Decoding unemployment persistence: an econometric framework for identifying and comparing the sources of persistence with an application to UK macrodata

As Røed (1997) notes, before Blanchard and Summers (1986) the idea of hysteresis already existed in economics. In fact Phelps (1972) used the term hysteresis. However, it was with their seminal paper that this concept came to the fore of labor market economics. In their (widely used) terminology “hysteresis” describes a very high (but not complete) dependence on the past, i.e., when the sum of auto-regressive coefficients is close but not necessarily equal to 1 (Blanchard and Summers 1986, Footnote 1). As has later been argued a better term for this is persistence (see, e.g., Franz 1990). However, in an empirical analytical context this often implies a failure to reject an exact unit root in the unemployment rate (i.e., the hypothesis that the sum is exactly equal to one). Therefore, this is often referred to as unit root hysteresis (see, e.g., Arestis and Sawyer 2009; Papell et al. 2000; Meng et al. 2017). This is to be distinguished from what has become known as genuine hysteresis (see, e.g., Amable et al. 1994; Göcke 2002). In this terminology, the present research relates only to (multivariate) unit root hysteresis and does not concern genuine hysteresis. I will clarify further on the use of concepts below.

The persistence or “unit root hysteresis” (see Footnote 1 and further below) of the UK unemployment rate has been studied extensively (see, e.g., the references in the surveys in Røed 1997; Gustavsson and Österholm 2009; Arestis and Sawyer 2009 and more recently Furuoka 2017a; Meng et al. 2017). It appears that overall the evidence in favor of “unit root hysteresis” remains mixed. Both the choice of methods and sample seem to influence on the conclusions.

Additional important differences relative to Jacobson et al. (1997) are that their analysis is based on a partial VAR and a so-called Common-Trends approach. Moreover, in their model, equilibrium unemployment depends on unobserved variables, whereas here all variables are observable.

Note that, this “cointegration approximation” in general also provides a means of robustifying the statistical inference (see Johansen 2006; Hoover et al. 2008).

See, e.g., Blanchard (2006).

See, e.g., the surveys in Røed (1997), Gustavsson and Österholm (2009), Arestis and Sawyer (2009) and more recently Furuoka (2017a) and Meng et al. (2017).

See the survey in Røed’s paper from 1997 and for more recent examples, García-Cintado et al. (2015) and Caporale et al. (2016).

In addition, the matter is even further complicated in a multivariate context, since when a unit root is rejected, this need not be inconsistent with hypotheses of slow adjustment: For example, in open economies, other stabilizing mechanisms, such as real wage resistance, may be present and may dominate the destabilization caused by persistence generating mechanisms (see, e.g., Carlin and Soskice 2006).

All results generalize straightforwardly with more lags.

An example, for which this approximation is also derived explicitly, forms a theoretical model (as below), see Møller and Sharp (2013) or Klemp and Møller (2015).

Recalling that the remaining roots obey \(\left| z\right| >1.\)

For example, often I(2) seems to be a useful statistical approximation for time series of nominal prices and wages whose time plots are very smooth or slowly changing.

In these remaining cases it is thus the roots of \(P_{1}(z)\) that are approximated by \(z=1\) and parameter restrictions ensure that \(x_{1t}^{c}\) obeys I(1) or I(2), for the second and third column of the table, respectively, etc. (see Møller 2013).

For this period the assumption of constant long-run parameters was supported by the recursively estimated log-likelihood maximum in the R-form (see, e.g., Juselius 2006). Both forward recursive estimation (to assess constancy from the middle to the end of the sample) and backward recursive estimation (to assess constancy from the beginning to the middle of the sample) were performed. The recursive estimation results can be obtained upon request. Finally, only two dummy variables were needed: an unrestricted impulse dummy (being equal to 1 in 1999:01 and zero otherwise) and a transitory dummy variable being 1 in 2001:01 and − 1 in 2001:02 and zero otherwise. Note that an unrestricted impulse takes account of a break/level shift in the variables that nevertheless cancels in the cointegration relations.

Note that, as already pointed out in Blanchard and Summers (1986) persistence is not only associated with recessions and depressions, but also seems to characterize “normal times.” Hence, it still seems reasonable to analyze the persistence phenomena based on a sample that excludes the crisis.

For this type of model, the latter is not unique and is often referred to as a medium-run and not a long-run equilibrium. A “true” unique long-run equilibrium (steady state) would additionally entail a constant net-foreign asset-to-income ratio to ensure external balance (see Carlin and Soskice 1990; Layard et al. 2005; Carlin and Soskice 2006; Groth 2009). However, to keep this analysis simple this is disregarded here.

See for example Blanchard (2000).

An alternative approach to modeling the wage-unemployment dynamics could be to assume the presence of a threshold for (absolute) unemployment changes below which wages do not react at all. Only when unemployment changes exceed this threshold, sufficient wage pressure will occur and wages begin to react. In the present context such an extension could built on threshold cointegration (see, e.g., Balke and Fomby 1997), with non-stationarity implied by, \(\omega _{3}+\omega _{4}=0\), but only within a band (below the threshold). However, such an analysis is beyond the scope of this study and is thus better left as a separate analysis for future research. Nevertheless, I am still grateful to an anonymous referee for pointing this out.

All estimation is based on PcGive, OxMetrics 6.10 and CATS in RATS (see Doornik and Hendry 1998; Doornik 2010; Dennis et al. 2006, respectively).

This particular condition is analyzed in detail in Møller (2013).

See Johansen (1996), on normalization in general. Here, the normalization of the cointegrating matrix has simply been chosen for computational ease.

See the discussion in Juselius (2006).

This is standard practice in the reduced rank regression method (see Johansen 1996).

This is generally not the case (see Johansen 2005; Lütkepohl 2005).

The zero restrictions, which were exclusively motivated by insignificance, contributed to simplifying the estimated \(\beta _{c}\) matrix considerably.

See, e.g., Røed (1997), Andersen (2010), O’Shaughnessy (2011), Delong and Summers (2012), Blanchard et al. (2015) and Meng et al. (2017).

See the discussion and references in Footnote 16.