Abstract
This chapter investigates the time series properties of the unemployment rate of the Spanish regions over the period 1976–2011. For that purpose, we employ the PANIC procedures of Bai and Ng (2004), which allows us to decompose the observed unemployment rate series into common factor and idiosyncratic components. This enables us to identify the exact source behind the hysteretic behaviour found in Spanish regional unemployment. Overall, our analysis with three different proxies for the excess of labour supply renders strong support for the hysteresis hypothesis, which appears to be caused by a common stochastic trend driving all the regional unemployment series.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This is a broader category than SPEE unemployment (“paro registrado”) since it includes on-the-job search (intended to improve the labour status, to search for another job compatible with the current one, etc.), on-the-study search, agrarian workers receiving a special unemployment subsidy, especial temporary or part-time employment search, among other categories. Another SPEE proxy to which we could resort is non-occupied job seekers (DENOS being the Spanish acronym), an intermediate proxy between SPEE job seekers and registered unemployment rates.
- 2.
We keep up with the extant literature in the field by using seasonally adjusted data rather than unadjusted data. Our main results remain unchanged when we employ seasonally unadjusted data and are available from the authors upon request.
- 3.
An additional advantage of using this framework is that, whereas the application of other panel unit root tests with a factor structure such as those of Moon and Perron (2004) and Pesaran (2007) assumes that both common and idiosyncratic components have the same order of integration, the PANIC approach is flexible enough as to allow for a different order of integration in the common factor(s) and idiosyncratic components.
- 4.
The asymptotic distribution of \( ADF_{{\hat{e}}}^{c} (i) \) coincides with the Dickey-Fuller (DF) distribution for the case of no constant, while that of \( ADF_{{\hat{e}}}^{\tau } (i) \) is proportional to the reciprocal of a Brownian bridge.
- 5.
If the observed series are correctly decomposed into the common and idiosyncratic components, the latter (i.e. the defactored data) should by assumption be cross-sectionally independent. The PANIC approach has the further advantage that the common factors and indiosyncratic components are estimated consistently irrespective of their order of integration.
- 6.
The same holds for the case of a trend, where \( \pi_{{\hat{e}}}^{\tau } (i) \) is the p-value associated with \( ADF_{{\hat{e}}}^{\tau } (i) \). The pooled statistics for the trend specification are denoted as \( P_{{\hat{e}}}^{\tau } \) and \( Z_{{\hat{e}}}^{\tau } \). We should point out that under a factor structure, it is not appropriate to pool individual unit root tests for the observed series, since the limiting distribution of the test would contain terms that are common across cross-sectional units. In contrast, “pooling of tests for \( \hat{e}_{it} \) is asymptotically valid under the more plausible assumption that \( \hat{e}_{it} \) is independent across i” (Bai and Ng 2004, p. 1140).
- 7.
The latter is based on the average of pair-wise correlation coefficients (\( \hat{\rho }_{ij} \)) of ordinary least squares (OLS) residuals obtained from standard ADF regressions for each individual. The order of the autoregressive model is selected using the t-sig criterion in Ng and Perron (1995), with the maximum number of lags set at \( p = 4(T/100)^{1/4} \). Pesaran’s test is given by \( CD = \sqrt {2T/(N(N - 1))} \left( {\sum\nolimits_{i = 1}^{N - 1} {\sum\nolimits_{j = i + 1}^{N} {\hat{\rho }_{ij} } } } \right)_{{}} \mathop \to \limits^{d} N(0,1) \). The CD statistic tests the null hypothesis of cross-sectional independence, is distributed as a two-tailed standard normal distribution and exhibits good finite-sample properties. In addition, Breusch and Pagan (1980) test the null hypothesis of cross-sectionally independent errors via the following Lagrange Multiplier (LM) statistic \( CD_{lm} = T\sum\nolimits_{i = 1}^{N - 1} {\sum\nolimits_{j = i + 1}^{N} {\hat{\rho }_{ij}^{2} } } \mathop \to \limits^{d} \chi_{N(N - 1)/2}^{2} \).
- 8.
Note also that even though the information criteria for determining the optimal number of common factors work reasonably well in simulations, their practical application is difficult since they are usually found to select the maximum number of common factors allowed (Gengenbach et al. 2010, p. 219). Nevertheless, given that the four information criteria select either one or two common factors, which are much lower than the maximum number permitted, we are confident that the optimal number of common factors is correctly estimated.
- 9.
Unlike the Bai and Ng (2004) information criteria for selecting the optimal number of common factors (stationary and non-stationary) that applies to first-differenced data, the IPC p panel information criteria of Bai (2004) for determining the number of non-stationary common factors is applied to level data. The consistency of the IPC p information criteria requires the idiosyncratic component to be I(0), result that we find below.
- 10.
We also tested the unit root hypothesis with the tests of Pesaran (2007) and Moon and Perron (2004) and we could reject the unit root null hypothesis at the 1 % for the latter for the specification without trends (\( t_{a}^{*} = - 11.42, t_{b}^{*} = - 4.93,\) and CIPS = –1.73), and fail to do so for the specification with trends for all these tests (\( t_{a}^{*} = - 0. 0 4 7, t_{b}^{*} = -0. 0 5 1, \) and CIPS = −2.46). As noted above, the rejection of the nonstationarity null with the Moon and Perron (2004) tests for the no-trend specification should not be surprising, since they exhibit large size distortions in the presence of cross-cointegration, because the common trends are confused with the common factors and hence removed from the data in the defactoring process.
- 11.
As pointed out above, the presence of cross-sectional dependence prevents us from reporting the pooled ADF statistics associated with the observed unemployment rate series.
- 12.
The same results essentially follow for the specification with a trend.
- 13.
Since the IC p and BIC 3 criteria may not appear to perform optimally for small-N panels, and considering that the IPC p criteria favour the presence of one common stochastic factor, we present the results of the PANIC analysis for these two proxies assuming the existence of only one common factor, though highlighting that the PANIC main results are fairly robust to considering three and two common factors in the respective SPEE excess labour supply measures.
- 14.
As far as the idiosyncratic series associated with the job seekers rate, the ADF statistic rejects the unit root null at the 10 % or better for 10 regions.
References
Bai J (2004) Estimating cross-section common stochastic trends in non-stationary panel data. J Econometrics 122(1):137–183
Bai J, Ng S (2002) Determining the number of factors in approximate factor models. Econometrica 70(1):191–221
Bai J, Ng S (2004) A PANIC attack on unit roots and cointegration. Econometrica 72(4):1127–1177
Breitung J, Das S (2005) Panel unit root tests under cross-sectional dependence. Stat Neerl 59(4):414–433
Breitung J, Pesaran MH (2008) Unit roots and cointegration in panels. In: Matyas L, Sevestre P (eds) The econometrics of panel data: fundamentals and recent developments in theory and practice. Kluwer Academic Publishers, Dordrecht, pp 279–322
Breusch TS, Pagan AR (1980) The lagrange multiplier test and its application to model specifications in econometrics. Rev Econ Stud 47(1):239–253
Carrión-i-Silvestre JL, Del Barrio T, López-Bazo E (2005) Breaking the panels: an application to the GDP per capita. Econometrics J 8(2):159–175
Chang Y (2002) Nonlinear IV unit root tests in panels with cross-sectional dependency. J Econometrics 110(2):261–292
Choi I (2001) Unit root tests for panel data. J Int Money Finance 20(2):249–272
Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74(366):427–431
Garrido L, Toharia L (2004) What does it take to be (counted as) unemployed? the case of Spain. Labour Econ 11(4):507–523
Gengenbach C, Palm FC, Urbain JP (2010) Panel unit root tests in the presence of cross-sectional dependencies: comparisons and implications for modelling. Econometric Rev 29(2):111–145
Hadri K (2000) Testing for stationarity in heterogeneous panel data. Econometrics J 3(2):148–161
Maddala GS, Wu S (1999) A comparative study of unit root tests with panel data and a new simple test. Oxford Bull Econ Stat 61(s1):631–652
Moon HR, Perron B (2004) Testing for a unit root in panels with dynamic factors. J Econometrics 122(1):81–126
Moon HR, Perron B (2007) An empirical analysis of non-stationarity in a panel of interest rates with factors. J Appl Econometrics 22(2):383–400
Ng S, Perron P (1995) Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. J Am Stat Assoc 90(429):268-281
Pérez Infante JI (2006) Las Estadísticas del Mercado de Trabajo en España. Ministerio de Trabajo y Asuntos Sociales, Madrid
Pesaran MH (2004) General diagnostic tests for cross section dependence in panels. Institute for the Study of Labor (IZA), Discussion Paper No. 1240
Pesaran MH (2007) A simple panel unit root test in the presence of cross-section dependence. J Appl Econometrics 22(2):265–312
Romero-Ávila D, Usabiaga C (2008) On the persistence of Spanish unemployment rates. Empir Econ 35(1):77–99
Smith LV, Leybourne S, Kim T, Newbold P (2004) More powerful panel data unit root tests with an application to mean reversion in real exchange rates. J Appl Econometrics 19(2):147–170
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 The Author(s)
About this chapter
Cite this chapter
García-Cintado, A., Romero-Ávila, D., Usabiaga, C. (2014). PANIC Analysis of Spanish Regional Unemployment. In: Spanish Regional Unemployment. SpringerBriefs in Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-03686-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-03686-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03685-4
Online ISBN: 978-3-319-03686-1
eBook Packages: Business and EconomicsEconomics and Finance (R0)