Self-employment and parental leave

Abstract

The main objective of this paper is to analyse the extent to which self-employment in Sweden has an impact on the use of parental leave. Our results show that during the child’s first 2 years, Swedish female self-employed use on average 46 fewer days of parental leave (15 %) than female wage earners, while male self-employed use on average 27 fewer days of parental leave (71 %) than their wage earner counterparts. We argue that the shorter average duration of parental leave among male self-employed is due both to relatively higher costs of absence and to a parental leave participation effect where some male self-employed with high performance-related income do not take parental leave at all. Given that all mothers take parental leave independently of employment status, we do not find any significant parental leave participation effect for female self-employed. Instead, we find a significant employment selection effect where women with high performance-related income choose self-employment explaining the shorter average duration of parental leave among female self-employed.

Appendices

Appendix 1

1.1 The function $l^{*} = l^{*} (b,w_{0} ),$ has the following properties: $\partial l^{*} /\partial b \ge 0$ and $\partial l^{*} / \partial w_{0} \le 0$

Proof

(2) may be formulated as an implicit function $F(l^{*} ,b,w_{0} ) = \frac{\partial V}{\partial l} + \frac{{\partial w_{1} }}{\partial l}\gamma_{1} = 0$. Differentiate F with respect to l, b and w ₀:

$$\frac{\partial F}{\partial l} = \frac{{\partial^{2} V}}{{\partial l^{2} }} + \frac{{\partial^{2} w_{1} }}{{\partial l^{2} }}\gamma_{1} \le 0$$

$$\frac{\partial F}{\partial b} = \frac{{\partial^{2} V}}{\partial l\partial b} \ge 0$$

$$\frac{\partial F}{{\partial w_{0} }} = \frac{{\partial^{2} V}}{{\partial l\partial w_{0} }} \le 0$$

The total derivative of F is

$${\text{d}}F(l,b,w_{0} ) = {\text{d}}l\frac{\partial F}{\partial l} + {\text{d}}b\frac{\partial F}{\partial b} + {\text{d}}w_{0} \frac{\partial F}{{\partial w_{0} }} = 0$$

We can thus calculate:

$$\frac{\partial l}{\partial b} = - \frac{\partial F/\partial b}{\partial F/\partial l} \ge 0,$$

$$\frac{\partial l}{{\partial w_{0} }} = - \frac{{\partial F/\partial w_{0} }}{\partial F/\partial l} \le 0$$

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1.2 The function $l^{*} = l^{*} (b,w_{0} ,\alpha , \, \beta ),$ has the following properties: $\partial l^{*} /\partial b \ge 0,\,\partial l^{*} /\partial w_{0} \le 0,\,\partial l^{*} /\partial \alpha \le 0,$ and $\partial l^{*} /\partial \beta \le 0$

Proof

We assume that the individual chooses $l^{*}$ that maximizes the function

$$V + W = V\left( {l^{*},b,w_{0} } \right) + \alpha \left( {H - \frac{1}{2}\beta l^{2} } \right)\gamma_{1}$$

The first-order condition for $l^{*}$ that maximizes V + W is

$$\frac{\partial V}{\partial l} - \alpha \beta \gamma_{1} l = 0$$

We regard this condition as an implicit function F($l^{*}$, b, w ₀, α, β) = 0.Differentiate F with respect to l, b, w ₀, α and β:

$$\frac{\partial F}{\partial l} = \frac{{\partial^{2} V}}{{\partial l^{2} }} - \alpha \beta \gamma_{1} \le 0,$$

$$\frac{\partial F}{\partial b} = \frac{{\partial^{2} V}}{\partial l\partial b} \ge 0,$$

$$\frac{\partial F}{{\partial w_{0} }} = \frac{{\partial^{2} V}}{{\partial l\partial w_{0} }} \le 0,$$

$$\frac{\partial F}{\partial \alpha } = - \beta \gamma_{1} l \le 0,$$

$$\frac{\partial F}{\partial \beta } = - \alpha \gamma_{1} l \le 0.$$

The total derivative of F is

$${\text{d}}F\left( {l,b,w_{0} } \right) = {\text{d}}l\frac{\partial F}{\partial l} + {\text{d}}b\frac{\partial F}{\partial b} + {\text{d}}w_{0} \frac{\partial F}{{\partial w_{0} }} + {\text{d}}\alpha \frac{\partial F}{\partial \alpha } + {\text{d}}\beta \frac{\partial F}{\partial \beta } = 0$$

We can thus calculate:

$$\frac{\partial l}{\partial b} = - \frac{\partial F/\partial b}{\partial F/\partial l} \ge 0,$$

$$\frac{\partial l}{{\partial w_{0} }} = - \frac{{\partial F/\partial w_{0} }}{\partial F/\partial l} \le 0,$$

$$\frac{\partial l}{\partial \alpha } = - \frac{\partial F/\partial \alpha }{\partial F/\partial l} \le 0,$$

$$\frac{\partial l}{\partial \beta } = - \frac{\partial F/\partial \beta }{\partial F/\partial l} \le 0$$

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Appendix 2

See Tables 7, 8, 9, 10, 11.

Table 11 Tobit regression estimates—sum of paid parental leave net days in year 0 and year 1 for the second child for males