## Abstract

The relationship between unemployment and self-employment has been studied extensively. Due to its complex, multifaceted nature, various scholars have found a large array of different results, so that the exact nature of the relation is still not clear. An important element of the relation is captured by the recession-push hypothesis which states that in times of high unemployment individuals are pushed into self-employment for lack of alternative sources of income such as paid employment. We make two contributions to this literature. First, we argue that official unemployment rates may not capture the ‘true’ rate of unemployment as it does not include ‘hidden’ unemployed who are out of the labour force. Therefore, we propose a new method where the ‘recession-push’ effect relates not only to the (official) unemployed but also to the inactive population. Second, we argue that the magnitude of the recession-push effect is non-linear in the business cycle, i.e. the effect is disproportionally stronger when economic circumstances are worse. We provide empirical support for our hypotheses by estimating an econometric model on Spanish data.

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## Notes

- 1.
Binks and Jennings (1986) propose a secondary and complementary effect. As firms close down in recessions the availability and affordability of second-hand capital equipment increases, reducing barriers to entry.

- 2.
- 3.
Harrison and Hart (1983), Binks and Jennings (1986) and Hamilton (1989) are UK examples. US examples include Ray (1975), Highfield and Smiley (1987), Steinmetz and Wright (1989), Hudson (1989) and Audretsch and Acs (1994). Other examples include Blanchflower (2000), Bögenhold and Staber (1991), Meager (1994), Storey (1991, 1994), Robson (1991, 1996, 1998a, b), Black et al. (1996), Parker (1996), Cowling and Mitchell (1997), Storey and Jones (1987), Acs et al. (1994), Foti and Vivarelli (1994), Lin et al. (2000), Cullen and Gordon (2002), Parker and Robson (2004), Georgellis and Wall (2005), Torrini (2005), and Golpe and Van Stel (2008).

- 4.
In this sense a correct interpretation of the scope of microeconometric results should play a key role for conciliating the apparently contradictory microeconometric and macroeconometric evidence. For instance, the usual finding of a significant business cycle effect on the probability to become entrepreneur should be well-interpreted. The usual microeconometric estimates are done on the basis of a conditioned probability. Hence, the scope of a significant business cycle effect should be limited only to individuals who have a certain range of characteristics. An incorrect extrapolation of this type of results is a frequent source of misinterpretations.

- 5.
In the Spanish case, this problem is particularly serious. On the one hand, it is difficult to understand, for international observers, how Spanish society can assimilate such high unemployment rates without considering the role of the hidden economy in Spain (see Schneider 2005, for an international comparison). In this sense, the high and persistent unemployment rate has been confirmed, in several studies, as a key cause of the size of the shadow economy in Spain (see, Ahn and de la Rica 1997; Alañón and Gómez-Antonio 2005; or Dell’Anno et al. 2007). On the other hand, in 2002, the operational definition of unemployment was changed in Spain, in order to advance towards the European harmonization (COM 1987/2000). As a result, the unemployment series had to be reconstructed according to the new active job search definition.

- 6.
The International Classification by Status in Employment (ICSE-93) consists of the following groups: employees; employers; own-account workers; members of producers’ cooperatives; contributing family workers; and workers not classifiable by status.

- 7.
Let us define the employment rate (

*e*_{ t }) as the employment to population (aged 16+) ratio, the paid-employment rate (*w*_{ t }) as the paid-employment to population (aged 16+) ratio, the self-employment rate (*s*_{ t }) as the self-employment to population (aged 16+) ratio, the unemployment rate (*u*_{ t }) as the unemployment to population (aged 16+) ratio, while the labour participation rate (*p*_{ t }) consists of the economically active population (aged 16+) as a percentage of the total population of that same age group. The relation between the rates defined above is given by the two following identities:*w*_{ t }+*s*_{ t }=*e*_{ t }and*u*_{ t }+*e*_{ t }=*p*_{ t }. - 8.
We computed the unemployment threshold as follows. Given that our threshold has been defined as an employment rate (38.82%), we have checked that this value corresponds to period 1987/I. In this quarter, the “pseudo” unemployment rate (defined as the difference between active people and employment plus people not included in our self-employment definition), is 9.76%. Using this unemployment rate value, 22 quarters have unemployment rates above this value. Specifically, it concerns periods 1984:4–1986:1 and 1987:1 and 1993:1–1996:3. On the other hand 14 quarters are below the

*employment*threshold (1984:4–1986:3 and 1987:1 and 1993:4–1994:4), 12 of which correspond to quarters with values above the*unemployment*threshold. However, considering the 22 periods for which unemployment exceeds the unemployment threshold, only 12 of them correspond to periods where employment is below its specific threshold. This illustrates that it matters a lot whether to compute the threshold in terms of employment or in terms of unemployment. - 9.
Johansen’s approach is based on maximum likelihood estimation of the VECM, by step-wise concentrating the parameters out, i.e. maximizing the likelihood function over a subset of parameters, treating the other parameters as known, and giving the number

*r*of cointegrating vectors, where the matrix*β*is the last to be concentrated out. - 10.
The test is denoted by \( \sup L{M^0} = \mathop{{\sup }}\limits_{{{\gamma_L} \leqslant \gamma \leqslant {\gamma_U}}} LM\left( {{\beta_0},\gamma } \right) \), where

*β*_{0}is the known value of*β*(in our case*β*= − 1). The sup LM^{0}is a heteroskedastic-consistent LM test statistic for the null hypothesis of linear cointegration against the alternative of threshold cointegration. We have used the bootstrap method developed by Hansen and Seo (2002) to calculate asymptotical critical and p-values. - 11.
It can be shown that the long-term parameter between both series is close to −1 (see Table 9 in Appendix C). Therefore we have used the threshold cointegration test sup LM

^{0}, for a fixed*β*equal to −1, in order to facilitate interpretations. Note that the ECM term (*w*_{ t−1}−*βs*_{ t−1}) is now (*w*_{ t−1}− ( − 1)*s*_{ t−1}) =*e*_{ t−1}, i.e., the employment rate.

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## Appendices

### Appendix A: Statistical tests

In this appendix we present results from several statistical tests which guided us throughout our empirical analysis. First, we show results from unit root tests to see whether or not the variables from our model are stationary. Second, we report the diagnosis on the lag length. Third, we present the Johansen’s reduced rank regression approach to test for cointegration. Fourth and finally, we report the tests of threshold cointegration proposed by Hansen and Seo (2002).

### Unit root tests for paid-employment rate and self-employment rate

When using time series data, it is often assumed that the data are non-stationary and thus that a stationary cointegration relationship needs to be found in order to avoid the problem of spurious regression. For these reasons, we begin by examining the time-series properties of the series. We use a modified version of the Dickey and Fuller (1979, 1981) test (DF) and a modified version of the Phillips and Perron (1988) tests (PP) proposed by Ng and Perron (2001) for the null of a unit root, in order to solve the traditional problems associated to conventional unit root tests. Ng and Perron (2001) propose a class of modified tests, \( \bar{M} \), with GLS detrending of the data and using the modified Akaike information criteria to select the autoregressive truncation lag.

Table 4 reports test statistics of Ng-Perron tests, \( \overline M Z_{\alpha }^{{GLS}} \), \( \overline M Z_t^{{GLS}} \), \( \overline M SB^{{GLS}} \), \( \bar{M}P{T^{{GLS}}} \) and ADF tests. The second part of the table also reports critical values as tabulated in Ng and Perron (2001). All test statistics formally examine the unit root null hypothesis against the alternative of stationarity. At the 5% level, the null hypothesis of non-stationarity for the series in levels, *s* and *w*, cannot be rejected, regardless of the test. Accordingly, these two series are *I(*1*)*.

### Testing for the lag length

Cointegration analysis requires the model to have a common lag length. To select the lag length of the VAR we have used the Akaike information criterion (AIC), the Schwarz information criterion (SC), and the Hannan-Quinn (HQ) criterion. Although the SC and HQ criteria suggest that *k = 2*, the choice of *k* based on the Akaike information criterion suggests that *k = 3* is to be preferred. Hence, since the VECM variables are in first-differences, our estimates (see Tables 1, 2 and 3 in the text) incorporate two lags (see Table 5).

### Testing for cointegration

The results obtained from applying the Johansen reduced rank regression approach to our model are given in Table 6.^{Footnote 9} The two hypotheses tested, from no cointegration *r* = 0 (against the alternative of *n-r* = 2) to the presence of one cointegration vector (*r* = 1) are presented in the first two columns. The eigenvalues associated with the combinations of the *I(*1*)* levels of *x*
_{
t
} are in column 3. The next column reports the *λ*
_{max} statistics which test *r* = 0 against *r* = 1. That is, a test of the significance of the largest *λ*
_{
r
} is performed. The results suggest that the hypothesis of no cointegration (*r* = 0) can be rejected at the 5% level (with the 5% critical value given in column 5). The *λ*
_{
trace
} statistics test the null that *r = q,* where q = 0,1 against the unrestricted alternative that *r* = 2. On the basis of this test the null hypothesis is rejected. Hence, the tests for cointegration rank reject the null hypothesis of no cointegration.

### Testing for nonlinearity

Hansen and Seo (2002) proposed a heteroskedastic-consistent LM test, namely, sup LM^{0} (for a fixed *β*; *β* = − 1 in our case) for the null hypothesis of linear cointegration (i.e., there is no threshold effect) against the alternative of threshold cointegration. For the test, the p-value is calculated using a parametric bootstrap method (with 5000 simulations replications), as proposed by Hansen and Seo (2002).^{Footnote 10} Therefore, according to Table 7, threshold cointegration appears at the 1% significance level for the sup LM^{0} test, i.e., when β is fixed,^{Footnote 11} so that the null hypothesis of linear cointegration is strongly rejected.

### Appendix B: Derivation of model and error correction term interpretation

This appendix shows for our application that the error-correction term in the VECM can be interpreted as the employment rate.

Our benchmark model is given by the following expression, (rates expressed in levels):

the estimates of which are presented in Table 8 in Appendix C.

In order to contribute to a correct interpretation of the error correction term, observe that the error correction mechanism is derived from the relationship in first differences:

If *β* = − 1, then

Hence

As \( {e_t} = {w_t} + {s_t} \)

where

### Appendix C: Testing for the value of *β*

Table 8 reports OLS results for the relation between wage-employment and self-employment. Table 9 reports a Wald test where we test the null hypothesis of *β* = − 1, which is a basic assumption for fixing the beta value in order to facilitate the threshold interpretation. Using the Wald test, we cannot reject the null hypothesis.

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Congregado, E., Golpe, A. & van Stel, A. The ‘recession-push’ hypothesis reconsidered.
*Int Entrep Manag J* **8, **325–342 (2012). https://doi.org/10.1007/s11365-011-0176-1

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### Keywords

- Cointegration
- Non-linear
- Entrepreneurship
- Self-employment
- Unemployment

### JEL Classification

- C32
- J24
- M13