Testing hysteresis for the US and UK involuntary part-time employment

ABSTRACT

In this paper, we test the persistence of involuntary part-time employment, making use of large historical series for the US and UK. We adopted a comprehensive macro-econometric approach, based on a battery of panel and time series unit root and stationarity tests, also allowing for flexible specifications as fractional integration and structural breaks in the series. For both countries, our results provide robust evidence on the existence of a long memory process and a structural break in the mean of the series in The Great Recession surroundings. Importantly, these findings suggest that relevant shocks affecting labour market outcomes (e.g. The Great Recession) are likely to have long-lasting structural effects on underemployment shares. Fortunately, this result also leaves room for designing effective labour market policies to counteract structural underemployment in the long-run. Finally, the micro-economic roots of this aggregate behaviour claim for further investigation.

KEYWORDS:

• Involuntary part-time
• underemployment
• long-memory
• hysteresis
• persistence
• structural breaks

JEL CLASSIFICATION:

• J21
• E24
• C22

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ This term is often used to refer to any employment status that, in contrast to unemployment, involves working, albeit not at a full capacity. This implies that an unmet need or, in other words, an unsatisfied demand of work (e.g. mismatch in qualification, skills, hours of work, etc.). Throughout this document, it will be used interchangeably with ‘involuntary part-time’.

² In this article, we adopt the most common approach in empirical studies consisting of linking hysteresis to the presence of a unit root in a variable, as discussed by Røed (1997). However, we cannot overlook other approaches. An alternative approach, introduced by Jaeger and Parkinson (1994), sets a higher standard for hysteresis. According to this approach, hysteresis occurs when cyclical changes impact the natural rate of a variable, even if the natural rate follows a unit root process. In such cases, temporary shocks can have lasting effects, and the business cycle remains interconnected with the natural rate. This implies that a unit root is a necessary but not a sufficient condition for hysteresis.

³ The whole robustness section methodology will be explained in deeper detail in the appendix of the article.

⁴ Any endogenous ADF-type test requires a trimming procedure, aimed at creating a regression window to estimate recursively the test equation including each possible break-date from the start to the end of the window. Much has been said on such topic, but following Banerjee et al. (1992), Andrews (1993), Perron and Vogelsang (1992a) and Perron and Vogelsang (1992b), we decided to set the trimming window to $\lambda =[0.15,0.85]$. This appears to be, according to the very first authors, a convenient choice that would account for both the necessity of keeping the regressions minimum length high enough to affirm a Gaussian approximation of the estimates and to possibly capture break points even at an early or late stage of the time series.

⁵ Endogenous tests have gone a long way in the past years. Some extensions to the aforementioned Perron and Vogelsang (1992a) tests are well represented by the two shift in mean test by Clemente et al. (1998) and, most recently, by the Lagrangean Multiplier test of Lee and Strazicich (2003). In recent years, a relatively innovative test by Narayan and Popp (2010) has been built based on maximizing the statistical significance of the break-point rather than the absolute value of the t-statistic for the break-date. All such tests offer a significant contribution in terms of statistical improvement of the analysis but are not free from the data mining critique, where break over-parametrization leads to over-fitting of the model.

⁶ When the Schwarz-Bayesian and Hann-Quinn criteria are employed for lag selection, regardless of any deterministic specification. When the far less conservative Akaike criteria is employed, the null is unrejected for the non-trending test and strongly rejected when a trend is nested in the test equation. Judging by the time pattern of the series in its level and differences, the most realistic test model equation should contain an intercept only (although accounting for it does not generally change the results). The slightly offsetting result of the test for the LLC test with the over-parameterized suggestion made by the AIC however, would tell us that, even if cross-sectional spillover has been accounted for, some additional investigation at the national level would be needed. All tests contain contemporaneous cross-sectional averages as added regressors. We also attempted a top-down t-test procedure, and it can be made available upon request.

⁷ A Bartlett Kernel with 11 lags, given by Schwert maximum length criteria, was also tested. Results for such specification allowed us to not reject the I(1 or 0) null in the first differences specification and reject the I(0) null in levels.

⁸ Further test specifications are mentioned below these tables and detailed in the methodology section.

⁹ https://www.nber.org/research/data/us-business-cycle-expansions-and-contractions.

¹⁰ https://www.ons.gov.uk/economy/grossdomesticproductgdp/methodologies/communicatingtheukeconomiccycle.

¹¹ Details on the following procedures and an explanation on why it is convenient to use them in our context will be shown in the appendix..

¹² Some weak rejection of the homogeneous null was found at 10% in the level series for IPT, but following the Dickey and Pantula (1987) algorithm, such result can obviously be ignored.

¹³ Although, we might say, rather unnecessarily given our application.

¹⁴ One example would be the demeaning procedure of each variable under study.

¹⁵ Given the nature and the shape of our data, we shall focus on model 3 from the authors, including only mean shifts.

Additional information

Funding

The authors acknowledge funding from the Spanish Ministry of Science, Innovation and Universities (Ministerio de Ciencia, Innovaci on y Universidades) under grant PID2020-115183RB-C22, the Spanish Ministry of Economy, Industry and Competitiveness (Ministerio de Econom a, Industria y Competitividad) and the Regional Government of Andalusia (Junta de Andaluc a) through Research Group SEJ-487 (Spanish Entrepreneurship Research Group { SERG), and from Research and Transfer Policy Strategy (Estrategia de Pol tica de Investigaci on y Transferencia, UHU).