structure of observed incomes and of income expectations. It is the first test that is directly related to answering our research question on whether social network effects can explain the accuracy of income expectations. We will perform two sets of regressions, one for each dataset. Both regressions will be robust to account for possible heterogeneity. We will then compare the results to see how accurately factors that explain the expected median income explain the observed income. When they are accurate, this indicates a high quality of forecast. We expect to find that the network effect of parental educational attainment will affect expected and observed income differently.
In these two regressions, the dependent variable will be the natural logarithm of expected median annual income and the natural logarithm of observed income. Both will be regressed on the above described dummy variables for the network effects of parental educational attainment. Unfortunately, as discussed in section 3.4, parental income rank has too few observations in the “Studie en Werk” dataset to be part of these regressions.
Furthermore, we will control for gender, high school math grade and an indicator for
university educational achievement (this indicator, unfortunately, involves one exam grade in the UvA Human capital dataset, “grvak”, while it involves an average grade, “tentgem”, in the Studie en Werk dataset).
Natural logarithms are often used in human capital theory and usually fit the data better. They make the comparison between coefficients from different datasets more effective. If there would be a large difference between income expectations and observed income, the coefficients might still be of comparable value when expressed as percentages rather than as absolutes. One of the dummy variables of each social network variable is excluded to avoid the dummy trap. The regressions will look as follows:
Equation 3.2 Equation 3.3
19 After we have estimated the coefficients in both regressions, we will test if each
individual coefficient is statistically different from its counterpart in the other regression. If an “expectational” coefficient is significantly different from its “observed” counterpart, which would indicate that all respondents in the subgroup wrongly estimate the median income. We will test this using a T test. One can use a T-test for different populations if one uses
combined standard errors (McClave and Sincich, 2002, pp 639). We will discuss whether such a test provides enough evidence to allow for the use of variables with conceptual differences.
Equation 3.4
3.7. Testing for the social network effect on the forecasting gap.
Comparing the wage structure is one method of answering the research question. It, however, has the drawbacks that it does not allow us to test the influence of social network effects that are measured by the population density of a respondent’s hometown, or parental income rank, and does not allow us to control for how many years of education a student has been
following, because those variables were not included in the “Studie en Werk” dataset. Secondly, there is some statistical white noise in the comparison between expected median incomes and observed incomes. The median and the mean are two different statistical concepts. If observed median and mean incomes are statistically different, the coefficients from “UvA Human Capital” and the “Studie and Werk” datasets could not be compared from a conceptual point of view.
We will, therefore, employ a second method of answering the research question which might give us a more intuitive form of reporting inaccuracies in forecasting. To do this, we will define a new variable called the Forecasting gap. This variable will be the logarithm of median income expectations (Incmsc) minus a personalized median income. This means that we will calculate a median income for each subgroup that corresponds to a variable that we found to be significant from the above regression in the “Studie en Werk” dataset. It will indicate the gap between the observed income for that subgroup and its forecast. Accurate estimates will have a smaller gap than inaccurate estimates. The gap can both be positive and negative.
20 The reason we restrict the calculation of personalized median incomes to subgroups based on significant variables is because medians of subgroups based on insignificant variables should not be significantly different from the general median. All respondents that will not belong to a subgroup based on a significant variable will have the general median deducted.
If all respondents in the same subgroup estimate the median income correctly, the coefficient of the variable relating to that subgroup, for example, students from low density areas, will not be significantly different from zero. As an added bonus, the regression table will clearly indicate whether a subgroup that significantly misestimates either underestimates or overestimates. Variables that effect accuracy of estimates, as measured by the forecasting gap, will be clearly shown with significance and sign. Our focus will be on the variables that indicate social network effects: population density, parental educational attainment and parental income rank. All of these variables are dummy variables. This means that, for
network variables, a negative coefficient indicates that a subgroup of respondents, on average, misestimates. If variables were defined on a scale, a negative coefficient could indicate a decrease in overestimation. Equation 3.5
3.8. Testing for the variation: group variance.
Another important way to test if social networks have an important informational effect on the accuracy of income expectations is to evaluate whether the distributions of expectations in one social network are smaller than those in other social networks. If members of one social network, for example, respondents with high parental educational attainment, all face a lower cost in attaining reliable information about incomes, they will all consume more information and, therefore, have more accurate individual estimates. The distribution of income expectations of this social network need to be smaller than that of another group, for example, respondents with high parental educational attainment.
21 We will test this by calculating the standard deviations of the natural logarithm of the expectations of median income for each group according to social network variables of population density, parental educational attainment and parental income.
The resulting variances will then be F-tested against each other to determine whether the differences between group variances are significantly different to each other (McClave, 2001, pp 493). We will check if group variances within each of the three network effects, significantly differ from each other.
Equation 3.6.
Some of these subgroups will be rather small. The standard deviations can, therefore, be highly influenced by an overlap between the studied effects and another unobserved variable. It might, for example, be the case that all respondents in the low parental income rank subgroup are male. This might distort our results. This is an unfortunate constraint of the data in combination with this particular methodology.
3.9. Testing for the variation: individual range.
The above method mostly looked at the distribution of income expectations on a group level. The certainty that respondents feel in their estimate can also be indicated on an
individual level by defining the variable Individual Range by adding up the variables
“pm25”and “pm75” which indicate the mathematical probability that respondents give to the situations of earning 25% more or 25% less than the median.
The less informed a respondent is about his income estimate, the higher the individual range will be. We will, therefore, perform a robust regression on Individual range using the usual variables for social network, gender, years of education and educational achievement.
Equation 3.7
22 3.10. Optimism
In the experimental economic literature, we find numerous examples of respondents who are irrationally optimistic: on average, respondents report that they expect to personally perform better than average. This irrational optimism might account for lower accuracy of
expectations. It is, therefore, interesting to analyse if such irrational optimism is associated with certain social networks.
To that effect, we exploit the fact that the difference between the probability of earning 25% above or below the mean should be zero if incomes are symmetrically distributed. If this difference is positive, it can be said that respondents are irrationally optimistic. The new variable “Optimism” will thus be defined as the difference between variables “pm25” and “pm75”.
By regressing Optimism on the same independent variables as in 3.6, we can
determine whether Optimism can be explained on the basis of social networks. We could, of course, find positive and negative coefficients for Optimism. A negative coefficient would indicate pessimism: the respondent believes that the chance that he will earn less than the median income is larger than the chance that he will earn above median. Irrational pessimism has the same conceptual value as irrational optimism: it indicates a difference in probabilities that should not exist. We don’t work with an absolute version of “Optimism” because the differences between optimism (positive coefficient) and pessimism (negative coefficient) might be useful in the analysis of social network effects.
If we find significant optimism or pessimism appears together with positive or
negative coefficients in the regression of sections 3.6, we might explain the wrong estimation by optimism or pessimism. But if we find optimism or pessimism, which does not appear together with significant effects in the regressions of sections 3.7 or 3.6, then we appear to have an inconsistency. Maybe we are observing respondents which undertook sufficient search effort to accurately estimate the median income, but at the same time have undertaken insufficient search effort to conclude that they do not have a significant advantage over their classmates on the job-market.
Equation 3.8
23 3.11. Controlling for Foreigners.
False positives are a problem in quantitative research. Fortunately, we have the ability to check if our results are a false positive. Theoretically, Foreigners should not have access to Dutch social networks before arriving in the Netherlands to start their university education. Our theoretical framework assumes that the effect of social networks should take place before starting a university education. Foreigners, therefore, do not have the cost advantages when gathering information about wages. Since the cost of a search is thus higher for foreigners, there estimates should be less accurate. To make sure that the findings for foreigners did not offset the correlations in the domestic population, they have been excluded from the dataset. We can construct a new dataset based on excluded observations that relate to
foreigners. The foreigners who will seek employment outside of the Netherlands after graduation have been excluded from this sample. If we repeat the same tests on the forecasting gap in section 3.7, we should now find different results. If we find the same results, this would indicate that the effects that we do find are not the result of decreased search cost through social networks.
Of course, foreigners in this sample will not be a perfect representation. Some foreigners might have lived in the Netherlands before starting university education, while others might have had a distant Dutch acquaintance. Unfortunately, we cannot control for these exceptions using the variables in our data. Nevertheless, performing this test might help us discover a false positive which would have significant effects on the interpretation of our results. Equation 3.9
24 4. Results
In this section we will discuss the results of the tests that we performed in order to answer the research question.
4.1. How accurately do students estimate the median starting income?
A first step in our research is to check if students in general are able to accurately estimate the median starting income. We did this by, first, estimating the mean of the expected median income from the “UvA Human Capital” dataset; second, estimating the median from the income from the “Studie en Werk” dataset; third, performing a Z-test to see if these are significantly different.
Our expectations from the literature are that the two medians will not be significantly different from each other. Our hypothesis is, therefore, that the difference between these two medians is not significantly different from zero.
An important problem with our data is that the variable for the annual income at the first job “firstInc” has a low number of observations on which it is based. It also has a much lower value than the variable current annual income “currentInc”. Theoretically, this should not be the case because respondents only include recent graduates who have only been in the working force for several months. Presumably, the variable “firstInc” includes internships, as can be seen from the low minimum annual income 1500 Euros. This drags down the mean. Considering the low amount of only 80 observations for “firstInc”, it might be preferable to use “currentInc” as a benchmark for real median income; “currentInc” would still be an acceptable measure because the questionnaire is held under recent graduates
Table 1 gives us the descriptive statistics for the expected median incomes “incmsc” from the “UvA Human Capital” dataset. Table 2 gives us the descriptive statistics for the observed annual incomes “firstInc” and “currentInc” from the “Studie en Werk” dataset. We will perform a Z-test using the mean of the expected median income and the median of the observed annual incomes. This Z-test showed us that these two medians are, statistically, significantly different from each other. It rejects the hypothesis.
Equation 4.1
25 The fact that the expectations are significantly different from the observed income for recent mastergraduates in economics is an unexpected find. As we have seen in our literature review, authors like Webbink and Hartog (2004) have shown that, in general, expectations match realized incomes. An important difference is that this article compares data from multiple datasets. That could explain the anomaly. Another explanation would be that the two
estimates are too far apart. The UvA Human Capital dataset is from 2012, while the Studie en Werk dataset is from 2008. The inflation between those years compounds to 7.5 percent (inflation.eu 2015). Increasing the observed annual median income by that amount would not bring it the Z value below the critical value (CV).
The consequences of the difference between these two medians are mild. If they had been equal that would have indicated that on average respondents can estimate incomes accurately. Inaccurate estimates would be limited to a small number of respondents to whom clear characteristics could be associated. The fact that respondents do not, on average, estimate accurately, means that inaccuracy cannot be limited to a small number of observations. This makes it slightly harder to find factors that affect the accuracy of
expectations. Research would have to focus on an accuracy that is lower than average, rather than on a general accuracy of expectations.
Table 1. Summary of expected median incomes.
Variable Observations Mean Std. Dev
Incmsc 203 38431.75 30460.03
Note: Based on the UvA Human Capital dataset
Table 2. Summary of observed median and mean incomes.
Variable Observations Mean Median Std. Dev
“firstInc” 80 16345.35 16800 6021.284
“currentInc” 195 24070.95 23304 6283.21
26 4.2. Are the observed wage structure and the expected wage structure the same?
A test that can help us answer our research question on whether social network affect the accuracy of expectations is a statistical comparison between the observed and expected wage structures. To test this we first regress the log of the expected median incomes on parental educational attainment, gender, and the respondent’s educational attainment. We then regress the observed log of current income on similar variables. For both of these regressions we use regressions on robust standard errors. Finally we test if coefficients are significantly different in both tables using a number of t-tests.
Our expectations are that most of the coefficients from both regressions will not be significantly different from each other because we have no theoretical grounds to expect that our controls affect the accuracy of estimations. However, we do expect there to be a
significant difference between the variables for the social network effect of parental educational attainment. More specifically, we expect respondents with low parental
educational attainment to face a higher search cost and therefore to wrongly estimate median incomes.
One of the problems we face is that the expected median incomes and the observed current incomes are not defined in similar ways. They are conceptually different.
Unfortunately, we are unable to preform a test that will provide enough evidence to
reasonably assume that an observation can be compared to the expectation of a median. The regressions below work with logarithms. To prove that the assumption of equality would be reasonable we would have to compare whether they are similarly distributed. Unfortunately, we work with two separate datasets which make such a comparison of distributions too complex to perform.
A second problem is that there are no observations for parental income for respondents with a master in economics. In fact, only 6580 out of the 80255 respondents in the entire “Studie en Werk” dataset have an entry at that variable. We were, therefore, forced to drop the dummy variables for parental income rank from this comparison.
A third problem is that the variables for the grade of a specific course “grvak” and for the average educational achievement at university “tentgem” are not direct counterparts. They do, however, both indicate a respondent’s educational achievement at university.
The results of the first regression are presented in table 3. We find that most variables are not significantly different from zero. The only variable with a significant effect on the expectations of income are having a father with a low level of educational attainment.
27 Table 3. The effects of parental educational achievement and controls on expected median ln income (LN Incmsc).
Variable Coefficient Std. Error T
fathlow** .2364496 .1063656 2.22 fathhigh .0029036 .0639295 0.05 mothlow -.0726847 .1055251 -0.69 mothhigh -.0248701 .0638217 -0.39 male .1214244 .0690477 1.76 grvak .006476 .0150729 0.43 grademath .0242339 .0240888 1.01 Constant** 10.12397 .1927283 52.53
Note: Based on the UvA human capital dataset, concerns a robust regression over 202 observations, F = 1.88, prob (F) = 0.1983, based on a level of significance of 0.05.
In Table 4, we do a similar regression on the data from the Studie & Werk dataset. In this dataset, we find that none of the coefficients are significantly different from zero. This, interestingly enough, has the consequence that, according to our estimation, variation in observed incomes cannot be explained by a respondent’s gender, educational achievements or social network as measured by parental educational achievement.
Table 5 shows us whether the coefficients of both regressions are significantly different from each other. Not surprisingly, all the variables that were not significantly different from zero are also not significantly different from each other. It is, however, surprising that coefficients are not significantly different from each other, particularly when the two medians discussed in section 4.1 are significantly different from each other. The two variables that are significantly different from each other are those that indicate a low level of education for both parents. Unfortunately, the variables for low maternal educational
attainment do not significantly differ. This indicates that respondents with low levels of paternal educational attainment wrongly believe that they will earn a lower annual salary. We can, therefore, conclude that the expected wage structure, which is described in table 3, and the observed wage structure, which is described in table 4, mostly overlap. We find that respondents with low parental levels of education wrongly estimate the wage
structure. This indicates that the social network effects that we are interested in might have an effect on the accuracy of expected incomes. This confirms one possible social network effect, but fails to find evidence for another one in the case of maternal educational attainment.
28 Table 4. The effects of parental educational achievement and controls on observed median ln income (LN “currentInc”).
Variable Coefficient Std. Error T
fathlow -.0038614 .056889 1.20 fathhigh .0267334 .0495092 -0.07 mothlow -.0159546 .0487148 0.54 mothhigh -.1101102 .0627379 -0.33 male .0492801 .0411754 -1.76 Tentgem -.0006128 .0345642 1.02 mathgrade .0179852 .0177068 -0.02 Constant** 9.893536 .2714979 36.44
Note: Based on the UvA human capital data, concerns a robust regression over 134 observations, F = 0.79, prob (F) = 0.5986, based on a level of significance of 0.05.
Table 5. Comparison of the expected and observed wage structure (LN Incmsc and LN “currentInc”) Variable for observed income Coefficien t Variables for expected income
coefficient Comb.Std. Err. T
Man .0492801 Male .1214244 0.0803 -1.46 Fathlow** -.0038614 Fathlow** .2364496 0.1206 -1.98** Fathhigh .0267334 Fathhigh .0029036 0.0809 -0.01 Mothlow -.0159546 Mothlow -.0726847 0.1162 0.61 Mothhigh -.1101102 Mothhigh -.0248701 0.0895 0.17 Mathgrade .0179852 Grademath .0242339 0.0299 0.79 Tentgem -.0006128 Grvak .006476 0.0377 -0.17
Note: Based on the UvA human capital and Studie en Werk dataset, based on a level of significance of 0.05.
4.3. Do networks affect the forecasting gap?
Because of the lack of observations for parental income, the method used in 4.2 gives us too little information to answer our research question on whether social networks affect the accuracy of income expectations, as measured by the forecasting gap.
We thus perform a second test in which the new dependent variable Forecasting gap is defined. This variable was supposed to be the expected median income minus a personalized median income. However, because we did not find any variables which had a significant effect on observed income in table 4, we were unable to calculate personalized median
29 incomes with reliable interpersonal variation and used a generalized median income instead, that is, we subtract the same value for each individual. This, of course, has the effect that the test has coefficients which are identical to those in table 3, with the difference that the
intercept is lower. An important difference between the two regressions is that more variables have been included. Amongst these variables are variables for parental income rank and for population density. These are two important network effects that we wish to study to answer our research question.
Our expectations are that most variables do not significantly affect the variable Forecasting gap. Amongst the social network variables we expect that respondents with low parental educational attainment, indicated by fathlow and mothlow, misestimate and we, therefore, expect the coefficient related to those variables to be significantly different from zero. We expect respondents with a below average parental income rank, indicated by inc20 and inc40, to misestimate income. Those coefficients should also be significantly different from zero. Lastly, we expect respondents from hometowns with low population density to also face higher cost while acquiring information on incomes. We also expect the variable Rural to have a coefficient that is significantly different from zero.
In table 6, we see the results of the regression. We find that the variables for low paternal educational attainment “fathlow”, for high parental income rank “inc100” and for years in university “yearsinUvA” to be significantly different from zero. This last variable is a well-known control from the literature. Estimates are known to become more accurate the closer students come to graduation. The reason it is significant, here, might be because it decreases the amount of overestimation. To that effect we have done the same regression using an absolute version of “Forecasting gap” which can be found in the appendix, Table A.6. We find that “YearsinUva” is still significantly and negatively correlated with the variable, thus indicating that the longer a respondent is in university, the smaller their overestimation.
Just like in section 4.2, we see Paternal educational attainment confirmed as a network effect that increases the forecasting gap, while no proof can be found for the network effect of maternal educational attainment. This effect should not be understood as a decrease in
misestimation. In the absolute version of the regression in Table A.6, the symbol of the regression remains the same. Furthermore, this variable is a dummy variable. We also do not find any proof for the network effects of population density. Our hypothesis for the effects of parental income rank is rejected. While the variables for a parental income below average are
30 not significantly different from zero, the coefficient for the higher parental incomes “inc100” indicates that a respondent who self-evaluates his parents to be in the top 20% earners, is significant. Because of the lack of observations in the “Studie en Werk” dataset we cannot calculate if this variable significantly affects observed income. In the appendix, Table A.4 shows us that it was not possible to check if there are significant effects of parental income on observed income for the entire dataset of 80255 observations. The variable for high parental income “ouderinkhigh” is dropped when we control for the fact if a respondent has a master degree.
Therefore, only the effects of parental educational attainment as social networks effects can be said to affect the accuracy of income expectations, measured as the forecasting gap, in the manner that we predicted.
Table 6. The effects of social networks and controls on Forecasting gap
Variable Coefficient Std. Error T
fathlow** .7595421 .3360617 2.26 fathhigh .0327458 .2056804 0.16 mothlow -.0846537 .3768651 -0.22 mothhigh -.1809664 .2119966 -0.85 male .3941024 .2298607 1.71 Inc20 .2248275 .5254712 0.43 Inc40 .1363826 .3640644 0.37 Inc80 .2003147 .2229602 0.90 Inc100** .5211518 .2622148 1.99 Rural .1421285 .3080025 0.46 HighUrb .3178815 .189236 1.68 YearsinUva** -.2552321 .0622222 4.10 GradeMath -.1106137 .1078174 -1.03 Gradehighs -.0342762 .2015681 -0.17 Grvak .0022358 .0496144 0.05 Constant** -503.5086 124.8848 -4.03
Note: Based on the UvA human capital data, concerns a robust regression over 110 observations, F = 2.76, prob (F) = 0.0014, based on a level of significance of 0.05.
31 4.4 Can distributions indicate effects on accuracy? Variation
Another way to see if networks affect the accuracy of estimations is by looking at the variance of the income expectations across different groups. If a group of respondents is better
informed, their income estimations will be closer to each other than if that group would be less well informed, therefore, the variance of expected incomes within this group should be lower.
Our expectations are that standard deviations will decrease in size when hometowns have higher population density, parents are better educated and parents are richer. We will therefore use the F-ratio test to see if these are significantly different from each other. The test involves four sets of subgroup variances. The first set includes all of the variables that relate to population density, the second to parental income rank, the third to paternal educational attainment and the fourth to maternal educational attainment. We have tested all of the variables in one set against the variable that represents the highest value in each set. For example, we have tested low and median paternal educational attainment against high paternal educational attainment. Because it is not possible to test high paternal educational attainment against itself, these variables’ F-ratios and critical values have been indicated by X.
Group variations of income expectations are shown in table 7 per subgroup defined by their social network. What we find is that all the variances for population density are
significantly different from each other. It is remarkable that these variances are significantly different in the wrong way. We expected standard deviations to become smaller when social networks became larger because respondents would face lower search cost. Instead, we find increasing standard deviations. This indicates that respondents from hometowns with larger population density estimate less efficiently. This means that we will have to revise our understanding of the effect of population density on accuracy.
We face a similar problem when we consider parental income. We find that four out of five group variations are significantly different from each other. However, there is no clear pattern to the way in which these variations differ from each other. We, therefore, cannot confirm an effect on income expectations.
Lastly we have paternal and maternal educational attainment. Both of these perfectly follow our expectations. Variances for respondents with low parental educational attainment are significantly different from variances for respondents with high parental educational attainment. As parental educational attainment increases in size, standard deviations decrease in size. Our hypothesis for parental educational attainment is, therefore, confirmed.
32 As indicated in section 3.8, subgroups might face problems with heterogeneity. For example, the subgroup associated with low paternal educational attainment only has 13 observations. It is possible that all of these respondents also come from high population density cities. In that case, it is possible that the observed level of variation is due to population density rather than to educational attainment.
Table 7. Comparison of the group variances using a test on the F-ratio
Group Std. Dev. Observations CV (F) F
Low Density** .2324551 27 1.55 3.57 Medium Density** .3186418 80 1.43 1.90 High Density .4389978 96 x X parental Inc0-20** .2181067 7 2.17 2.50 parental Inc20-40** .7460515 15 1.84 4.68 parental Inc40-60 .3333595 58 1.53 1.07 parental Inc60-80** .2692038 75 1.53 1.64 parental Inc80-100 .3452714 47 x X
Fath educ low** .4570274 13 1.83 1.93
Fath educ mid .365086 108 1.35 1.24
Fath educ high .3297407 93 x X
Moth educ low** .5356322 16 1.84 2.53
Moth eudc mid .3645809 133 1.43 1.18
Moth educ high
.3370159 69 x X
Note: Based on the UvA human capital data, based on a level of significance of 0.05.
33 4.5. Can distributions indicate effects on accuracy? Individual Range
Another way of measuring how income estimates are distributed is by looking at the numeric value that individual respondents attach to the probability of earning 25 per cent more or 25 percent less than the median. This difference will be called the Individual Range. This individual range might be preferred to the group variance method that we used in section 4.4 because it uses a more detailed and lower level of observation.
Our expectations would be that respondents with low parental educational attainment, indicated by fathlow and mothlow, estimate on a greater confidence interval and we,
therefore, expect the coefficient related to those variables to be significantly different from zero. We expect respondents with a below average parental income rank, indicated by inc20 and inc40, to estimate income on a greater confidence interval. Those coefficients should also be significantly different from zero. Lastly, we expect respondents from hometowns with low population density, variable “rural”, to have a coefficient that is significantly different from zero.
In the regression below, we find that none of the coefficients is significantly different from zero. This means that we cannot confirm any social network effects from the results of this regression.
Table 8. The effects of social networks and controls on Individual Range.
Variable Coefficient Std. Error T
fathlow -.0598666 .0792593 0.76 fathhigh -.0787553 .0559804 1.41 mothlow .0565791 .0871733 0.65 mothhigh .0618794 .0597922 1.03 male .0171836 .0555219 0.31 Inc20 .0191126 .153334 0.12 Inc40 .0798592 .0878231 0.91 Inc80 -.0027245 .0564265 -0.05 Inc100 .0549314 .0684575 0.80 rural .0345761 .0722616 0.48 highUrb .0330254 .0485552 0.68 yearsinuva -.0041784 .0165226 0.25 grademath .0016675 .0261764 0.06 gradehighs .0573898 .0408246 1.41 grvak -.0063137 .0139252 -0.45 Constant 8.278104 33.15686 0.25
Note: Based on the UvA human capital data, concerns a robust regression over 162 observations, F = 0.68, prob (F) = 0.7985, based on a level of significance of 0.05.
