Abstract
The human personality predicts a wide range of activities and occupational choices—from musical sophistication to entrepreneurial careers. However, which method should be applied if information on personality traits is used for prediction and advice? In psychological research, group profiles are widely employed. In this contribution, we examine the performance of profiles using the example of career prediction and advice, involving a comparison of average trait scores of successful entrepreneurs with the traits of potential entrepreneurs. Based on a simple theoretical model estimated with GSOEP data and analyzed with Monte Carlo methods, we show, for the first time, that the choice of the comparison method matters substantially. We reveal that under certain conditions the performance of average profiles is inferior to the tossing of a coin. Alternative methods, such as directly estimating success probabilities, deliver better performance and are more robust.
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Notes
 1.
Similar approaches, as discussed here, are also used to provide advice, for instance, to young adolescent individuals seeking guidance on occupational choice.
 2.
For a review of the recent literature on entrepreneurshiprelated personality characteristics, see Kerr et al. (2017).
 3.
For an overview of studies analyzing the effect of risk attitudes on entrepreneurial activities, see also Kerr et al. (2017).
 4.
This kind of fit measure is widely used in psychology, and not only in entrepreneurship; see, inter alia, Chapman and Goldberg (2011).
 5.
Thus, this simplifying assumption can be relaxed by using a vector of personality variables instead of univariate Γ.
 6.
 7.
There are two possible interpretations of π with respect to risk consistent with the model setting. First, entrepreneurship is not associated with any risk such that π is the deterministic relative income (relative to alternative income). Second, entrepreneurship is associated with risk and π is the average relative income but the client is riskneutral and only cares about averages.
 8.
Typically, even if π can be measured without any problem, we would only have reliable historical data on it for a subset of individuals because it is a counterfactual for those who were never entrepreneurs.
 9.
Note that \(p_{\text {COIN}}=\mathbb {E}[\mathcal {S}_{\text {\textit {COIN}}}]=\mathbb {P}(\textbf {a}_{\text {\textit {COIN}}}= 1\wedge \textbf {t}= 1)+\mathbb {P}(\textbf {a}_{\text {\textit {COIN}}}= 0\wedge \textbf {t}= 0)\). The coin completely ignores historical and client data such that \(\mathbb {P}(\textbf {a}_{\text {\textit {COIN}}}=a)\) and \(\mathbb {P}(\textbf {t}=t)\) are independent. Hence, we get
 10.
For instance, Δ(ε,ε^{′}) = 1/2 implies that changing the similarity criterion by a certain amount would change the expected recommendation success rate by 50 percentage points in the same setting indicating that approach performance is unstable.
 11.
Selfemployment and wage work can take place at the same time or at different time points.
 12.
Note that the relatively low number of observations is due to the fact that we need sufficient information about individuals who generated incomes from selfemployment and wage work. This is also why we had to use the willingness to take risk as information instead of the Big Five. We show below that this choice does not affect the reasoning of our approach.
 13.
The code is provided upon request.
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Acknowledgments
We are indebted two anonymous referees as well as to the participants of the Entrepreneurship Residence Week, in particular to Moren Levesque, Simon Parker, and Mirjam van Praag for their helpful comments.
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Appendices
Appendix A: Proof of consistency
To establish consistency with the profilebased approach, we must essentially answer the following question: What happens to the distribution of the individual trait if we condition on entrepreneurial abilities? Let μ_{ΓE} denote the mean of Γ for entrepreneurs and let \(\mu _{\Gamma E^{\textsf {c}}}\) denote the mean of the personality trait for nonentrepreneurs. Similarly, denote the variance of personality trait, Γ, by \(\sigma _{\Gamma E}^{2}\), respectively \(\sigma _{\Gamma E^{\mathsf {c}}}^{2}\). It is straightforward to derive that
where κ = τ − μ_{π}, W(κ) = ϕ(κ)/[1 −Φ(κ)] > 0 where ϕ(⋅) is the density and Φ(κ) the distribution function of the standard normal distribution; V (κ) = −ϕ(κ)/Φ(κ) < 0; w(κ) = W(κ)[1 − W(κ)]; and v(κ) = V (κ)[1 − V (κ)].
As the correlation, ρ, determines how strong the connection is between the personality trait and entrepreneurial abilities, we focus on the role of this parameter. If trait and abilities are independent, the correlation between them is zero such that \(\mu _{\Gamma E}=\mu _{\Gamma E^{\textsf {c}}}=\mu _{\Gamma }\) and \(\sigma _{\Gamma E}^{2}=\sigma _{\Gamma E^{\mathsf {c}}}^{2}= 1\). In such a setting, we cannot construct a distinct personality profile of an entrepreneur. However, if traits and abilities depend on each other with nonzero correlation, there will be a personality profile of an entrepreneur given by μ_{ΓE}. To see this, note that ρ > 0 implies
such that there is a difference between the average trait of an entrepreneur and the average trait of a nonentrepreneur. The difference in Eq. A.3 increases in the correlation between trait and entrepreneurial abilities. Furthermore, the variance of the personality trait conditional on being an entrepreneur, \(\sigma _{\Gamma E}^{2}\), decreases if the correlation between trait and abilities increases, as can be clearly seen in Eq. A.2.
A personality or profileoriented approach has the following strategy. It takes the client’s personality trait, γ, and compares it to the typical trait, μ_{ΓE}, of an entrepreneur. If Γ and π are sufficiently correlated, the Γvalues of entrepreneurs will be concentrated in one place and Γvalues of nonentrepreneurs in another. Hence, similarity between the client’s γ and profile μ_{ΓE} is an indication that the client is an entrepreneur. If the correlation is weak, all Γvalues will be located in roughly one place independent from π such that similarity between the client’s trait, γ, and profile μ_{ΓE} has little meaning.
To show consistency with the variableoriented approach, let \({\Psi }\in \mathbb {R}\) denote a normally distributed variable with mean μ_{Ψ} and variance \(\sigma _{\Psi }^{2}\). Ψ is assumed to capture all factors affecting entrepreneurial abilities that are not related to the personality trait, represented by Γ, such that we can assume that Ψ and personality trait, Γ, are independent. The variableoriented approach is consistent with the following model of entrepreneurial abilities:
where a and b are nonzero constant scalars. For instance, let Γ represent extraversion (one of the Big Five personality traits). If a > 0, more extraversion will increase entrepreneurial abilities, which is in line with previous research (Costa et al. 1984; Zhao and Seibert 2006; Zhao et al. 2010). The difference between the variableoriented perspective and entrepreneurshipprone profiles is that in the model in Eq. A.4 there is no specific reference profile of an entrepreneur. The assumption underlying Eq. A.4 is that, given a > 0, the trait Γ simply positively relates to entrepreneurial abilities, i.e., a higher score in Γ is associated with higher abilities. The model in Eq. A.4 generates a joint distribution of personality trait and abilities that is consistent with our recommendation model. Notice that π in Eq. A.4 is normal (it is the sum of two normal independent variables) with the following parameters:
The covariance between π and personality trait Γ is given by
Furthermore, it can be demonstrated that π and Γ are jointly normal according to the model in Eq. A.4. The joint distribution of π in model (A.4) and personality trait Γ is bivariate normal if and only if Y = απ + βΓ is normal for any constant \(\alpha ,\beta \in \mathbb {R}\). It is obvious that Y is normal if either α = 0 or β = 0, as π and Γ are both normal. If α = β = 0, Y = 0 with probability 1, which corresponds to a normal distribution with mean and variance zero. Hence, we must demonstrate that Y is normal if α and β are both nonzero. Note that π and Γ are dependent and correlated. Furthermore, note that
where δ_{Γ} ≡ αa + β and δ_{Ψ} ≡ αb. Using independence and normality of Γ and π, the momentgenerating function of Y is given by
such that
Equation A.6 is the momentgenerating function of a normal distribution with mean δ_{Γ}μ_{Γ} + δ_{Ψ}μ_{Ψ} and variance \(\delta _{\Gamma }^{2}+\delta _{\Psi }^{2}\sigma _{\Psi }^{2}\). As Y is normal for any constant α and β, π and Γ must be bivariate normal. Without loss of generality, we can normalize a such that \(a^{2}= 1b^{2}\sigma _{\Psi }^{2}\) obtaining \(\sigma _{\Pi }^{2}= 1\) and ρ = σ(π,Γ). Hence, as our recommendation model, the model in Eq. A.4 generates a bivariate normal distribution for [Γ,π]^{⊤} with mean m and covariance Q.
Appendix B: Robustness
To check the robustness of the results obtained with GSOEP data, this appendix provides additional simulation results using 1,620 combinations of parameter values.
B.1 Simulation setup
Let l = 1,…,L denote all parameter combinations. Let S^{l} denote the recommendation performance of an arbitrary approach given parameter combination l. We consider L = 1, 620 combinations. As before, for every parameter combination, we compute 10,000 simulations with sample sizes n(Θ) = 1, 000 and n(Ω) = 100. Given a sample of historical and client data, we apply three approaches to the same simulated data:

general average scores (GAS);

average scores with an optimized similarity criterion, given that m and Q are known (OAS); and

the probabilitybased approach (PBA).
Parameters, which are given in Table 3, are selected in a way such that a high number of different conditions is covered. Correlation between personality trait and entrepreneurial abilities ranges from weak, ρ = 0.1, to strong, ρ = 0.9.
𝜖 is the nonoptimized similarity criterion of average scores. Following the general logic of entrepreneurshipprone personality profiles, we assume that to receive a recommendation for entrepreneurship the client’s personality trait must be sufficiently similar to the profile, and that sufficient similarity promises good recommendation results. Hence, we use a rather strict (small) similarity criterion for average scores. However, we consider two different similarity criteria to examine the effect of changes in similarity criteria on average success rates (to test the second requirement). In particular, if 𝜖 = 0.01, we say that the similarity criterion is strict, whereas 𝜖 = 0.15 is interpreted as a tolerant similarity criterion.
To compute 𝜖^{∗} for the optimized version of average scores, we numerically maximize Eq. 6 for every parameter combination. Given the assumption on μ_{π} and τ, we cover a wide range of population shares of entrepreneurs, which is demonstrated in Fig. 3.
B.2 Performance analysis using 1,620 parameter combinations
Benchmarking success probabilities
To get an overview over average performance, we compute the simulation average, approximating \(\mathbb {E}[\mathcal {S}^{l}]\), for every parameter combination l and every approach.
In Fig. 4, we plot the distribution of average recommendation. Figure 4 reveals that the general averagescores approach (GAS) substantially underperforms compared to all other approaches.
In Fig. 5, we only show distributions of average success rates for a high correlation between personality trait and entrepreneurial abilities (ρ = 0.9). Still, even when correlation between personality trait and entrepreneurial abilities is high, general average scores underperform in comparison to all other approaches.
In contrast to general average scores, optimized average scores (OAS) exhibit high average success rates, which are slightly inferior to the upper boundary of recommendation performance represented by the probabilitybased approach (PBA). The results on relative performance are consistent with those obtained with the GSOEP calibrated model.
Testing requirements
To test the first requirement, in Fig. 6, we plot average recommendation success rates of (a) the optimized averagescores approach and (b) the general averagescores approach as a function of the parameter combinations index, l. Optimized average scores (Fig. 6a) always fulfill the first requirement. In case of general average scores (Fig. 6b), average success rates are smaller than 50%, the approach is inferior to the coin, in about 44% of all parameter combinations. More specific, only if the population share of entrepreneurs is low (about 19% on average, ranging between about 2% and 50%), general average scores outperform the coin with respect to average recommendation success rates.
To test the second requirement, let \(l_{\varepsilon ,\varepsilon ^{\prime }}=(l_{\varepsilon },l_{\varepsilon ^{\prime }})\) denote a pair of parameter combination where all parameters besides the similarity criterion are exactly the same. Our simulationbased measure of robustness, the simulation counterpart of Δ(ε,ε^{′}), is
In Fig. 7, we present robustness measures for average scores. Changing from a strict (𝜖 = 0.01) to a tolerant (𝜖 = 0.15) similarity criterion, or vice versa, changes average recommendation success rates by about 11 percentage points at maximum. The results become more striking when we compare the strict and the tolerant criterion to the optimized similarity criterion 𝜖^{∗}. The difference in average success rates between the strict and the optimized criterion is 95 percentage points at maximum, while the success rate difference between the tolerant and the optimized criterion is approx. 84 percentage points at maximum. The results indicate that average scores are not robust—mistakes of the adviser can generate high costs (e.g., a loss in average recommendation success rates of 95 percentage points).
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Konon, A., Kritikos, A.S. Prediction based on entrepreneurshipprone personality profiles: sometimes worse than the toss of a coin. Small Bus Econ 53, 1–20 (2019). https://doi.org/10.1007/s1118701801118
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Keywords
 Advice
 Personality
 Entrepreneurship
 Profiles
JEL Classification
 C15
 D81
 L26