Overconfidence over the lifespan: Evidence from Germany

Journal Pre-proofs Overconfidence over the Lifespan: Evidence from Germany Tim Friehe, Markus Pannenberg PII: DOI: Reference:

S0167-4870(19)30047-9 https://doi.org/10.1016/j.joep.2019.102207 JOEP 102207

To appear in:

Journal of Economic Psychology

Received Date: Revised Date: Accepted Date:

23 January 2019 22 August 2019 8 September 2019

Please cite this article as: Friehe, T., Pannenberg, M., Overconfidence over the Lifespan: Evidence from Germany, Journal of Economic Psychology (2019), doi: https://doi.org/10.1016/j.joep.2019.102207

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Overconfidence over the Lifespan: Evidence from Germany Tim Friehe∗

Markus Pannenberg†

September 13, 2019

Abstract This paper investigates if and how overconfidence at the individual level changes over the course of a life. We provide age profiles of a novel continuous overconfidence measure and the probability of being overconfident, conditioning on personality traits (including the Big 5 and optimism), economic preferences, cognitive ability, and the individual’s socio-economic status. Our empirical work relies on representative panel data sets from Germany, and individuals’ both self-assessed and actual percentile in the monthly gross wage distribution are incorporated in our measure of overconfidence. We find that both the level of relative placement and the overplacement probability increase with age up to one’s fifties. Keywords: Confidence; Age; Wage distribution; Germany; SOEP JEL: D01, D91, J14

∗

University of Marburg, Public Economics Group, Am Plan 2, 35037 Marburg, Germany. CESifo, Munich, Germany. EconomiX, Paris, France. E-mail: [email protected]. † University of Applied Sciences Bielefeld, Department of Business and Economics, Interaktion 1, 33619 Bielefeld, Germany. IZA, Bonn, Germany. GLO, Maastricht, Netherlands. E-mail: [email protected].

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Introduction

1.1

Motivation and Main Results

The right level of confidence is widely believed to be a prerequisite for success in life (e.g., Chamorro-Premuzic 2013). Overconfidence, the overestimation of one’s own performance in an absolute or relative sense, has recently attracted much attention. It has been associated with serious potential consequences for the decision maker and society overall, including poor financial decision making; unwise sorting choices into competitive settings or compensation schemes; deleterious health decisions; and increased ideological extremeness (e.g., Barber and Odean 2001, Benartzi 2001, Camerer and Lovallo 1999, Dohmen and Falk 2011, Kahneman 2011, Levy and Tasoff 2017, Moore and Healy 2008, Odean 1999, Ortoleva and Snowberg 2015, Weinstein and Lyon 1999). Underconfidence also has serious downsides as it can, for example, inhibit and depress individuals (e.g., Pikulina et al. 2017). However, overconfidence has been labeled the “mother of all biases” by Moore (2018) and is considered to be the most consequential judgmental bias by Nobel laureate Kahneman.1 Despite the well-established role of overconfidence in negative individual and social outcomes, information from a representative sample concerning its prevalence and correlated factors is missing from the literature. As a result, there is currently no clear understanding of how overconfidence relates to age (Prims and Moore 2017, Moore and Schatz 2017). In the popular imagination, young people are considered to be rather overconfident, whereas old people are thought to be cautious and circumspect, anecdotally implying that overconfidence “will get better with age” (Reyna et al. 2011). Along these lines, Kovalchik et al. (2005) find evidence that young individuals are more prone to overconfidence when comparing the decision making of 51 young students (average age 20) to that of 50 healthy elderly (average age 82). In contrast, as overconfidence can be considered a facet of a person’s personality (Almlund et al. 2011: 23), it may also be expected to be relatively stable as one ages. With overconfidence being important for many economic choices, systematic 1

In an interview, Daniel Kahneman explains that – if he had to choose out of all biases affecting human judgment – he would select to eradicate overconfidence (theguardian.com/books/2015/jul/18/ daniel-kahneman-books-interview last accessed June 11, 2018).

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changes in overconfidence over a lifespan would have far-reaching consequences as a society ages. For example, if overconfidence was to increase with age, it would result in overall more choices distorted by the overconfidence bias in an aging society. Overconfidence can appear in one of three guises (Moore and Healy 2008): (i) overestimation of one’s actual performance, (ii) excessive precision in one’s beliefs (i.e., overprecision), and (iii) overplacement of one’s own performance relative to that of others. It is important to clearly distinguish these different “faces of overconfidence” (see, e.g., Grieco and Hogarth 2009). In this paper, we will focus on overplacement. For example, Burks et al. (2013) and Benoit et al. (2015) also focus on relative overconfidence whereas Chen and Schildberg-H¨orisch (2018) consider absolute overconfidence. This paper explores how both the level of relative placement (i.e., the difference between the self-assessed and the actual placement) and the probability of overplacement vary over a lifespan, providing age profiles for full-time employees from young adulthood until the end of the employment period in the middle of the sixties using representative data sets from Germany. We mainly rely on an Innovation Sample of the German Socio-Economic Panel (SOEP) with rich information about survey participants. We can condition this data on personality traits, economic preferences, cognitive ability, and further socio-economic attributes of our survey participants to account for individual heterogeneity in overconfidence levels. The measurement of overconfidence is clearly at the heart of any study on over- or underconfidence. The construct is at the level of the individual and is likely domain-specific (e.g., Merkle and Weber 2011). There are domains in which many individuals are overconfident, leading to the result that individuals are overconfident on average (e.g., Moore and Healy 2008, Pikulina et al. 2017). However, there are also domains in which the average individual is underconfident and this assessment masks heterogeneity with some overconfident subjects and many underconfident subjects (e.g., Clark and Friesen 2009, Moore and Schatz 2017). There exist study designs in the literature that do not attempt to measure overconfidence at the individual level but only at the group level, finding, for example, that 77 percent of the subjects state that they are (in some way) more able than the mean subject (e.g., Svenson 1981). Many contributions are interested in over2

confidence at the individual level but lack direct information on it, and thus must rely on proxies of overconfidence. For example, Barber and Odean (2001) use an individual’s gender, and much of the finance literature centers on CEO decision making regarding vested stock options of the firm or media portrayals of the CEO (e.g., Malmendier and Tate 2015). In experimental studies, researchers collect information about individual overconfidence levels from populations often constrained to students, usually by asking participants to compare themselves on specific quantifiable measures against other participants in that same experiment (e.g., Moore and Schatz 2017). For example, Burks et al. (2013) assess their participants in two tests of cognitive ability and ask about the subject’s perceived performance relative to that of the other session participants. In this study, we use a novel measurement of overconfidence at the level of the individual, stemming from the labor-market context and representative samples. Specifically, we use information about the self-assessed own placement (in percentiles) in the distribution of monthly gross wages for individuals of the same age. The survey response scale is thus unambiguous, which contrasts with some early studies on overplacement (e.g., Svenson 1981 asked about being a skillful driver). A positive difference between the perceived and the actual position indicates overplacement. In addition to overplacement, we study the age gradient of the continuous relative placement (i.e., the difference between the self-assessed and the actual percentile). Since in our case monthly gross wages proxy productivity, our data informs about the self-assessed position in the productivity/ability distribution, which is very similar to the overplacement implementations in laboratory experiments. Similarly, people may understand the position in the wage distribution as a direct performance measure. In contrast to the abstractions frequently deployed in experimental tasks, people understand the concept “monthly gross wage” very well and know it from everyday life. Moreover, our overconfidence measure carries information about the perceived relative individual earnings capacity, which is probably crucial for many economic choices. It seems intuitive, for example, that people who overplace themselves in the gross wage distribution will tend to overestimate their statutory pension entitlements from the Bismarckian public-pension system in Germany and therefore will tend to save less for old age, when all else is held equal. Despite the fact that the Federal Employment Agency provides data on gross wages across coarse age groups 3

and that German newspapers frequently provide information about the net household income distribution in Germany, it is likely that individuals lack complete information about the gross wage distribution of people of their own age.2 This feature of our novel overconfidence measure is shared with most contributions on overconfidence (see, e.g., the discussion in Benoit et al. 2015). We establish a robust relationship between age and overconfidence, controlling for other potential influences such as the individuals’ cognitive performance, labor-market status, personality, and economic preferences. Using ordinary least squares regressions and a partially linear semiparametric regression approach, we find that individuals’ relative placement increases with age up to one’s fifties. We also find that our relative placement measure is related to items of the Big 5 personality inventory (particularly conscientiousness, neuroticism, and extraversion), whereas there is no robust correlation with risk or time preferences. When we consider the overplacement probability of an individual at a given age, we obtain very similar results. There is a notable increase in the overplacement probability up to the fifties. Our results are robust to variations in the reference group used in the calculation of the distribution of monthly gross wages of individuals with a similar age and rounding of self-assessed percentiles, for example. In general, an age gradient may be difficult to isolate because measurements may also reveal changes across cohorts. For example, Malmendier and Nagel (2011) provide evidence that cohort effects can be very important when considering risk taking. In order to separate age from cohort effects when analyzing overconfidence, we run regressions including one of two cohort proxy variables. First, we include in our estimation the GDP growth rate averaged over each respondent’s impressionable years. The impressionable years hypothesis proposes that individuals are susceptible to attitude change during late adolescence and early adulthood and that susceptibility drops radically thereafter (e.g., Arnett 2000).3 Second, we follow recent literature in psychology and economics and use as a cohort proxy variable the average unemployment rate from the period centering around the point in time at which the individual started working (e.g., Bianchi 2014, 2

The Federal Employment Agency can be accessed at statistik.arbeitsagentur.de/Navigation/ Statistik/Statistik-nach-Themen/Beschaeftigung/Entgeltstatistik/Entgeltstatistik-Nav.html. With respect to newspapers, in the summer of 2018 alone, there were articles (at least) in Der Spiegel, Die Zeit, Die Welt, S¨ uddeutsche Zeitung, Manager Magazin, and Bild. Our Supplementary Material provides references. 3 Evidence that confirms the hypothesis is presented, for example, in Krosnick and Alwin (1989).

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Kahn 2010, Maclean 2013, Schwandt and von Wachter 2019). Indeed, we find that cohort effects are relevant for the level of relative placement or the overplacement probability, highlighting the importance of the cohort proxy variable for the true identification of the age gradient. Importantly, the age gradient of overconfidence we find in the data is robust to the inclusion of both cohort proxy variables. In our discussion of the results, we refer to potential drivers of the overconfidence age pattern. In addition, we present evidence that suggests that relative placement is economically relevant by turning to financial decision-making of households. Finally, we briefly refer to the possibility that our results depend on the cultural context.

1.2

Related Literature

Our paper studies an overconfidence measurement regarding the individuals’ position in the distribution of monthly gross wages of all full-time employees, and how overconfidence evolves over the life course using representative samples from Germany. In a related paper, Prims and Moore (2017) investigate how the three different types of overconfidence, that is, overestimation, overplacement, and overprecision, correlate with age using experimental subjects recruited via mTurk, for example, and having them perform tasks and guess their absolute and relative performance on these tasks. They find a positive relationship between age and overprecision but no significant correlations regarding overestimation and overplacement.4 However, Prims and Moore (2017) highlight that many dimensions differ between young and old individuals which cannot be controlled for in their experiments. In contrast, we are able to include information about various individual characteristics in our empirical models using representative survey data. Our main interest – how an important individual trait evolves over the lifespan – was considered in the preceding literature with respect to economic preferences and personality traits (e.g., Golsteyn and Schildberg-H¨orisch 2017, Mata et al. 2018, Schildberg-H¨orisch 2018, Sunde and Dohmen 2016).5 For example, Dohmen et al. (2017) and Schurer (2015) explore how risk 4

Similarly, Ortoleva and Snowberg (2015) report a positive correlation between overprecision and age. With respect to personality development across the lifespan, Almlund et al. (2011), Borghans et al. (2008), Cobb-Clark and Schurer (2012, 2013), and Specht (2017) provide insightful contributions. 5

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preferences change with age, finding that the willingness to take risks generally decreases with age. With respect to this relationship between a key economic preference and age, Bonsang and Dohmen (2015) find that – conditional on socio-demographic characteristics – about half of the age-related cross-sectional difference in the willingness to take risks can be explained by cognitive skills. Papers dealing with financial decision-making of the elderly similarly put a possible decline in cognitive ability at the center of attention (e.g., Gamble et al. 2015, Korniotis and Kumar 2011, Pak and Babiarz 2018). It appears that the confidence in managing one’s own finances does not adjust appropriately to reflect the deterioration of cognitive ability as well as the decline in financial literacy in old age (e.g., Finke et al. 2017, Pak and Chatterjee 2016). This gap tends to produce overestimation or overprecision in the financial domain when elderly grow older. Against the background of this literature, we understand the importance of being able to include cognitive ability into our empirical specifications. In our regression analysis, we rely on two widely-used measures of cognitive skill to isolate age effects on confidence. Our overconfidence measure uses the self-assessed own position in the distribution of monthly gross wages. Similar survey data information regarding various types of household income was used in studies about the demand for redistribution. Cruces et al. (2013), Engelhardt and Wagener (2018), and Karadja et al. (2017) are interested in how individuals in Argentina, Germany, and Sweden, respectively, position themselves in some kind of distribution related to household income and how this bears on their demand for redistribution.6 The studies also describe information treatments, that is, how individuals’ demand for redistribution responds to receiving information about their true relative position. The present paper contributes to the literature on overconfidence by exploring age profiles. Interestingly, there is also no established understanding with respect to how a number of other individual characteristics bear on overconfidence (e.g., Moore and Dev 2017). For example, H¨ ugelsch¨afer and Achtziger (2014) find that male students are overconfident and female students 6

Karadja et al. (2017) ask about the position in the national total annual income distribution, Cruces et al. (2013) consider total monthly income at the household level, and Engelhardt and Wagener (2018) inquire about the relative position in terms of the standard of living. The measure that we use is thus much closer to the productivity of the respondent, as there is no possible distortion from capital income, for example.

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are underconfident in an experimental task that tests for overestimation. In contrast, De Paola et al. (2014) find no significant main gender effect for either overestimation or overplacement in their regression analysis, also relying on a student sample. Similarly relying on a student sample, Dankova and Servatka (2019) revisit the relationship between overplacement and excess entry established by Camerer and Lovallo (1999) for a population consisting of male participants, and find that the relationship does not obtain in their data from a mixed gender subject population. In our study that concerns overplacement in a representative sample of full-time employees, we find no robust significant gender effect across specifications and overplacement measures. This is consistent with Moore and Schatz (2017) emphasizing that several studies find no gender differences regarding overplacement.

1.3

Plan of the Paper

The structure of the paper is as follows. Section 2 presents the data. In Section 3, we present our empirical analysis and results. We discuss the robustness of our results at the end of Section 3. Section 4 provides a discussion of our results, while Section 5 concludes.

2

Data

Our empirical analysis is primarily based on the SOEP Innovation Sample (SOEP-IS). The SOEPIS is a nationally representative, longitudinal data set created in 2012 with the intention to improve the well-established German Socio-Economic Panel (SOEP-Core). Like the SOEP-Core, the SOEP-IS is representative for the population of private households in Germany (e.g., Richter and Schupp 2015). We use SOEP-IS data from the years 2013, 2014, and 2015. The present paper relies on a measure of the perceived relative monthly gross wage that was collected in the SOEP-IS in the year 2014 (i.e., we consider a cross section and add information about our individuals from the survey years 2013 and 2015). Specifically, the question we use asks: “Imagine one would randomly select 100 German residents of your age, what do you think: How many of these 100 people would have a higher monthly gross wage than you?”.7 This question was answered 7

The survey also asks about the self-placement in terms of net household income. We focus on individual monthly gross wages instead of net household income for two reasons: (1) We think that the monthly gross

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by survey participants of one subsample of the SOEP-IS (namely I3) with full-time employment. The information allows us to calculate the self-assessed percentile in the monthly gross wage distribution of the respective age group for all survey respondents with full-time employment and valid information. With respect to the distribution of the monthly gross wages, we exploit very rich information about 10,161 full-time employees from the SOEP-Core in the contemporaneous year.8 To calculate a measure of overconfidence at the individual level, we must first define the age ranges for the reference group presented in the survey question, namely “German residents of your age”. In 2014, we have information on the perceived individual position in the monthly gross wage distribution as well as their reported monthly gross wage for 462 full-time employees between 18 and 65 years of age. We use rolling windows to define the age-specific reference groups such that individuals with age t consider individuals with ages t − 2, ..., t + 3 to be part of their reference group.9 For each full-time employee, we calculate the observed percentile in the agespecific monthly gross wage distribution, using monthly gross wage information from all full-time employees in the SOEP-Core 2014. Our measure of overconfidence is then defined as perceived percentile minus actual percentile in the age-specific monthly gross wage distribution. A positive difference indicates overplacement of one’s own monthly gross wage relative to those earned by others in the respective age-specific reference group, that is, it signifies overconfidence. The level of the difference is our relative placement measure and informs about the severity of the mismatch between the perceived and the actual percentile for each respondent. Since our relative placement measure is an integral part of our study, it is important that both the age distribution and the monthly gross wage distribution for the 462 respondents from our representative SOEP-IS working sample are comparable to the distributions for the representative wage is a better indicator of individual productivity than the net household income, because the latter is heavily influenced by income redistribution. (2) We suspect that household net income is much more difficult to assess, since, for instance, tax laws and social policies (e.g., child allowances) moderate how total annual gross income at the household level translates into net household income. 8 In Section 3.2.3, we present results from regression exercises in which we calculate the distribution of monthly gross wages using only individuals from the SOEP-IS sample. 9 In Section 3.2.3, we provide more discussion about who may be part of the reference group and the robustness of our results.

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SOEP-Core study 2014. Table 7 in our appendix provides evidence that the distributions of age and the monthly gross wage are very similar in fact. Our working sample closely matches the SOEP-Core study in other respects as well. For example, the share of male employees in the SOEP-IS working sample is 0.67 and compares with 0.65 in the SOEP-Core study 2014. Our paper seeks to describe individual heterogeneity in terms of overplacement with a focus on age conditioning on personality, economic preferences, cognitive ability, and further socioeconomic indicators. For example, Burks et al. (2013) hypothesize that overconfidence may be a function of personality traits. In terms of personality, we consider the Big 5 personality inventory (e.g. Costa and McCrae 1992), which includes the traits openness, conscientiousness, extraversion, agreeableness, and neuroticism. This taxonomy is generally viewed as a set of core dimensions that provides a useful way to describe individual differences in personality (Specht et al. 2014). Table 8 in our appendix presents a definition and correlated trait descriptors for the Big 5 traits. The Big 5 personality trait scores represent respondents’ self-assessments in the form of ratings of how well specific statements describe their personality on a scale from 1 (“not at all true”) to 7 (“completely true”).10 Our Big 5 personality variables are generated by standardizing the sum of the scores of the dimension-specific questions. They were collected in the survey year 2013. A higher value of the derived variable represents a stronger intensity of that trait. In addition to the information about the Big 5 traits, we consider optimism as a personality trait that is easily confounded with overconfidence, since optimism represents the tendency to overestimate the occurrence of preferred outcomes (e.g., Heger and Papageorge 2018). Hence, to make a clear distinction between overconfidence and optimism, we include a covariate measuring optimism stemming from the survey year 2014 in our regression analysis. Optimism is incorporated as a dummy variable which equals 1 if a respondent reports being optimistic about the future.11 In terms of relating overconfidence to economic preferences, we consider risk and time preferences. Our measure of individual risk preferences is based on the question: “How do you see 10

Dehne and Schupp (2007) describe the implementation of the Big 5 inventory in the SOEP and the reliability of measurements. 11 Heger and Papageorge (2018) find a positive correlation between overconfidence and optimism measures in their data.

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yourself: Are you generally a person who is fully prepared to take risks or do you try to avoid taking risks?”. Respondents provide answers using a 11-point Likert scale from 0 (“risk averse”) to 10 (“fully prepared to take risks”). The risk information was experimentally validated by Dohmen et al. (2011). We use the risk information from the survey year 2013 in our regression exercises. The relationship between risk attitudes and absolute overconfidence takes center stage in Murad et al. (2016). Considering time preferences, we use response information (also from survey year 2013) from the question: “How would you describe yourself: Are you generally an impatient person, or someone who always shows great patience?” with answers provided on a 11-point Likert scale from 0 (“very impatient”) to 10 (“very patient”). The patience information was experimentally validated by Vischer et al. (2013). Cognitive ability might be related to our data on relative placement and overplacement. For instance, information must be collected and processed to come up with an estimate of the perceived percentile in the monthly gross wage distribution. The SOEP-IS 2014 provides two measures of cognitive ability, one relating to word recognition as a measurement of crystallized abilities and the other with symbols and numbers measuring fluid abilities. We standardize both measures of cognitive ability. Both measures correspond to modules of the Wechsler Adult Intelligence Scale and are used in Anger and Schnitzlein (2017), for example. In addition to age in years, we include in our set of covariates a gender dummy variable which is equal to one when the respondent is male, a dummy variable which is equal to one when the respondent was born in Germany, and a dummy variable which is equal to one when the subject holds a university degree. Moreover, we incorporate a host of variables describing the individual’s labor-market status including the monthly gross wage, the number of hours worked, the number of years with the current employer, employer size, own autonomy on the job, and whether respondents are employed in a white- or blue-collar job or are self-employed. This information stems from the SOEP-IS 2014. Moreover, we consider two cohort proxy variables to control for possible cohort effects in Section 3.2.2. First, for each subject, we consider the GDP growth rate averaged over its particular

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impressionable years (e.g., Arnett 2000), that is, the period between 18 and 25 years of age.12 Second, for each respondent, we include the unemployment rate averaged over a window of +/− 2 years around 21 years of age.13 The center is 21 years of age as it is the average age at first job for full-time employees in Germany according to the SOEP-Core 2014.14 Note, that we use different average rates for West and East Germany for both variables. The second cohort proxy variable can be used only for a subset of our working sample because there was no official unemployment during the times of the German Democratic Republic. In other words, when we run regressions incorporating the average unemployment rate around the time of labor market entry, we exclude older subjects from East Germany because we lack meaningful unemployment data. The idea of including these covariates in our empirical specifications is that they can help to disentangle age from cohort effects because we do observe a given average GDP growth rate or a given average unemployment rate for very different cohorts. Table 9 in our appendix presents the descriptive statistics for the variables used in our paper except our overconfidence measures (which are discussed in detail in Section 3.1).

3

Empirical Analysis and Results

In this section, we first summarize key features of our relative placement measure and describe how it is related to both the actual position in the monthly gross wage distribution and age. Next, we present results from regression exercises that seek to assess the relationship between the relative placement and age conditional on personality, economic preferences, cognitive ability, and further socio-economic attributes of the individual. We also analyze the relationship between the overplacement probability and age conditional on our covariate vector. Finally, we consider the robustness of our key results. 12

The GDP data for the years 1947 to 1989 for East and West Germany and from 1990 to 1991 for West Germany are from Ritschl and Spoerer (1997). The GDP data from 1990 to 1991 for East Germany are from Sleifer (2006), and are available at: histat.gesis.org/histat/. The data for the period 1992 to 2017 stem from the German Statistical Offices (see statistik-bw.de/VGRdL/tbls/?lang=en-GB). 13 Unemployment rates are sourced from the Federal Statistical Office and available for West Germany for the years 1947 to 2017 and for East Germany for the years 1991 to 2017. 14 We do not have information on the individual age at first job for SOEP-IS respondents.

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3.1

Overconfidence over the Life Course and Across the Wage Distribution: Descriptive Evidence

Are full-time employees’ perceptions of their position in the monthly gross wage distribution biased and, if yes, how? Figure 1 clearly shows that full-time employees in Germany, on average,

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overplace themselves.

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-80 -60 -40 -20 0 20 40 60 80 relative placement: perceived percentile-observed percentile

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Note: SOEP-IS & SOEP-Core 2014

Figure 1: Histogram of Relative Placement Measure. Our relative placement measure is substantially skewed to the right with a mean of 7.45 (see Table 1) and a median of 3. The majority of full-time employees under study are overconfident. The absolute value of the mean bias is about 25 for the population of overconfident individuals and 13 for the set of underconfident individuals (see Table 1), implying that deviations of self-assessment and actual position are relatively large on average. Accordingly, if we allow for a prediction error of +/- 5 percentiles (or even +/- 10), we still observe that 46 (40) percent of employees are overconfident. In our data, the perceived and the observed percentile match for only 3 percent of the full-time employees.

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Table 1: Descriptive Statistics for Measure of Relative Placement and Overplacement. Monthly Median Mean SD Incidence of Mean when Mean when Gross Wage Rel. Placement Rel. Placement Rel. Placement Overplacement Overplacing Underplacing All 3 7.45 24.40 0.54 24.75 -13.37 27 28.87 25.13 0.86 34.79 -8.51 1st quintile 2nd quintile 16 16.53 20.75 0.75 25.31 -10.70 3 3.27 19.85 0.54 17.36 -13.33 3rd quintile -5 -5.05 16.40 0.35 12.12 -14.57 4th quintile -10 -10.43 10.57 0.14 6.32 -14.01 5th quintile Notes: SOEP-IS 2014 & SOEP-Core 2014. N = 462. SOEP weights are used. Relative placement is calculated as the difference between the perceived and the actual percentile in the age-specific monthly gross wage distribution. The age-specific monthly gross wage distribution is calculated for all respondents within a five-years-rolling age window. There is overplacement (underplacement) when the relative placement measure is positive (negative).

Considering quintiles of the monthly gross wage distribution (see Table 1), we find that underplacement (overplacement) is more pronounced for high-wage (low-wage) earners, but that overplacement (underplacement) is still an important phenomenon in the top (bottom) of the gross wage distribution. In addition, we find that high-wage earners give considerably more homogeneous responses in terms of the standard deviation. Overconfidence at the group level (i.e., positive average values of the relative placement measure) results for the wage earners in the lowest three quintiles. It is noteworthy that the mean of the relative placement measure for subjects qualified as underconfident is relatively stable across gross wage quintiles whereas the mean for subjects qualified as overconfident decreases notably. Figure 2 provides more detailed evidence for a systematic relationship between the perceived and the actual position in the monthly gross wage distribution. Overplacement is prevalent up to the 60th percentile of the observed gross monthly wage distribution. In contrast, this holds for underconfidence only for the residual part of the same distribution. In our regression exercises below, we use wage vigintile fixed effects for each vigintile in the observed monthly gross wage distribution to control for a possibly non-linear relationship between the perceived and the actual relative wage position. This is analogous to the analysis in Karadja et al. (2017). In addition, we also include the monthly gross wage in order to control for effects from variations of the gross wage within fixed wage vigintiles. Note that including both wage vigintile fixed effects and the monthly gross wage in our empirical specifications entails exploiting individual variation only regarding the

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mean perceived wage percentile 20 40 60 80

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perceived position in the monthly gross wage distribution.

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40 60 observed wage percentile

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Note:SOEP-IS & SOEP-Core 2014. Reference group: rolling five-years age group.

Figure 2: Perceived and Observed Relative Wage (Averaged for Each Percentile).

Figure 3 provides our first descriptive insights into the relationship of relative placement and age.15 A lower relative placement level seems to be particularly likely among young individuals. Taking the estimated raw age profile at face value, we observe a strictly concave relationship between age and relative placement levels. The raw change of our overconfidence measure over the lifespan amounts to 10 percentile points, which is greater than the mean relative placement in our data.

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Non-parametric local mean smoothing is applied to estimate the changes by age.

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relative placement 4 5 6 7 8 9 10 11 12

Raw age profile of overplacement

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40 age

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Figure 3: Age Groups and Relative Placement.

3.2 3.2.1

Overconfidence Over the Life Course: Regression Results Main Results

We are interested in the age gradient of relative placement conditional on personality, cognitive ability, both risk and time preferences, both demographic and socio-economic indicators, and wage vigintiles fixed effects. To study that relationship, we employ two empirical strategies. First, we start with an ordinary least squares regression including a quadratic function of age to model the relationship between relative placement and age. Second, we use Robinson’s semiparametric regression estimator to allow for more flexibility in the relationship between relative placement and age.16 In addition, we want to explore the age gradient of the overplacement probability at 16

The employed partially linear model specifies the conditional mean of relative placement as the usual linear regression function of all covariates except age and an unknown smooth function of age. The parameters of the parametric part of the model are estimated using ordinary least squares regression after a transformation which eliminates the unknown function. In a second step, standard nonparametric methods can be used to recover the unknown smooth function of age (see, e.g., Henderson and Parmeter 2015: 228-238; Verardi and Debarsy 2012). To test for the appropriateness of the quadratic approximation of the nonparametric function of age in the ordinary least squares specifications, we use the test suggested by H¨ ardle and Mammen (1993). We use Verardi and Debarsy’s Stata-tool semipar to estimate the parameters and test statistics of interest.

15

the individual level, again conditional on the full vector of control variables. For that purpose, we present the results from a Probit specification with a dependent variable set equal to one when the subject overplaces the own rank (i.e., shows overconfidence) and zero otherwise. In Columns (1) and (2) of Table 2, we report results from our ordinary least square regression and the semiparametric regression explained above. Relative placement clearly increases with age up to the fifties. In Column (1), the coefficients of the quadratic function of age are significantly different from zero and imply a maximum at 48 years of age. This result confirms the descriptive evidence obtained from Figure 3 about a strictly concave relationship between age and the relative placement level. The plot that documents the age dependence as assessed in the semiparametric regression from Column (2), Figure 4, also shows this pattern. The estimated change of the relative placement measure over the full age range is slightly greater than the raw change documented in Figure 3. According to the H¨ardle and Mammen-test-statistics, we cannot (can) reject the null hypothesis that the quadratic (linear) function is an appropriate approximation of the unknown smooth function of age.17 17

Menkhoff et al. (2013) provide a study on overconfidence of financial investors. Although they are primarily concerned about overestimation, they also have a measure proxying overplacement. In this regard, they find that age tends to have a weakly negative effect on the self-assessed performance relative to other investors.

16

Table 2: Main Results: Relative Placement and Overplacement

Age

(1) Rel. Placement OLS 1.565∗ (0.623)

(2) Rel. Placement Semiparametric

(3) Overplacement Probit 0.176∗∗ (0.0594)

(4) Overplacement Average Partial Effects 0.0146∗∗ (0.00219)

Age2

-0.0162∗ (0.00696)

Male

-3.814 (2.164)

-2.751 (2.324)

-0.450∗ (0.206)

-0.0951∗ (0.0435)

German

1.288 (3.217)

2.588 (3.319)

0.412 (0.287)

0.0871 (0.0600)

Cognitive Ability (crystallized)

0.649 (1.272)

0.258 (1.264)

-0.00246 (0.107)

-0.000520 (0.0226)

Cognitive Ability (fluid)

0.158 (1.023)

-0.354 (1.108)

0.149 (0.108)

0.0316 (0.0228)

Risk Tolerance

-0.622 (0.434)

-0.720 (0.459)

0.0151 (0.0412)

0.00319 (0.00870)

Patience

-0.407 (0.337)

-0.253 (0.373)

-0.0671 (0.0352)

-0.0142 (0.00736)

Optimism

-0.757 (1.855)

-0.471 (1.945)

0.0369 (0.172)

0.00779 (0.0363)

Conscientiousness

-2.272∗ (1.055)

-2.020 (1.138)

-0.291∗∗ (0.0925)

-0.0615∗∗ (0.0192)

Agreeableness

1.867 (0.976)

2.106∗ (1.041)

0.138 (0.0992)

0.0293 (0.0207)

Extraversion

2.725∗ (1.093)

2.370∗ (1.158)

0.0624 (0.0988)

0.0132 (0.0208)

Openness

-1.754 (0.971)

-1.168 (1.023)

0.0691 (0.0925)

0.0146 (0.0195)

Neuroticism

-1.606 (1.080)

-1.150 (1.099)

-0.341∗∗ (0.106)

-0.0720∗∗ (0.0220)

University Degree (Yes=1)

-2.845 (2.133)

-4.119 (2.331)

-0.261 (0.230)

-0.0552 (0.0485)

0.000821 (0.000989)

-0.00677∗∗∗ (0.000935)

-0.000781∗∗∗ (0.000117)

-0.000165∗∗∗ (0.0000235)

Hours Worked (per Week)

-0.190 (0.154)

-0.241 (0.159)

-0.0233 (0.0123)

-0.00492 (0.00260)

Tenure (in years)

-0.0725 (0.103)

-0.0993 (0.108)

-0.0161 (0.0106)

-0.00340 (0.00223)

White Collar (Yes=1)

3.999 (2.584)

6.049∗ (2.598)

0.0801 (0.253)

0.0169 (0.0534)

Self Employed (Yes=1)

6.043 (3.760)

7.582 (4.057)

1.006∗ (0.424)

0.212∗ (0.0887)

Firm Size: 200 < Employees < 2000

3.360 (2.379)

2.278 (2.511)

0.330 (0.243)

0.0696 (0.0511)

Firm Size: Employees ≥ 2000

2.979 (2.372)

0.0289 (2.558)

0.544∗ (0.229)

0.115∗ (0.0475)

Autonomy (Yes=1)

0.367 (2.206) Yes

0.406 (2.371) Yes

-0.00142 (0.231) Yes

-0.000299 (0.0487) Yes

415 0.592

415 0.534

415 0.449

415

Monthly Gross Wage

Wage Vigintile Fixed Effects N R2 /P seudo R2

-0.00132 (0.000698)

Notes: Results from ordinary least squares, semiparametric, and probit regressions. The resulting age profile from the semiparametric specification in Column (2) is reported in Figure 4. Age, gender, nationality, economic preferences, and Big 5 are taken from SOEP-IS 2013, while optimism and cognitive ability stem from SOEP-IS 2014. The variables are all scaled such that a higher value means, for example, a higher cognitive ability or a higher willingness to take risks. Labor-market status variables are taken from SOEP-IS 2014. SOEP weights are used. Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

17

-40

-20

relative placement 0 20

40

Age profile of relative placement

15

20

25

30

35

40 age

45

50

55

60

65

Note: SOEP-IS & SOEP-Core 2014

Figure 4: Relationship of Relative Placement and Age Conditional on Covariate Vector

The relationship between age and the overplacement probability is much better approximated by a linear function, as is documented in Column (3) of Table 2 and Figure 5 that is based on the regression in Column (3). The overplacement probability more than triples from something below 0.2 at 18 years of age to something above 0.6 in the early fifties. Similar to the age profile of relative placement, middle-aged full-time employees are significantly more likely to overplace their monthly gross wage than full-time employees in their twenties.

18

0

overplacement probability .2 .4 .6

.8

Age profile of overplacement probability

15

20

25

30

35

40 age

45

50

55

60

65

Note: SOEP-IS & SOEP-Core 2014

Figure 5: Relationship of Overplacement Probability and Age Conditional on Covariate Vector

Before we address the potential concern about the separation of age and cohort effects in the next section, we briefly address some results regarding the relationship of our overplacement measure and other covariates. Table 2 shows that the coefficients of our two cognitive ability measures are always not statistically significant different from zero. Hence, we do not find a relationship between relative placement and measures of fluid and crystallized intelligence (which both decline in old age). Moreover, our regression results suggest that there is no statistically significant relationship between relative placement and our lagged measures of risk and time preferences. This also holds for our optimism proxy variable. In contrast, we find significant correlations between the lagged Big 5 personality traits and both overconfidence measures. The evidence is such that full-time employees with a higher conscientiousness score (i.e., employees who are efficient and well organized) and full-time employees with neurotic tendencies exhibit a significantly lower overplacement probability. Moreover, relative placement tends to be higher for employees who are more extraverted (i.e., more sociable and enthusiastic). In Columns (3) and (4), we find that male respondents are significantly less likely to overplace their monthly gross 19

wage than females. This contrasts with the widely held belief about the relationship between overconfidence and gender (see, e.g., Barber and Odean 2001). However, Moore and Schatz (2017) explain that the evidence so far is not at all clear cut. Moreover, we point out that our finding is not robust in regression exercises to be discussed below. 3.2.2

Disentangling Age and Cohort Effects

One might be concerned that cohort effects confound the estimated age gradients in Table 2.18 To deal with this issue, we include two different cohort proxy variables into our regression exercises that build on a similar idea. First, we include the GDP growth rate averaged over the impressionable years of our full-time employees, that is, over the period in which they were 18 to 25 years of age. For example, Giuliano and Spilimbergo (2014) show that having experienced a recession during the impressionable years has a long-lasting effect on the locus of control and redistribution preferences. The second variable that we consider to help disentangle cohort and age effects is the unemployment rate averaged over a period centered around the average age at first job (21 +/− 2 years of age), following other papers in economics and psychology. Bianchi (2014) shows that individuals who entered the job market in a period characterized by high unemployment are less likely to be narcissistic later in life than those who come of age in more prosperous times, Schwandt and von Wachter (2019) report long-term economic implications from entering the job market during high unemployment periods such as a substantial reduction in lifetime earnings, and Maclean (2013) reports on important health implications of unemployment rate at job entry (e.g., entering the labor market during periods with high unemployment lowers probability of developing depressive symptoms among women). The basic idea of our approach is that GDP growth rates and unemployment rates averaged over the years of emerging adulthood are valid proxy variables for overconfidence patterns across cohorts, because cohorts tend to show different average levels of overconfidence due to varying economic prospects during these very influential (and possibly subsequent) years. In our dataset, we find evidence in support of the hypothesis that our cohort proxy variables are relevant for overconfidence as approximated by our relative 18

Since we have information about the relative placement only from the year 2014, we cannot address potential period effects.

20

placement measurement (see Table 3). The qualitative inference is consistent in the sense that less favorable macroeconomic conditions during the years of emerging adulthood increase the level of relative placement in later life stages. Table 3: Results with Cohort Proxy Variables: Relative Placement and Overplacement (1) (2) (3) Rel. Placement Rel. Placement Overplacement OLS Semiparametric Probit Cohort Proxy Variable: Average GDP Growth Rate 1.569∗ 0.177∗∗ (0.618) (0.0601)

Age

-0.0154∗ (0.00689)

Age2

Age

-2.585∗ -0.116 -2.001∗ (0.892) (1.243) (0.0895) 415 415 415 0.597 0.540 0.451 Cohort Proxy Variable: Average Unemployment Rate 0.403∗∗ 0.0711∗∗ (0.124) (0.0123)

Av. Unemployment Rate N R2 /P seudo R2

1.332∗∗ (0.359) 367 0.611

0.0157∗∗∗ (0.00238)

-0.00127 (0.000703)

Av. GDP Growth Rate N R2 /P seudo R2

(4) Overplacement Av. Partial Effects

2.046∗∗ (0.559) 367 0.560

0.0480 (0.0307) 367 0.430

-0.0245 (0.0188) 415

0.0157∗∗ (0.00247) 0.0106 (0.00676) 367

Notes: Results from ordinary least squares, semiparametric, and probit regressions. The resulting age profile from the semiparametric specification in Column (2) is reported in Figure 6. Figure 6 also reports plots based on estimates from Column (3). Age, gender, nationality, economic preferences, and Big 5 are taken from SOEP-IS 2013, while optimism and cognitive ability stem from SOEP-IS 2014. The variables are all scaled such that a higher value means, for example, a higher cognitive ability or a higher willingness to take risks. Labor-market status variables are taken from SOEP-IS 2014. SOEP weights are used. Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

With respect to our main results, we find that the age gradient is qualitatively robust to the inclusion of these two cohort variables.19 For example, the implied relative placement maximum is at 51 years of age considering the specification in Column (1) with the average GDP growth rate as cohort proxy variable. However, we note that the quadratic term is no longer significant when we incorporate the average unemployment rate. When we incorporate the average GDP growth, 19

The estimated parameters for the set of covariates in these specifications is similar to the ones presented in Table 2, which is why we abstain from presenting the whole set of estimated parameters.

21

according to the H¨ardle and Mammen-test-statistics, we cannot (can) reject the null hypothesis that the quadratic (linear) function is an appropriate approximation of the unknown function. In other words, this still suggests the strictly concave relationship described above (see Figure 6). However, when we incorporate the average unemployment rate into our empirical model, we can reject neither null hypothesis according to the H¨ardle and Mammen-test-statistics. Consistently, the plot building on the semiparametric regression using the average unemployment rate shows that the age profile does not flatten out to the same extent as was true either without cohort proxy variable or with the average GDP growth as the cohort proxy variable (see Figure 6).20 Similarly, the results for the age gradient of the overplacement probability and the related plots match the findings presented above. Considering, for example, the average partial effect of age, results in Section 3.2.1 are very similar to the findings obtained when cohort variables are included. 20

It is important to remember that we have to drop full-time employees who lived in the former socialist German Democratic Republic (GDR) around the average age of labor market entry, the reason being that the official rate of unemployment was zero in the former German Democratic Republic.

22

Age profile of relative placement - specification with average unemployment rate -

-40

-40

relative placement -20 0 20

relative placement -20 0 20

40

40

Age profile of relative placement - specification with average GDP growth -

15

20

25

30

35

40 age

45

50

55

60

65

15

Note: SOEP-IS & SOEP-Core 2014

20

25

30

35

40 age

45

50

55

60

65

60

65

Note: SOEP-IS & SOEP-Core 2014

Age profile of overplacement probability

Age profile of overplacement probability

- specification with average GDP growth -

0

0

overplacement probability .2 .4 .6 .8

overplacement probability .2 .4 .6 .8

1

1

- specification with average unemployment rate -

15

20

25

30

35

40 age

45

50

55

60

65

15

Note: SOEP-IS & SOEP-Core 2014

20

25

30

35

40 age

45

50

55

Note: SOEP-IS & SOEP-Core 2014

Figure 6: Relationship of Relative Placement Level/Overplacement Probability and Age Using Average GDP Growth (Unemplyoment) Rate.

In summary, all of our results indicate that the wage-related overconfidence of full-time employees in Germany significantly increases over a lifespantime from 20 years to 50 years of age. 3.2.3

Reference Group Variation

The survey item that is key for our analysis asks participants to respond to the question: “Imagine one would randomly select 100 German residents of your age, what do you think: How many of these 100 people would have a higher monthly gross wage than you?”. Accordingly, in our main analysis, we compare the individual response to the observed position in the age-specific distribution of monthly gross wages of all full-time employees in the SOEP-Core 2014. It is clear from the definition of our key overconfidence variables, relative placement and overplacement, that identifying the appropriate reference group is an important step in our analysis. In this section, we consider a variation of the reference groups along two dimensions. First, we maintain the idea of the survey item and compare the perceived percentile to the percentile in the 23

age-specific distribution of monthly gross wages, but now create this distribution using only gross wage observations from the SOEP-IS (instead of the SOEP-Core). More importantly, in a second step, we consider the possibility that subjects do not actually respond to the survey question in the sense of thinking about the population at large. Instead, respondents may create an age-specific reference group in their mind that is (perhaps subconsciously) guided by some criterion. In this regard, we consider the possibility that the reference group is composed of either individuals with both the same age and the same gender or the same age and the same educational background (either with or without university degree). This means that we compute each individual’s relative placement level as the difference between the perceived percentile and the observed percentile in the age-specific distribution of monthly gross wages of full-time employees with the same gender or educational background as the respondent.21 We know from other contexts that similar others are more important (e.g., when it comes to status consideration; see, e.g., Falk and Knell 2004) such that it is plausible to believe that they may also play a more prominent role when subjects think about the reference distribution of gross wages. The age gradients that we obtain when the monthly gross wage distribution stems from fulltime employees of the SOEP-IS 2014 are qualitatively similar to those described in Section 3.2.1 (see Table 4 and Figure 7).22 A contrast results in that the overplacement probability – like relative placement – has a concave relationship with age in this set of results. With respect to the semiparametric regression in Column (2), according to the H¨ardle and Mammen-test-statistics, we cannot (can) reject the null hypothesis that the quadratic (linear) function is an appropriate approximation of the unknown function when we incorporate the average GDP growth rate as a cohort variable. However, in the empirical model that includes the average unemployment rate, the linear specification also cannot be rejected.23 21 The percentiles of the gender-age-specific and the education-age-specific monthly gross wage distributions are calculated using the SOEP-Core. We apply the same rolling age window within five years of age as in Section 3.2.1. 22 Unfortunately, we do not have enough full-time employees with valid information on monthly gross wages in the SOEP-IS 2014 to calculate percentiles of the respective wage distribution when we use an age window with −2/ + 3 years around the age of every single respondent. Therefore, in case of the SOEP-IS 2014, we apply rolling windows with -3/+3 years around the particular age. 23 Since the estimated coefficients of our standard covariate vector are similar to those documented in the previous section, we abstain from presenting the whole set of parameter estimates.

24

Table 4: Results with Reference Group SOEP-IS 2014: Relative Placement and Overplacement (1) (2) (3) Rel. Placement Rel. Placement Overplacement OLS Semi Probit Cohort Proxy Variable: Average GDP Growth Rate 1.597∗∗ 0.242∗∗∗ (0.596) (0.0644)

Age

-0.0153∗ (0.00667)

Age2

Age

-2.153 -0.132 -1.910∗ (0.935) (1.307) (0.0810) 415 415 415 0.486 0.443 0.356 Cohort Proxy Variable: Average Unemployment Rate 0.525∗∗∗ 0.0575∗∗∗ (0.133) (0.0116)

Av. Unemployment Rate N R2 /P seudo R2

1.415∗∗∗ (0.367) 367 0.503

0.00959∗∗∗ (0.00212)

-0.00237∗∗ (0.000764)

Av. GDP Growth Rate N R2 /P seudo R2

(4) Overplacement Av. Partial Effects

1.855∗∗∗ (0.550) 367 0.474

0.112∗∗∗ (0.0295) 367 0.329

-0.0305 (0.0186) 415

0.0132∗∗∗ (0.00247) 0.0257∗∗∗ (0.00649) 367

Notes: Results from ordinary least squares, semiparametric, and probit regressions. The resulting age profiles from the semiparametric specification in Column (2) are reported in Figure 7. Age, gender, nationality, economic preferences, and Big 5 are taken from SOEP-IS 2013, while optimism and cognitive ability stem from SOEP-IS 2014. The variables are all scaled such that a higher value means, for example, a higher cognitive ability or a higher willingness to take risks. Labor-market status variables are taken from SOEP-IS 2014. SOEP weights are used. Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

We now turn to the possibility that the reference group considered by survey respondents is not composed of 100 randomly selected Germans of a similar age, despite the wording of the survey item. If survey respondents do not consider the actual age-specific distribution of monthly gross wages of all German citizens but of some biased distribution, it is plausible that the bias results from an over-weighting of similar peers in the reference group. The availability heuristic would be one possible driver of such a distortion (Tversky and Kahneman 1973). It is also a possibility that information about the wages of similar others is more emotionally relevant, implying that it will be recalled better at a later point in time (e.g., Laudenbach et al. 2019).

25

Table 5: Results with Gender-Age-Specific Reference Groups: Relative Placement and Overplacement (1) (2) (3) Rel. Placement Rel. Placement Overplacement OLS Semi Probit Cohort Proxy Variable: Average GDP Growth Rate 1.495∗ 0.208∗∗∗ (0.639) (0.0554)

Age Age2

-0.0151∗ (0.00715)

Male

-1.298 (2.335)

Age

0.0136∗∗∗ (0.00243)

-0.00180∗∗ (0.000657) 5.791∗ (2.516)

0.563∗∗ (0.195)

-2.601 0.0463 -1.962∗ (0.948) (1.431) (0.0804) 415 415 415 0.587 0.510 0.448 Cohort Proxy Variable: Average Unemployment Rate 0.353∗∗ 0.213∗∗ (0.125) (0.0741)

Av. GDP Growth Rate N R2 /P seudo R2

(4) Overplacement Av. Partial Effects

0.120∗∗ (0.0407) 0.00984 (0.0171) 415

0.0156∗∗∗ (0.00273)

-0.00181∗ (0.000917)

Age2

Male

-0.739 (2.509)

6.048∗ (2.657)

0.561∗∗ (0.202)

0.123∗∗ (0.0441)

Av. Unemployment Rate

1.217∗∗ (0.369) 367 0.596

2.109∗∗∗ (0.596) 367 0.534

-0.0189 (0.0418) 367 0.437

-0.00416 (0.00919) 367

N R2 /P seudo R2

Notes: Results from ordinary least squares, semiparametric, and probit regressions. The resulting age profile from the semiparametric specification in Column (2) is reported in Figure 7. Age, gender, nationality, economic preferences, and Big 5 are taken from SOEP-IS 2013, while optimism and cognitive ability stem from SOEP-IS 2014. The variables are all scaled such that a higher value means, for example, a higher cognitive ability or a higher willingness to take risks. Labor-market status variables are taken from SOEP-IS 2014. SOEP weights are used. Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

We specifically consider the possibility that people place their monthly gross wages in the age-specific distribution of individuals with the same gender or the same educational level. The results deliver findings that match qualitatively the results described in detail in our main analysis (see Tables 5 and 6 and Figure 7). In particular, the increasing trend of overplacement from the twenties to the early fifties is supported quite well by the evidence. This pattern is more easily seen 26

in Figure 7 for the cases in which the average GDP growth is used as the cohort proxy variable, that is, the cases in which we have 415 instead of 367 observations. When we use gender-age-specific reference groups in our empirical models including one of the two cohort proxy variables, we find that male respondents have a significantly higher probability of overplacing their gross wage (see Table 5). This suggests that the female respondents’ selfassessments are less likely to be exaggerated when the age-specific gross wage distribution (used to calculate their observed percentiles) does not include men who earn higher gross wages on average. The cause of this changing pattern may be gender-specific differences in the composition of the age-specific reference group, gender-specific differences in knowledge about the gross wage distribution, or other differences, which we cannot isolate with our data. A similar phenomenon results for full-time employees who have a university degree, as we now observe a positive and significant effect (see Table 6).

27

Table 6: Results with Education-Age-Specific Reference Groups: Relative Placement and Overplacement (1) (2) (3) Rel. Placement Rel. Placement Overplacement OLS Semi Probit Cohort Proxy Variable: Average GDP Growth Rate 1.155∗ 0.141∗ (0.583) (0.0570)

Age Age2

-0.0108 (0.00664)

Av. GDP Growth Rate N R2 /P seudo R2 Age

0.0151∗∗∗ (0.00265)

-0.000881 (0.000653) 1.948∗∗∗ (0.341)

0.417∗∗∗ (0.0619)

-1.607 -2.410 -0.137 (0.989) (1.453) (0.109) 415 415 415 0.624 0.534 0.457 Cohort Proxy Variable: Average Unemployment Rate 0.416∗∗∗ 0.0719∗∗∗ (0.124) (0.0132)

-0.0294 (0.0230) 415

University Degree (Yes= 1)

8.063∗∗ (2.788)

(4) Overplacement Av. Partial Effects

21.10∗∗ (3.008)

0.0158∗∗∗ (0.00268)

University Degree (Yes= 1)

10.09∗∗∗ (2.689)

22.29∗∗∗ (2.977)

2.119∗∗∗ (0.334)

0.465∗∗∗ (0.0664)

Av. Unemployment Rate

1.200∗∗∗ (0.349) 367 0.640

2.516∗∗∗ (0.595) 367 0.577

0.0465 (0.0288) 367 0.443

0.0102 (0.00632) 367

N R2 /P seudo R2

Notes: Results from ordinary least squares, semiparametric, and probit regressions. The resulting age profile from the semiparametric specification in Column (2) is reported in Figure 7. Age, gender, nationality, economic preferences, and Big 5 are taken from SOEP-IS 2013, while optimism and cognitive ability stem from SOEP-IS 2014. The variables are all scaled such that a higher value means, for example, a higher cognitive ability or a higher willingness to take risks. Labor-market status variables are taken from SOEP-IS 2014. SOEP weights are used. Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

28

Age-specific Reference Groups from SOEP-IS

- specification with average GDP growth -

- specification with average unemployment rate -

relative placement -30 -25 -20 -15 -10 -5 0 5 10 15 20

relative placement -30 -25 -20 -15 -10 -5 0 5 10 15 20

Age-specific Reference Groups from SOEP-IS

15

20

25

30

35

40 age

45

50

55

60

65

15

Note: SOEP-IS 2014

20

25

30

35

40 age

45

50

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Note: SOEP-IS 2014

- specification with average unemplyoment rate -

relative placement -30 -20 -10 0 10 20 30

relative placement -30 -20 -10 0 10 20 30

40

40

50

Age- & Gender-specific Reference Groups

- specification with average GDP growth 50

Age- & Gender-specific Reference Groups

15

20

25

30

35

40 age

45

50

55

60

65

15

Note: SOEP-IS & SOEP-Core 2014

20

25

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45

50

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65

Note: SOEP-IS & SOEP-Core 2014

Age- & Education-specific Reference Groups

- specification with average GDP growth -

- specification with average unemplyoment rate -

-30 -20 -10

relative placement -30 -20 -10 0 10 20 30

40

relative placement 0 10 20 30 40 50

50

Age- & Education-specific Reference Groups

15

20

25

30

35

40 age

45

50

55

60

65

15

Note: SOEP-IS & SOEP-Core 2014

20

25

30

35

40 age

45

50

55

60

65

Note: SOEP-IS & SOEP-Core 2014

Figure 7: Semiparametric Regression: Age Profiles of Relative Placement Level.

3.3

Robustness Checks

In this section, we first present results we obtain when we disregard individuals at the extremes of the distribution of monthly gross wages, the rationale for such an exclusion being that people at the top (bottom) seemingly can less likely overplace (underplace) themselves in the distribution. Moreover, we address the potential effects of survey respondents’ rounding their assessments for their own reported position in the distribution. It is probable that at least some full-time employed individuals reported rounded values of their position estimates (see Manski and Molinari 2010, for 29

example). This could introduce deviations of perceived from actual positions not truly attributable to overconfidence. Lastly, we explore whether a different risk tolerance measure, namely a proxy for risk attitudes in the financial domain, yields different results. Without tails of the distribution of the monthly gross wage distribution When we think of the actual distribution of monthly gross wages, it holds that individuals at the very bottom (top) will in all likelihood overplace (underplace) their monthly gross wage.24 To exclude possible influence from this fact, we run regressions in which we exclude individuals from the lower and the upper 5% of the distribution, finding that our results are robust. For example, with respect to relative placement, we find a significant, strictly concave age profile with a maximum at 51 years of age, and when considering the overplacement probability, we find evidence for a significant linear trend in age (see Table 1 and Figure 1 in our Supplementary Material). Rounding In our main analysis, we calculate relative placement by subtracting the observed percentile in the monthly gross wage distribution from the perceived percentile. Most of the fulltime employees in the sample report their perceived relative wage as multiples of five, which gives an indication of rounding. To check whether potential rounding affects our result, we conduct the following simple test: We round the observed percentiles of the monthly gross wage distribution to the closest multiple of five and calculate relative placement as perceived position minus rounded observed position in the wage distribution. We thereby lower the risk of discrepancies between the perceived and the actual position in the monthly gross wage distribution that are due to rounding by respondents. Table 2 and Figure 2 in our Supplementary Material show that the estimated age profiles are very similar to the age profiles documented in Section 3.2.1. Financial Risk Preferences The SOEP-IS 2014 collects information on risk attitudes in different domains. In our main analysis, we include the self-reported general willingness to take risks. It may be argued that using risk attitudes regarding financial investments is also meaningful for 24

However, note that our descriptive analysis in Section 3.1 reveals that overplacement (underplacement) are still very important phenomena in the highest (lowest) quintile of the wage distribution.

30

the study at hand, as our overconfidence measure is created using relative monthly gross wages.25 When we employ the self-reported willingness to take risk in financial matters in our regression exercises, we find age-specific overplacement profiles, which are very similar to the profiles presented in the main part of our analysis. Moreover, the willingness to take risk in financial matters is positively correlated with the overplacement probability (see Table 3 in our Supplementary Material).26

4 4.1

Discussion Possible Determinants of the Overplacement Measure and its Age Gradient

The key variable in our analysis is the difference between the individual’s self-assessed and the observed placement in the age-specific distribution of monthly gross wages of German residents. Observing that a subject overplaces or underplaces the own monthly gross wage can possibly be explained by different factors. In the remainder of this section, we will highlight important factors and conjecture about the extent to which they may be responsible for the age pattern we find. Overconfidence Despite the great interest in overconfidence, the psychological mechanisms generating overconfidence are not very well understood (Burks et al. 2013). From an economic point of view, several rationales for motivated beliefs have been suggested (see Benabou and Tirole 2016 for a review): (1) For example, Brunnermeier and Parker (2005) and K¨oszegi (2006) suggest that people may derive ego-utility from optimistic beliefs about the self and/or the own future. The benefit of higher current and anticipated well-being due to optimistic beliefs may come at the cost of choices that are suboptimal for the agent as they diverge from accurate beliefs. The age gradient that we observe may be explained using this approach when the factor that constrains optimistic beliefs, namely the cost of suboptimal choices, becomes less important over time (e.g., as fewer choices with long-term implications need to be made). However, in this context, it must 25 For example, Bonsang and Dohmen (2015) focus solely on financial risk preferences in their study of risk attitudes and cognitive aging. 26 This finding is consistent with the results presented in Murad et al. (2016).

31

be noted that the results in Burks et al. (2013) do not support the importance of this channel. (2) Benabou and Tirole (2002) emphasized the motivational value of optimistic beliefs and showed that they can help present-biased agents overcome self-control problems. This approach finds support in experimental data reported in Chen and Schildberg-H¨orisch (2018). Against the background of this theory, if present bias increases with age (Friehe and Pannenberg 2019 present evidence that it might), then more overconfidence may be a response to counter the demotivation of effort resulting from the change in time preferences. (3) Optimistic beliefs can serve as a social signal. The idea may be cast as “the easiest and most effective way to lie is to lie to yourself first” (Burks et al. 2013, p. 951) and found support in the data of Burks et al. (2013) and Schwardmann and van der Weele (forthcoming). When considering a professional context, it would seem that forming a network and establishing favorable first impressions are aspects that lose some of their importance with age (e.g., L¨ockenhoff 2018). On the other hand, it may be that older individuals can to a lower extent rely on future prospects when comparing themselves to others, such that it may be more important socially to be able to report an already-achieved good standing. Generally, in order to uphold optimistic beliefs, individuals must engage in strategic ignorance, reality denial, or self-signaling (Benabou and Tirole 2016). There is evidence that older individuals have a special preference for emotionally positive information and for analyzing negative information at a more superficial level (e.g., Carstensen 2006), which is consistent with the age gradient we find in the data. Bayesian Updating/Information/Reference Groups Benoit and Dubra (2011) present an important critique of much of the early literature on overconfidence by noting that agents who know the distribution of ability levels but are unsure about their own ability, and who perform correct Bayesian updating, may seem overconfident at some points in time by the measures sometimes used. When transferred to our context, it is reasonable to assume that individuals know their monthly gross wage but may lack precise information about the distribution of monthly gross wages. Individuals could actively seek information about the gross wage distribution but will usually have little reason to do so, as information on the general wage distribution will usually

32

not be relevant for status considerations, negotiating the own remuneration, etc. Accordingly, individuals may form their belief about the distribution using signals that they receive, for example, when reading newspapers or talking to friends, colleagues, and relatives. Whereas the newspaper information channel would help form an unbiased belief about the distribution, the friends and family channel will probably induce a distorted wage distribution in the individuals’ perception (e.g., Anger and Schnitzlein 2017). For this reason, Section 3.2.3 explored the implications of considering a selected reference group for the age gradient. Importantly, the way in which the reference group is selected may itself be age-dependent. Along these lines, Carstensen (2006) reports that older people tend to have smaller networks and are less interested in broadening their horizon. As explained above, Bonsang and Dohmen (2015) explain that a big share of the age-dependence of risk attitudes can be explained by the age-dependence of cognitive abilities. Similarly, it may be conjectured that older individuals have greater difficulties in updating their beliefs according to Bayes’ rule, for example. However, our regression exercises include two standard measures of cognitive ability and Fisk (2005), for example, finds no age-related differences in probabilistic reasoning. A possible hypothesis is that more experienced individuals (as measured by age or tenure) will obtain a better understanding of the wage distribution and, accordingly, are more likely to be correct in their assessment of the own percentile in the gross wage distribution. We explore this learning hypotheses using a simple correlation analysis. Based on our data with the rounded relative placement measure, we can distinguish three outcomes: underplacement (40%), correct assessment of wage position (9%), and overplacement (51%). Using this outcome variable in a multinomial probit model including our standard set of covariates, we do not find that the probability of having a correct assessment is a function of age (or tenure), whereas the probability for overconfidence is a function of age similar to the results presented in the main part of our paper. The results are detailed in Table 4 in our Supplementary Material.

33

Personality There is heterogeneity with respect to overconfidence that is also partly driven by personality differences. Our results in Table 2 highlight conscientiousness, neuroticism, and extraversion as important personality traits out of the Big 5 with a notable influence on either relative placement or the overplacement probability. Extraversion is – like all Big 5 items – a higher level construct that also includes aspects of social potency (e.g., Wolf and Ackerman 2005). Burks et al. (2013) find evidence for a relationship between overconfidence and social potency. Similarly, self-esteem appears to be positively associated with extraversion (Robins et al. 2001). Personality evolves over the course of a life (e.g., Specht 2017). For example, there are studies documenting that self-esteem increases throughout adulthood up to the sixties (Robbins and Trzesniewski 2009). Such a development is principally consistent with the age gradient of relative placement in our data when seen in combination with the positive and statistically significant coefficient of extraversion. Similarly, using data from Germany, Lucas and Donnellan (2011) document an age profile for extraversion that peaks in the fifties.

4.2

Confidence and Financial Decision Making

Financial choices made over a lifespan are very important for old age. Policymakers in most countries are rightly concerned about the financial security of aging populations; much data indicates shortcomings in savings and insufficient preparations for unexpected emergencies and retirement (e.g., Lyons et al. 2018). With the criticality of sound financial decisions in mind, it is interesting to analyze whether our wage-related relative placement measure is significantly related to financial decision making. To this end, we use information about savings for wealth accumulation and information on outstanding loans taken out to finance consumption or other big-ticket items at the household level which are both included in the SOEP-IS 2015. Our simple correlation analysis indicates that wage-related relative placement is concomitant with more consumption loans and/or less savings for wealth accumulation purposes (see Table 5 in our Supplementary Material). If we combine these results with the increasing age profile of the overconfidence probability described in Section 3.2, our results imply that during the period of life when saving for old age should start at the latest, full-time employees are increasing in overconfidence, which in turn reduces sav-

34

ings for wealth accumulation purposes. Note that our result might be Germany-specific because statutory pension entitlements from the German Bismarckian public-pension system heavily depend on wages and our overconfidence measure relies on the perceived position in the gross wage distribution.

4.3

Overconfidence and Culture

Our study relies on survey data from Germany. The extent to which our results will carry over to other cultural contexts is an interesting question. In fact, studies exist that compare countries or regions according to their overconfidence ratings. For example, Stankov and Lee (2014) compare measurements for an overprecision task and find notable heterogeneity in the measured difference between actual and predicted accuracy. Closer to our overplacement measure, Moore et al. (2018) present studies with information about all three forms of overconfidence. Focusing particularly on the comparison between individualistic and collectivistic societies, the authors do not find that overplacement is a concept that depends very much on the cultural context. However, apart from the tendency to be overconfident, it may be that the degree to which individuals have a good understanding of the income distribution differs across countries. For example, in Sweden, it is possible to learn about anyone’s income tax returns, which contrasts markedly with the circumstances in Germany. Greater (non-)transparency about the own position in the distribution may leave less (more) room for motivated belief formation, for example.

5

Conclusion

Human judgment is plagued by several cognitive biases. The susceptibility to bias can be expected to depend on age. Using data from representative panel studies from Germany, this paper documents that wage-related overconfidence is related to age. Specifically, we find that the relative placement of one’s wage income increases with age until the early fifties. With overconfidence potentially affecting key economic choices, systematic changes in wage-related overconfidence over a lifespan can be expected to have far-reaching consequences in an aging society. Our paper shows that novel wage-related overplacement measures follow clear patterns over 35

much of the working life. We document the relevance of our measures in the domain of financial decision making. However, our study has its limitations. First, we analyze a cross-section of two measures of relative overconfidence, where longitudinal data with information about all three overconfidence facets would be ideal. Such longitudinal data would allow analysis of a full age-period-cohort model of overconfidence as well as the temporal stability of different facets of wage-related overconfidence. Second, we cannot relate our wage-related overplacement measure to overconfidence measures from the literature (that are collected in the context of specific experimental tasks, for example) since the SOEP-IS does not provide appropriate data. As a result, we cannot contribute to the interesting research question about the potential context-specificity of overconfidence.

Acknowledgments We thank three anonymous reviewers and the editor Carlos Alos-Ferrer for numerous very helpful comments. We are also very grateful for suggestions received from Hannah Schildberg-H¨orisch, Laslo Goerke, and Mario Mechtel.

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Appendix Table 7: Relating SOEP-IS 2014 to SOEP-Core 2014 Using Percentiles. Variable SOEP-Core (N = 10, 161) SOEP-IS Working Sample (N = 462) SOEP-Core (N = 10, 161) SOEP-IS Working Sample (N = 462) Notes: SOEP weights are used.

Mean P5 P 10 Monthly Gross Wage 3,323.188 1,200 1,518 3,280.44 1,200 1,550 Age 43.7521 25 27 42.043 23 26

P 25

P 50

P 75

P 90

P 95

2,100 2,100

2,880 3,000

3,994 4,000

5,500 5,500

6,800 6,600

34 30

45 43

53 52

58 58

61 61

Table 8: Big 5 Personality Traits (e.g., Almlund et al. 2011, Table 3). Description of Trait

Correlated Trait Descriptors Openness

Individual differences in the tendency to be open to new aesthetic, cultural, and intellectual experiences

Imaginative, artistic, excitable, wide interests, curious, unconventional Conscientiousness

The tendency to be responsible and hardworking; located at one end of a dimension of individual differences (conscientiousness versus lack of direction)

Efficient, organized, not careless, ambitious, not lazy, not impulsive

Extraversion An orientation of one’s interests and energies toward the outer world of people and things rather than the inner world of subjective experience Agreeableness The tendency to act in a cooperative, unselfish manner; located at one end of a dimension of individual differences (agreeableness versus disagreeableness) Neuroticism A chronic level of emotional instability and proneness to psychological distress

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Friendly, sociable, self-confident, energetic, adventurous, enthusiastic Forgiving, not demanding, warm, not stubborn, not show-off, sympathetic Worrying, irritable, not contented, shy, moody, not self-confident

Table 9: Descriptive Statistics. N Mean Age 415 41.97 Male 415 0.654 German 415 0.874 Cognitive Ability (crystallized) 415 0.0473 Cognitive Ability (fluid) 415 0.421 (General) Risk Tolerance 415 5.114 Financial Risk Tolerance 409 2.540 Patience 415 6.127 Conscientiousness 415 0.0655 Agreeableness 415 -0.0557 Extraversion 415 -0.00380 Openness 415 0.0447 Neuroticism 415 -0.112 Optimism 415 0.421 University Degree (Yes= 1) 415 0.245 Monthly Gross Wage 415 3254.5 Hours Worked (per Week) 415 43.63 Tenure (in Years) 415 11.02 White Collar (Yes= 1) 415 0.703 Self-Employed (Yes= 1) 415 0.105 Firm Size: 200 ≤ Employees < 2000 415 0.220 Firm Size: Employees ≥ 2000 415 0.267 Autonomy (Yes= 1) 415 0.290 Average GDP Growth Rate 415 1.945 Average Unemployment Rate 367 8.14 Notes: SOEP-IS. SOEP weights are used.

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STD 12.42 0.476 0.333 0.922 0.953 2.312 2.229 2.540 0.943 0.995 1.065 0.993 0.929 0.494 0.431 1743.1 8.184 10.18 0.458 0.307 0.415 0.443 0.454 1.071 3.21

Research Highlights “Overconfidence over the Lifespan: Evidence from Germany” x

We provide age gradients for one’s own relative placement and overplacement probability

x

Novel overconfidence measures stem from representative survey and refers to labor market

x

We include very rich information at the individual level into regression exercises

x

Relative placement and the overplacement probability increase with age up to one's fifties