Part-time entrepreneurship and financial constraints: evidence from the Panel Study of Entrepreneurial Dynamics

Abstract

To date, entrepreneurship literature overlooks part-time entrepreneurs, i.e., those who devote time to entrepreneurial ventures and wage employment at the same time. In contrast, recent evidence from the Global Entrepreneurship Monitor, a large cross-national study on the level of entrepreneurial activity, establishes that 80% of nascent entrepreneurs also hold regular wage jobs. This paper offers a model of entrepreneurial entry under financial constraints where individuals choose between wage employment, part-time, and full-time entrepreneurship. Those who become nascent entrepreneurs must further decide how much capital to invest and what proportion of time to spend in business. I test this model using data from the Panel Study of Entrepreneurial Dynamics, which covers start-ups and nascent entrepreneurs. My findings show that part-time entrepreneurs are not affected by financial constraints. The analysis suggests that industry barriers, risk aversion, and learning by doing might be other factors worth investigating.

Appendix: Solution to the optimization problem

The entrepreneur’s desired investment and time spent in the start-up are obtained by maximizing his net income with respect to k and δ.

$$ \mathop{{\rm max}}\limits_{0\leqslant \delta \leqslant 1,\hbox {}k\geqslant 0}\pi(k,\delta ;\theta)=\theta k^{\alpha}\delta^{\beta}+r(z-k)+w(1-\delta). $$

The Lagrangean for this maximization problem is

$$ \pounds = \theta k^{\alpha}\delta ^{\beta}+r(z-k)+w(1-\delta)-\mu _{1}(\delta -1)+\mu _{2}\delta +\mu _{3}k. $$

The first-order and the complementarity slackness conditions are

$$ \begin{aligned} &\frac{\theta \alpha k^{\alpha}\delta ^{\beta}}{k}=r,\\ &\frac{\theta k^{\alpha}\beta \delta ^{\beta}}{\delta}=w+\mu _{1},\\ &-\mu _{1}(\delta -1)=0,\,\mu _{1}\,\geqslant\, 0,\\ &\mu _{2}\delta =0,\,\mu _{2}\,\geqslant\, 0, \\ &\mu _{3}k=0,\,\mu _{3}\,\geqslant\, 0, \\ &\delta \,\leqslant\, 1. \end{aligned} $$

The optimal solution can be an interior solution when individuals choose to be part-time entrepreneurs, or a corner solution when they are either full-time entrepreneurs or wage workers. Hence, there are three possible outcomes: one interior and two corner solutions.

1.1 Case 1: Interior solution

In this case μ ₁ = 0 and the necessary conditions for the optimal amount of capital and relative time spent in start-up are

$$ \begin{aligned} &\alpha \frac{\theta k^{\alpha}\delta^{\beta}}{k}=r,\\ &\beta \frac{\theta k^{\alpha}\delta ^{\beta}}{\delta}=w\\ &\delta <1. \end{aligned} $$

Thus, the optimal factor input ratio is $\frac{k^{\ast}}{\delta^{\ast}}= \frac{\alpha}{\beta}\frac{w}{r},$ and the net income can be rewritten as

$$ \pi(k^{\ast},\delta ^{\ast};\theta)=(1-\alpha -\beta)\theta k^{\ast \alpha}\delta ^{\ast \beta}+rs+w. $$

Since the production function exhibits decreasing returns to scale $(\alpha+\beta <1), k^{\ast}$ and δ ^* are determined as

$$ k^{\ast} =\theta^{\frac{1}{1-\alpha-\beta}}\left(\frac{\alpha}{r} \right)^{\frac{1-\beta}{1-\alpha -\beta}}\left(\frac{\beta}{w} \right)^{\frac{\beta}{1-\alpha -\beta}}, $$

(22)

$$ \delta^{\ast} =\theta^{\frac{1}{1-\alpha -\beta}}\left(\frac{\alpha}{r}\right)^{\frac{\alpha}{1-\alpha -\beta}}\left(\frac{\beta}{w} \right)^{\frac{1-\alpha}{1-\alpha -\beta}}. $$

(23)

If the production function has constant returns to scale (α + β = 1), the optimal factor input ratio is still equal to $\frac{\alpha }{\beta}\frac{w}{r}$. However, the optimal levels k ^* and δ ^* are not determined, and there is no rent under the optimal factor input ratio. In this case, $\pi (k^{\ast },\delta ^{\ast };\theta)=rs+w$, or the entrepreneurial income would be the same as the wage worker’s income.

Both k ^* and δ ^* are nonnegative, with the exception of the case when θ is zero. Thus, to ensure that all conditions hold and that (22) and (23) form the interior solution of the maximization problem, δ ^* must satisfy the condition 0 < δ ^* < 1. From (23), $0<\theta ^{\frac{1}{1-\alpha -\beta}}\left(\frac{\alpha}{r}\right) ^{\frac{\alpha}{1-\alpha -\beta}}\left(\frac{\beta}{w}\right) ^{\frac{1-\alpha}{1-\alpha -\beta}}<1,$ or $0<\theta <\left( \frac{r}{\alpha}\right)^{\alpha}\left(\frac{w}{\beta}\right) ^{1-\alpha}.$

The entrepreneurial net income is

$$ \pi(k^{\ast},\delta^{\ast };\theta)= (1-\alpha -\beta)\theta ^{\frac{1}{1-\alpha -\beta}}\left(\frac{\alpha}{r}\right) ^{\frac{\alpha}{1-\alpha -\beta}}\left(\frac{\beta}{w}\right) ^{\frac{\beta}{1-\alpha -\beta}}\,+\,rz\,+\,w, $$

with a positive rent from entrepreneurial ability

$$ (1-\alpha -\beta)\theta^{\frac{1}{1-\alpha -\beta}}\left(\frac{\alpha }{r}\right)^{\frac{\alpha}{1-\alpha -\beta}}\left(\frac{\beta}{w}\right)^{\frac{\beta}{1-\alpha -\beta}}>0 $$

at the optimal levels of k and δ.

1.2 Case 2: Corner solutions

When $\mu_{1}\neq 0,\,\delta =1$. Individuals choose full-time entrepreneurship. The net income is $\theta k^{\alpha }\delta ^{\beta }+r(z-k),$ and the optimal solution becomes $k^{\ast }=\left(\frac{\theta \alpha }{r}\right)^{\frac{1}{1-\alpha }}$ and δ ^* = 1. In this case, $\theta \geqslant \left(\frac{r} {\alpha}\right)^{\alpha}\left(\frac{w}{\beta}\right)^{1-\alpha }.$.

Finally, when θ = 0, individuals become wage workers only. In this case, δ = 0 and the net income for a full-time wage worker is w + rz.

This model generalizes the entrepreneurial choice model developed by Evans and Jovanovic (1989) and Xu (1998). The solution in the general case can be summarized in the following way:

$$ \begin{array}{ll} \hbox {Full-time entrepreneur for}&\theta\, \geqslant\, \left( \frac{r}{\alpha}\right)^{\alpha}\left(\frac{w}{\beta}\right) ^{1-\alpha}\\ \hbox{Part-time entrepreneur for}&0 <\theta <\left(\frac{r} {\alpha} \right)^{\alpha}\left(\frac{w}{\beta}\right)^{1-\alpha}\\ \hbox{Wage worker for }&\theta =0 \\ \end{array}. $$