Determinants of novice, portfolio, and serial entrepreneurship: an occupational choice approach

Abstract

In this paper, we first develop an original theory in which, based on their individual skills and the quality of their business, entrepreneurs can keep their original business (and thus remain novice entrepreneurs), start and keep a new business in the same or another sector along their current business (therefore becoming portfolio entrepreneurs), transfer or shut their original business down to either start a new one (turning themselves into serial entrepreneurs), or enter the labor market as wage workers. We then use the insights from our theory to develop three main hypotheses that are finally tested for a 10-year panel dataset (2001 to 2010) of more than 4000 Vietnamese manufacturing firms. We estimate an occupational choice model and a survival model and find that (i) a greater endowment of human capital is associated with a higher likelihood of a business owner to become a serial or a portfolio entrepreneur; (ii) a higher quality of the new business is associated to a higher likelihood that it is run by any type of habitual entrepreneur. Particularly, high entrepreneurial skills together with a high-quality business positively influence the likelihood of an individual to be serial or portfolio entrepreneur; (iii) ceteris paribus, firms run by serial or portfolio entrepreneurs tend to stay in business longer, although high-quality ones run by novice entrepreneurs endowed with high entrepreneurial skills are those with the lowest probability to leave the market.

Appendices

Appendix 1. Proofs

Proof of proposition 1

Differentiating expression (4) with respect to γ, the first-order condition for the maximization of ${V}^P\left(q,s,\widehat{q},\gamma \right)$ is

$$ q{K}^s{\gamma}^{\ast \left(s-1\right)}-\widehat{q}{\left[\left(1-\tau \right)K\right]}^s{\left(1-{\gamma}^{\ast}\right)}^{s-1}=0 $$

(10)

which can be rewritten as

$$ \frac{\gamma^{\left(s-1\right)}}{{\left(1-\gamma \right)}^{s-1}}=\frac{\widehat{q}}{q}{\left(1-\tau \right)}^s $$

(11)

Solving Eq. (11) for γ always yields an interior solution γ^∗ ∈ (0, 1). In fact, when s < 1, ${R}_1\left(\gamma \right)=\frac{\gamma^{\left(s-1\right)}}{{\left(1-\gamma \right)}^{s-1}}$ is always decreasing in γ, with $\underset{\gamma \to 0}{\lim }{R}_1\left(\gamma \right)=+\infty$, and R₁(1) = 0. Since the right-hand side of (11) is constant with respect to γ and positive, there will always exist a value 0 < γ^∗ < 1 such that $\frac{\gamma^{\left(s-1\right)}}{{\left(1-\gamma \right)}^{s-1}}=\frac{\widehat{q}}{q}{\left(1-\tau \right)}^s$.

The second-order condition for a maximum is

$$ \left(s-1\right)q{K}^s{\gamma}^{s-2}+\left(s-1\right)\widehat{q}\left(1-\tau \right){\left(1-\gamma \right)}^{s-2}<0 $$

(12)

Being (s − 1) < 0, the second-order condition is always satisfied and γ^∗ is a maximum.

Finally, totally differentiating the first-order condition in (7) with respect to γ, $\widehat{q},$ and τ yields

$$ \frac{{\mathrm{d}\gamma}^{\ast }}{\mathrm{d}\widehat{q}}=\frac{{\left(1-\tau \right)}^s{\left(1-{\gamma}^{\ast}\right)}^{s-1}}{\left[{q\gamma}^{\ast \left(s-2\right)}+\widehat{q}{\left(1-\tau \right)}^s{\left(1-{\gamma}^{\ast}\right)}^{s-2}\right]\left(s-1\right)}<0 $$

(13)

since (s − 1) < 0. Similarly

$$ \frac{{\mathrm{d}\gamma}^{\ast }}{\mathrm{d}q}=-\frac{{\gamma^{\ast}}^{s-1}}{\left[{q\gamma}^{\ast \left(s-2\right)}+\widehat{q}{\left(1-\tau \right)}^s{\left(1-{\gamma}^{\ast}\right)}^{s-2}\right]\left(s-1\right)}>0 $$

(14)

and

$$ \frac{{\mathrm{d}\gamma}^{\ast }}{\mathrm{d}\tau }=\frac{\widehat{q}{\left(1-\tau \right)}^{s-1}{{\left(1-\gamma \right)}^{\ast}}^{s-1}}{\left[{q\gamma}^{\ast \left(s-2\right)}+\widehat{q}{\left(1-\tau \right)}^s{\left(1-{\gamma}^{\ast}\right)}^{s-2}\right]\left(s-1\right)}<0 $$

(15)

Thus, γ^∗ is increasing in q and decreasing in $\widehat{q}$ and τ when s < 1.

Finally,

$$ \frac{{\mathrm{d}\gamma}^{\ast }}{\mathrm{d}s}=-\frac{{q\gamma}^{\ast \left(s-1\right)}\ln \left(\gamma \right)-\widehat{q}{\left(1-\tau \right)}^s{\left(1-{\gamma}^{\ast}\right)}^{s-1}\Big[\ln \left(1-\gamma \right)+\ln \left[1-\tau \Big)\right]}{\left[{q\gamma}^{\ast \left(s-2\right)}+\widehat{q}{\left(1-\tau \right)}^s{\left(1-{\gamma}^{\ast}\right)}^{s-2}\right]\left(s-1\right)} $$

(16)

being γ and τ ∈(0, 1), then all the natural logarithms in expression (16) are negative numbers. Therefore, the numerator is positive if $\widehat{q}$ is large relative to q and τ is small. Given the minus sign in front of the r.h.s., a positive numerator implies that γ^∗ is increasing in s (since s < 1 and the denominator is negative). Vice versa, the numerator is negative if $\widehat{q}$ is small relative to q and τ is large. This implies that, in this case, γ^∗ is decreasing in s.■

Proof of Proposition 2

Given s = 1, the value ${V}^P\left(q,s,\widehat{q},\gamma \right)$ in expression (4) is linear in γ and can be written as

$$ {V}^P\left(q,1,\widehat{q},\gamma \right)=\frac{qK}{1-\beta }-\frac{\beta \left(1-\gamma \right)K}{1-\beta}\left[q-\left(1-\tau \right)\widehat{q}\right] $$

(17)

which is increasing in γ (and thus maximized at γ = 1) if $q\ge \widehat{q}\left(1-\tau \right)$, whereas it is decreasing in γ (and thus maximized at γ = 0) if $q<\widehat{q}\left(1-\tau \right)$.■

Appendix 2. t test on the equality of means of age, firm age, and education among novice, serial, and portfolio; and tabulation of ownership types adopted by novice, serial, and portfolio

Analysis of the statistical differences in age, firm age, and education among novice, serial, and portfolio entrepreneurs

Table 4 Age—novice and habitual entrepreneurs

Table 5 Age—serial and portfolio entrepreneurs

Table 6 Firm age—novice and habitual entrepreneurs

Table 7 Firm age—serial and portfolio entrepreneurs

Table 8 Education—novice and habitual entrepreneurs

Table 9 Education—serial and portfolio entrepreneurs

Table 10 Tabulation of legal ownership

Appendix 3. The survival equation. A formal analysis

In this paper, we use three different estimation models: the nonparametric Kaplan–Meier estimator, the semiparametric Cox proportional hazards regression, and the parametric Weibull model.

The Kaplan–Meier estimator is a nonparametric estimator of the survival function S(t). If all the failure times are ordered and labeled t_(j) such that t₍₁₎ ≤ t₍₂₎ …  ≤ t_(n), the estimator is given by $\widehat{S}(t)=\prod \limits_{j\mid {t}_{(j)}\le t}\left(1-\frac{d_j}{n_j}\right)$, where d_j is the number of entrepreneurs who exit at time t_(j), and n_jis the number of entrepreneurs who are still in the business at the time and are therefore still “at risk” of experiencing exit.

The Cox hazard function for entrepreneur i is h_i(t) = h₀(t) exp(s_i q_i K_i, θ), where h₀(t) is the baseline hazard function when all covariates are zero. The parameters θ are estimated by maximizing the partial log likelihood given by $\sum \limits_f\log \left(\frac{\exp \left({s}_i\ {q}_i\ {K}_i,\theta \right)}{\sum_{i\in r(f)}\exp \left({s}_i\ {q}_i\ {K}_i,\theta \right)}\right)$, where the first summation is over all failures exit f, and the second summation is over all entrepreneurs r(f) who are still at risk at the time of failure.

The Weibull model assumes the Weibull distribution for T with parameters λ and p, denoted T~W(λ, p), if T^p~E(λ). The cumulative hazard is H(t) = (λt)^p, the survivor function S(t) = exp(−(λt)^p), and the hazard is λ(t) = λ^ppt^p − 1. Both semiparametric and parametric survival models are estimated by maximum likelihood estimation technique.

Appendix 4

Table 11 Summary statistics and matrix of correlation