We do not have any micro-theoretical underpinning which suggests a particular functional form for the basic relationship between 1, and Ut, but a preliminary plot of the data suggested that the relationship is non-linear, and that some kind of log-linear or semi-log function might be appropriate for estimation. Annual observations for 1, and Ut are obtainable from the AGR data set for 1970-89 (with 1, being calculated as a residual from these data). As far as U, is concerned, one option would be simply to include a dummy variable in the model for the 4-year period 1986-89 when the policy was in operation. Data on the number of
Oberbriickungsgeld recipients are, however, available for each of these four years, and given
that this number fluctuated considerably during the period (from a low of less than 6,000 in 1986 to a peak of nearly 18,000 in 1988), the assumption of a constant policy intensity, implicit in the use of a dummy variable is clearly not valid, and it is preferable to set U, equal to the total number of scheme participants in each year.
Table 6.2 shows the results of ordinary least squares estimation of a model with a semi-logarithmic relationship between I^ and ln(U^. Four versions of this model are estimated. In version 1, 1, is simply regressed against ln(U,). Whilst this yields a clear positive and statistically significant coefficient on ln(U^, as would be expected from inspection of Figure 3 above, the Durbin-Watson statistic lies below the lower bound of acceptance (at both 5%
and 1%), indicating a strong possibility of (first order) autocorrelation. This suggests that important variables may have been omitted from the model, or indeed that the observed correlation between 1, and ln(UJ may be a spurious one.
In Version 2 which includes a time trend, the overall fit of the equation is improved slightly, and ln(U^ retains its significance. Interestingly, the time trend itself has a significant coefficient, but with a negative sign. This suggests not that the initial bivariate relationship between 1, and ln(U^ was a spurious one, due to both variables being subject to similar time trends, but rather that 1, is subject to an underlying downward trend, which has been modified by the strong upward influence of growing unemployment during the period. Again however, the Durbin-Watson statistic, although somewhat larger, is still suggestive of autocorrelation, and possible omitted variables. Version 3 and 4 of the model, therefore, explore the possibility
that the key omitted variable is the labour market policy variable Of
Table 6.2: Regression estimates
Model I (1970-89) 2 (1970-89) 3 (1970-85) 4 (1970-89)
Dependent
variable
I. I, I. It
Constant -42.662 -83.516 -121.936 -108.796
(4.034)* (4.660)* (8.538)* (6.605)*
ln(UJ 17.112 24.981 32.890 30.214
(11.254)* (7.695)* (12.193)* (9.786)*
t -1.282 -3.104 -2.513
(2.652)** (6.292)* (4.583)*
u. 0.927
(3.191)*
0.88 0.91 0.96 0.95
D-W 0.55 0.60 1.70 1.64
F-stat 126.66* 88.06* 166.14* 93.81*
Units of measurement are thousands;
Absolute values of t-statistics are given in parentheses;
* indicates significance at 1%; ** significance at 5% (2-tailed tests for t-stats.)
Version 3 is identical to version 2, but estimated over the shorter period 1970-85. I.e. it
excludes the period in which Oberbrlickungsgeld operated. If Oberbriickungsgeld is indeed
the key omitted variable from the model, we would expect version 3 of the model to perform better than version 2, since we have excluded the period when the omitted variable would have been relevant. The results tend to confirm this expectation, with the model fitting slightly better than before, but more importantly, it now shows no evidence of autocorrelation, with the Durbin-Watson statistic lying above the upper bound of acceptance. The estimated coefficients retain their significance and signs.Finally, version 4 covers the whole estimation period 1970-89, and includes the
Oberbriickungsgeld variable U,. This equation performs rather well. The overall fit is good,
there is no evidence of autocorrelation, and the coefficients on all three independent variables are highly significant, with the coefficient on (j, having the expected positive sign, and the other two coefficients retaining their signs from previous versions of the model.
As we have no theoretical basis for the particular functional form used, however, some further examination of the sensitivity of the estimated model to changes in the functional form seemed worthwhile, and Table 6.3 presents estimates of further versions of the basic model.
Versions la to 4a, are equivalent to versions 1 to 4 respectively, the difference being that the
dependent variable in each case is the logarithm of the inflow to from unemployment to self-employment, ln(IJ. In each case, however, the pattern of results is broadly unchanged, with the signs and significance of the coefficients remaining the same, and as before only versions
3a and 4a exhibit an absence of serial correlation. Finally version 5a replaces the 0, variable
with its logarithm, but with no notable effect on the results, which appear, therefore, to berobust to several alternative functional forms.
Table 6,3: Regression estimates
Model la(1970-89) 2a( 1970-89) 3a(I970-85) 4a( 1970-89) 5a( 1970-89) Dependent
variable
inc;) Ind.) Ind.) Ind.) Ind.)
Constant 2,512 1,845 1,364 1,561 1,474
(16,630)* (7,715)* (6,443)* (6,688)* (6,683)*
ln(U^ 0,259 0,387 0,486 0,452 0,464
(11.910)* (8,940)* (12,161)* (10,544)* (11.172)*
t -0,021 -0,044 -0,036 -0.039
(3,247)* (5.962)* (4,759)* (5,201)*
u. 0,012
(2,854)**
ln(U^ 0,070
(3,307)*
0,89 0,93 0,96 0,95 0,96
D-W 0,53 0.72 1,82 1,69 1,70
F-stat 141,84* 113.8* 177,04* 110,48* 123,86*
Units of measurement are thousands;
Absolute values of t-statistics are given in parentheses
* indicates significance at 1%; ** significance at 5% (2-tailed tests for t-stats,)
How are we to interpret these findings, which apparently confirm that all three of our independent variables have an important role to play in explaining the development of inflows into self-employment over time?
As far as the "unemployment push" hypothesis is concerned, the evidence supports it only in its weak form, that is to say in the form which concerns only the sub-flow from unemployment to self-employment, and which says simply that this flow increases in response to an increase in unemployment. The stronger version of the hypothesis, however, which argues that the rate of flow from unemployment to self-employment (or the probability of an
unemployed person becoming self-employed) increases as the unemployment level increases, is not supported by the evidence. Indeed the estimated equations given in Tables 6.2 and 6.3 confirm that the flow rate (I/U,) tends to decrease with increasing unemployment (at least for all levels of unemployment within a feasible range). The even stronger version of the hypothesis (i.e. that the total flow into self-employment, from all sources, increases with unemployment) is yet to be tested, since it also depends on how the other two sub-flows from self-employment (from dependent employment, and from economic inactivity) respond to increasing unemployment Examining the latter two relationships econometrically is beyond the scope of this short paper, but as we have already seen (see the discussion in Chapter 4 above), there are theoretical reasons to anticipate that these relationships may embody discouragement effects as well as "unemployment push".
Turning to the time trend, our results appear to suggest that but for the influence of unemployment and labour market policy, the flow from unemployment to self-employment is on a long-term downward trend in Germany, falling at a rate of 2-3,000 per year. This result is interesting, but some caution should be exercised in interpreting it, given our reservations about the construction of the self-employed data in the AGR. Further caution is also necessary, since it should be remembered that the AGR self-employment data include unpaid family woricers. This group, in Germany as elsewhere, is particularly concentrated in certain sectors (such as agriculture), and is subject to a long-term historical decline (OECD Labour Force statistics suggest, for example, that the total number of such workers fell from just under two million to some 850 thousand, over the twenty year period 1966-86). It is possible, therefore, that the observed negative time trend may simply be reflecting the inclusion of this group in the data.
Nevertheless, the significant results for the policy variable are of particular interest. If the coefficient on U, in version 4 of the model is taken at face value, it would seem not only that Uberbrilckungsgeld has a significant positive effect on the inflow into self-employment, but, in line with the cross-section multi-country analysis in section 6.3 above, that the deadweight effect associated with the scheme is extremely small. That is, for every, 100