El peligro de los márgenes

Using the estimated annuities, the structural models of transition probabilities between the alternative employment states dependent employment and self-employment (4.10) can be estimated.61 Table 15 shows the coefficients resulting from the likelihood maximisation and the marginal effects in brackets where applicable. For each gender, the model of entry into self-employment from dependent employment is shown in the left and the model of exit from self-employment towards dependent employment in the right column. A positive sign of a coefficient indicates that the corresponding variable increases the probability of a transition to

61 _{Estimations of the structural models based on next year’s expected income and variance only are conducted}

the alternative employment state, and the marginal effects show the changes in percentage points. A university degree, for example, increases the probability of entering self- employment ceteris paribus by 0.31 percentage points for dependently employed men.

The estimates for the structural parameters ρ and α are given at the bottom of the table, along with their robust standard errors. The coefficient of the risk adjusted differential between net income from self-employment and from dependent employment α is significant in all models and positive in the models of entry into self-employment and negative in the models of exit. The four models thus consistently confirm the hypothesis that a higher risk adjusted net income in self-employment in comparison to dependent employment induces people both to becom e and to remain self-employed as the probability of entry is increased and the probability of exit is decreased.

The coefficient of constant relative risk aversion ρ is positive in all models, indicating risk aversion, and significant except for self-employed women, for whom the null hypothesis of risk neutrality cannot be rejected. The estimated degrees of risk aversion are low for self- employed men, moderate for de pendently employed men and high for dependently employed women and lie in the range reported by the literature (e.g. Holt and Laury 2002; Binswanger 1980). Considering that far more women are dependently employed than self -employed, this finding is also in line with Dohmen et al. (2005), who found that women are generally more risk-averse than men. Self-employed men and women are clearly less risk-averse than employees, which is consistent with the hypothesis that risk aversion deters people from choosing self-employment. The finding that self-employed women may even be risk-neutral, and thus less risk-averse than self-employed men, is consistent with the low share of the self- employed among women in Germany, which may imply that only the least risk-averse women choose self-employment.

Table 15: Maximum likelihood estimation results of structural transition probabilities

Variable /

Structural Parameter

Coefficient / Estimated Value [Marginal Effect] / (Robust Standard Error)

Men Wom en Dep. Employment to Self-Employment Self-Employed to Dep. Employment Dep. Employment to Self-Employment Self-Employed to Dep. Employment duration -0.2871*** -0.4063*** -0.3512*** 0.0989 [-0.0003] [-0.0023] [-0.0001] [-0.0003] dur_sq 0.0144*** 0.0190*** 0.0226** -0.0110 dur_cu -0.0003** -0.0002** -0.0004** 0.0002 highschool 0.0581 -0.3719 0.4404* 0.0379 [0.0002] [-0.0050] [0.0006] [0.0009] apprenticeship 0.6211*** 0.9556*** -0.1408 -0.2506 [0.0022] [0.0150] [-0.0002] [-0.0057] highertechncol 1.0105*** 0.7282** 0.3013 -0.5874 [0.0052] [0.0122] [0.0004] [-0.0125] university 0.6715*** -0.1744 0.0848 -1.0386*** [0.0031] [-0.0024] [0.0001] [-0.0220] age_bgn 0.0169 -0.1962*** 0.0392 -0.0933 [0.0001] [-0.0028] [0.0000] [-0.0022] age_bgn_sq -0.0010 0.0018** -0.0008 0.0005 workexp_bgn 0.0166 0.0005 0.0219 -0.0011 [0.0001] [0.0000] [0.0000] [-0.0000] unemexp 0.0539 -0.0878 0.1292 0.0170 [0.0002] [-0.0013] [0.0002] [0.0004] nchild 0.0649 0.0478 -0.0085 -0.3060* [0.0002] [0.0007] [-0.0000] [-0.0072] east 0.1612 0.1330 0.4094 0.7336* [0.0006] [0.0020] [0.0005] [0.0193] north -0.0877 -0.3617 -0.1032 -0.4847 [-0.0003] [-0.0046] [-0.0001] [-0.0097] south -0.3348** -0.1882 0.0658 -0.2811 [-0.0011] [-0.0026] [0.0001] [-0.0062] otherhhinc -0.0016 0.0020* -0.0134* 0.0019 [-0.0000] [0.0000] [-0.0000] [0.0000] spouse_empl 0.2786* -0.0337 -0.1052 -0.3828 [0.0011] [-0.0005] [-0.0001] [-0.0083] spouse_selfempl 0.6076 0.0999 1.6129*** 0.9143*** [0.0030] [0.0015] [0.0047] [0.0298] spouse_notempl 0.1447 0.3190 0.0323 [0.0006] [0.0051] [0.0000] constant -4.4727*** 1.9618 -5.2585*** -0.5257 ρ 0.3909*** 0.1675*** 1.2933*** 0.0394 robust standard error (0.0508) (0.0500) (0.2295) (0.0396)

α 0.2621*** -0.2336*** 0.1362*** -0.3744*** robust standard error (0.0217) (0.0342) (0.0242) (0.0839) Wald χ2 141.121 131.807 81.581 38.704 log likelihood -1579.148 -522.740 -611.885 -198.598 transitions (N) 388 232 133 78 transitions (rate) 0.009 0.075 0.006 0.083

N 41365 3075 22076 945

The est imations are based on estimated annuities of net earnings and net earnings variance in self-employment and dependent employment. For self-employed women in the data, an unemployed/not working husband predicted a negative outcome (no transition) perfectly, so the 46 corresponding observations and the variable

spouse_notempl were excluded from this estimation. Stars (* / ** / ***) indicate significance at the 10% / 5% / 1% level, based on heteroscedasticity robust standard errors.

Source: Own calculations based on the SOEP 1984-2005 , full-time self-employed and dependently employed individuals.

Table 16 reports partial point elasticities of the transition probabilities with respect to the annuities of the expected value µy and the variance σy2of net income in self-employment and

in dependent employment. They were calculated by evaluating the estimated structural transition model at the mean values of the independent variables. All elasticities are significant except for the variance elasticities of the probability of exit from self-employment for women. All elasticities have the expected sign, indicating that higher net earnings in self- employment in comparison to dependent employment attract people to this state, whereas higher re lative variance deters people from choosing this option. For example, the leftmost column shows that a 1 % rise in the annuity of expected hourly net income in self- employment increases the probability of entering self -employment by 1.4 % if net income in dependent employment and the variance in both employment states do not change. Similarly, a 1 % drop in net wages also raises the probability of entry into self-employment by 1.15 % if the variance of net wages and the prospects in self-employment remain constant. The elasticities do not equal in absolute terms because of the different mean variance in the two employment states. If the annuity of the net hourly income variance in self-employment increases by 1 %, the probability of entry decreases by 0.16 %, ceteris paribus, and analogously, a 1 % rise in the variance of wages increases the probability of entry by 0.05 % .

Table 16: Partial e lasticities of transition rates with respect to after-tax µy and σy2

Partial Elasticity Variable: Annuity of...

(Robust Standard Error)

Men Women Dep. Employment to Self-Employment Self-Employed to Dep. Employment Dep. Employment to Self-Employment Self-Employed to Dep. Employment 1.4292 -2.4460 1.4541 -2.8227 Hourly net earnings from self-

employment (0.2492)*** (0.4593)*** (0.6558)** (0.7888)*** -1.1459 1.7479 -0.0829 2.8001 Hourly net earnings from

dependent employment (0.2057)*** (0.4624)*** (0.0502)* (0.8489)*** -0.1579 0.5135 -0.6082 0.0545 Variance of hourly net earnings

from self-employment (0.0127)*** (0.0384)*** (0.3229)* (0.0420) 0.0471 -0.0042 0.0040 -0.0031 Variance of hourly net earnings

from dependent employment _{(0.0035)*** (0.0003)*** (0.0018)** (0.0024)} The partial elasticities give the percentage change of the transition probabilities induced by a discrete one percent change in the annuities of expected value or variance of income from one of the two employment types, evaluated at the mean values of the explanatory variables in the sample. Stars (* / ** / ***) indicate significance at the 10% / 5% / 1% level.

Source: Own calculations based on the SOEP 1984-2005, full-time self-employed and dependently employed individuals.

Based on the estimated hazard rates, the cumulative transition probabilities, given by the failure functions Fail(t), can be calculated for spells in self -employment and dependent

employment (see equation (4.15) in section 4.3.1). Figure 9 shows the cumulative probabilities of transition from self-employment to dependent employment, dependent on the spell duration, for a male and a female entrepreneur, evaluated at the respective mean values of the explanatory variables in the samples. The male entrepreneur has a higher cumulative transition probability than the female. Those women who choose to be self-employed – a much smaller share than among men, as mentioned before – have a lower probability of giving this status up again to switch to dependent employment, especially in the initial years. For the average male entrepreneur, the growth in the cumulative transition probability is largest in the first years of self-employment, which is explained by the high failure rates in the initial years of start-up firms. As the spell duration increases, the growth in the cumulative transition probability becomes smaller, as the firm has successfully taken the hurdles in its infancy years.

Figure 9: Cumulative probabilities of transition from self-employment to dependent empl.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Spell Duration (years) Male entrepreneur with average characteristics

Male entrepreneur with 10 % higher exp. net earnings annuity from self-empl. Female entrepreneur with average characteristics

Female entrepreneur with 10 % higher exp. net earnings annuity from self-empl. Source: Own calculations based on the SOEP 1984-2005, full-time self -employed and dependently employed individuals.

To illustrate the effect of net income, the figure additionally shows the cumulative transition probabilities of the man and the women if the net earnings annuity from self-employment is set to 10 % above the respective sample average. All other explanatory variables, including the annuity of net earnings from dependent employment and the variance annuities in both

employment states, are left unchanged (analogously to Table 16). These successful man and woman have lower cumulative transition probabilities at all spell durations than their average counterparts, because self-employment becomes relatively more attractive with higher expected income. The shapes of these curves are very similarly to those obtained with average net earnings annuities, however, indicating that the relative impact of net income does not change substantially over the spell duration in self-employment. The lower cumulative probabilities of exit can also be interpreted as the effect of a hypothetical tax cut which is granted exclusively to the self-employed. This interpretation is only valid if the hypothetical tax reform keeps the variance of net income unchanged.

Figure 10 shows the cumulative probabilities of transition from dependent employment to self -employment for a male and a female employee with average characteristics. A different scale of the y-axis is chosen than in Figure 9, as the probability of entry into self- employment is much lower than the probability of exit (relatively to the underlying populations). Men have a much higher probability of entry into self-employment than women. The growth in the cumulative transition probability decreases with longer tenure in dependent employment. Again, the figure also shows the cumulative probabilities when the annuity of expected net earnings from self-employment is set at 10 % above the average in the samples of men and women. This obviously increases the probability of transition to self-employment. The similar shapes of the curves before and after adjustment of the annuities illustrate that the relative effect of net income remains largely constant over the tenure in dependent employment. Again, the higher cumulative probabilities of entry into self -employment can be interpreted as the effect of a hypothetical exclusive tax cut for the self-employed, which does not change the variance of net income.

Figure 10: Cumulative probabilities of transition from dependent empl. to self-empl. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Spell Duration (years) Male employee with average characteristics

Male employee with 10 % higher exp. net earnings annuity from self-empl. Female employee with average characteristics

Female employee with 10 % higher exp. net earnings annuity from self-empl. Source: Own calculations based on the SOEP 1984-2005, full-time self -employed and dependently employed individuals.