Specification and Sensitivity Tests

In this section, I test the robustness of the results, starting with the validity of the assumptions underlying the DDD identification approach (see section 3.4). While these cannot be tested directly, I can check if influences were present immediately prior to the reforms which exclusively affected the treatment group. If so, it seems likely that this influence was also present during and after the reforms, which would make it impossible to separate out the effects of the reforms. To check this, placebo tests are employed. The idea of placebo tests is to define the DDD dummy variables as if the reform had taken place in a year prior to the true reform already. The years after the respective reform are excluded to avoid measuring the effect of the true reform. For the first placebo tests, I use two years before the reform 1994 (as the microcensus does not provide a cross -section for 1994), and for the second test, I use the year prior to the reform in 1999 (excluding the years before the 1994 reform from the sample to avoid measuring its effect). Table A 7 in the Appendix shows that the DDD coefficients are insignificant in both placebo tests. The corresponding triple dif ferences are also insignificant. If confounding factors on the treatment group other than the true reforms were present, the coefficient of the DDD interaction variables would pick up that effect in these placebo tests. Hence, the results of the tests support the validity of the identifying assumption of the DDD analysis.

It is still possible that a differential time trend between the self-employment rates in the treatment and control groups exists in other years which I have not included in the placebo tests. T his is tested by including a time trend in the self-employment probability model and interacting it with the dummy variables which indicate potential tradesmen and people with

expected income above the threshold. Again, the coefficient of the triple interaction would pick up a differential time trend.39 I only use the years between the first and the second reform; otherwise the triple interaction with the time trend would measure the effects of the reforms.40 Table A 8 shows that the coefficient of the time trend’s triple interaction is insignificant; the corresponding triple difference is also insignificant. This is further support for the absence of reform-independent differential time trends between the treatment and the control groups and thus for the identifying assumption.

Another specification check concerns the definition of treatment and control groups. As described in section 3.3.2, the tax reforms only applied to tradesmen with income above certain thresholds defined by the tax law. In the primary analysis, I used individually estimated expected income from self -employment to determine if somebody is affected by the reform. Future entrepreneurial income is uncertain, however, and individuals may hope that there is a certain probability of achieving an income above the threshold even if the point estimate of their expected income lies below. To account for this possibility, I check if the results of this analysis change if I assume that people with expected lower income also conclude that the tax reforms are relevant to them. The robustness test consists in defining lower income thresholds to distinguish between treatment and control groups and re- estimating the probability model of being self-employed. T he thresholds are reduced by 15 % (model A) and, alternatively, by 30 % (model B) of the standard deviation of real gross income per year in the sample, which is €14,063. In model A (model B), the share of people with expected self-employment income above the threshold assigned to the 1994 reform increases from 1.27 % to 1.72 % (2.31 %), and of those above the 1999 threshold from 6.21 % to 8.35 % (11.02 %).

Table A 9 provides the results of these tests. They show that the significance of the triple interactions is sensitive to the threshold, but only if the threshold is decreased substantially. In model A, the logit coefficient of the triple interaction a ×b ×c (DDD 1994) is negative and

39

The identifying assumption states that, in the absence of the reforms, the difference between the time trends in the self-employment rates of the potential high-income and low -income tradesmen would be the same as the difference between the time trends of the potential high-income and low-income liberal professionals. If this assumption holds, the coefficient of the triple interaction term is zero, because a difference in the time trends between the high -income and low -income self-employed would already be captured by the coefficient of the double interaction between the time trend and c (expected income above threshold); the additional information that someone is a potential tradesman would not be informative with respect to the self -employment rate.

40 _{A time trend tests before the first reform is equivalent to the first pre-reform test, and a time trend test after the}

second reform would also only cover two cross-sections and would be likely to pick up a delayed effect of the second reform.

insignificant, and the coefficient of a × d ×e (DDD 1999) is positive and significant, as in the main estimation. The estimated triple difference corresponding to a × d ×e (DDD 1999), which represents the effect of the two tax reforms together, is 0.38 percentage points. This is smaller than the result from the main estimation (0.79 percentage points). The result is consistent with a weaker response, or no response at all, of individuals with expected income up to 15 % below the threshold set in the tax law, in comparison to those with expected income above it. In model B the coefficients of both triple interactions are insignificant. As in this model additional people with expected income even further below the threshold are assigned to the treatment group, the insignificant average effect on this group gives some support to the original assumption that those sufficiently below the threshold did not respond to the reforms.

Finally, the sensitivity of the results to the modelling of income taxation was checked. The function used to calculate gross income from estimated net income does not account for joint taxation of married couples (see section 3.3.2). For the main beneficiaries of German income splitting, i.e. married bread-winners whose spouse earns substantially less or nothing, gross income will thus be overestimated. Thus, both for tradesmen and liberal professionals, too many people tend to be assigned to the high-income group. To test the robustness of the results, I repeat the estimation of the probability of being self-employed using the sub-sample of the unmarried only, without the variables indicating the spouse’s employment status and income. In this estimation, the logit coefficients of the triple interactions were positive and significant for both reforms. The triple differences, which were also significant, were 3.43 for the first and 1.34 percentage points for the second reform. This confirms the general result that the tax cuts increased the probability of self-employment. It also indicates that the response of unmarried people in the treatment group to the reforms was substantially stronger than that of the whole population, perhaps because of their younger average age and greater flexibility.