The ‘recession-push’ hypothesis reconsidered

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.

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).

Table 4 Unit root tests Ng-Perron

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).

Table 5 Results for choosing the lag length of the VAR model based on the AIC, SC and HQ criteria

Testing for cointegration

The results obtained from applying the Johansen reduced rank regression approach to our model are given in Table 6.⁹ 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.

Table 6 Johansen cointegration test

Testing for nonlinearity

Hansen and Seo (2002) proposed a heteroskedastic-consistent LM test, namely, sup LM⁰ (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).¹⁰ Therefore, according to Table 7, threshold cointegration appears at the 1% significance level for the sup LM⁰ test, i.e., when β is fixed,¹¹ so that the null hypothesis of linear cointegration is strongly rejected.

Table 7 Hansen-Seo tests of threshold cointegration

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):

$$ {w_t} = \mu + \beta \,{s_t} + {\varepsilon_t}, $$

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:

$$ \left\{ \eqalign{ \Delta {s_t} = \gamma_0^s + \gamma_1^s\Delta {s_{{t - 1}}} + \gamma_2^s\Delta \,{w_{{t - 1}}} + {\alpha^s}{\varepsilon_{{t - 1}}} \hfill \cr \Delta {w_t} = \gamma_0^w + \gamma_1^w\Delta {s_{{t - 1}}} + \gamma_2^w\Delta \,{w_{{t - 1}}} + {\alpha^w}{\varepsilon_{{t - 1}}} \hfill \cr }<!endgathered> \right. $$

If β = − 1, then

$$ {w_t} = \mu + ( - 1)\,{s_t} + {\varepsilon_t} \Rightarrow {\varepsilon_t} = {w_t} - \mu + {s_t} $$

Hence

$$ \left\{ \eqalign{ \Delta {s_t} = \gamma_0^s + \gamma_1^s\Delta {s_{{t - 1}}} + \gamma_2^s\Delta \,{w_{{t - 1}}} + {\alpha^s}{\left( {{w_t} - \mu + {s_t}} \right)_{{t - 1}}} \hfill \cr \Delta {w_t} = \gamma_0^w + \gamma_1^w\Delta {s_{{t - 1}}} + \gamma_2^w\Delta \,{w_{{t - 1}}} + {\alpha^w}{\left( {{w_t} - \mu + {s_t}} \right)_{{t - 1}}} \hfill \cr }<!endgathered> \right. $$

$$ \left\{ \eqalign{ \Delta {s_t} = \gamma_0^s - \mu {\alpha^s} + \gamma_1^s\Delta {s_{{t - 1}}} + \gamma_2^s\Delta \,{w_{{t - 1}}} + {\alpha^s}{\left( {{w_t} + {s_t}} \right)_{{t - 1}}} \hfill \cr \Delta {w_t} = \gamma_0^w - \mu {\alpha^w} + \gamma_1^w\Delta {s_{{t - 1}}} + \gamma_2^w\Delta \,{w_{{t - 1}}} + {\alpha^w}{\left( {{w_t} + {s_t}} \right)_{{t - 1}}} \hfill \cr }<!endgathered> \right. $$

As ${e_t} = {w_t} + {s_t}$

$$ \left\{ \eqalign{ \Delta {s_t} = c_0^s + \gamma_1^s\Delta {s_{{t - 1}}} + \gamma_2^s\Delta \,{w_{{t - 1}}} + {\alpha^s}{e_{{t - 1}}} \hfill \cr \Delta {w_t} = c_0^w + \gamma_1^w\Delta {s_{{t - 1}}} + \gamma_2^w\Delta \,{w_{{t - 1}}} + {\alpha^w}{e_{{t - 1}}} \hfill \cr }<!endgathered> \right. $$

where

$$ \left\{ \eqalign{ c_0^s = \gamma_0^s - \mu {\alpha^s} \hfill \cr c_0^w = \gamma_0^w - \mu {\alpha^w} \hfill \cr }<!endgathered> \right. $$

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.

Table 8 OLS results for the relation between wage-employment and self-employment

Table 9 Wald test ${H_0}:\beta = - 1$