*5.3. LL-Relations and the βE-Coefficient*

The following results apply to the five recessions during the period 1977 to 2010, but the COVID-19 recession in 2020 is an exception for all results. Figure 3d shows months where both EM leads GDP and the β<sup>E</sup> *coefficient* is less than 0.5, that is, less than the "neutral" slope of 1.0. This result support both our hypotheses. Hypothesis 1 (**H1**), that the EM leads GDP and EM decreases faster than GDP before and during a recession was supported. The NBER recessions come after sharp bends in the trajectories and away from optimal EM and GDP in Figure 3a (NBER recession dates are shown by red dots in Figure 3a–d). The leading relation for EM before a recession was also found by Hamilton (2018). Hypothesis 2, (**H2**), that GDP leads EM and β<sup>E</sup> (GDP/EM) decreases before and during an expansion, was also supported (Figure 2a,b). The COVID-19 recession in 2020 was, in contrast to the "classical economy overheating" recessions, initiated by the COVID-19 pandemic and caused at least partly by a supply side shock (Hobbs 2020).

#### *5.4. US Economy*

Jobless abatement measures: Hypothesis 3, (**H3)**, that we could infer macroeconomic conditions where leading or lagging relations between EM and GDP were significant, was not supported. Changes in LL relations were closely associated with recessions but distributed over the whole economy "map". However, the finding that the NBER recession dates come after a sharp bend in the trajectories describing the US economy in Figure 3 may offer some clues. Several studies suggest various factors that may explain variations in Okun's β coefficient, such as changes in working hours and labor productivity (Cazes et al. 2013; Elhorst and Emili 2022), nominal wages, (Donayre and Panovska 2021 Okun's beta and wages covary positively, p. 9), labor legislation, (Cazes et al. 2013) and a mismatch in job search (Mukoyama and Sahin 2009; Gimbel and Sinclair 2020). The selection of variables used to build the PCA plots was chosen primarily to construct and validate the score plot for the US economy. We were not able to extract reasonable information from the loading plot in Figure 3b that could be used to associate any of the variables with the "jobless recovery" issue.

### *5.5. Policy Implications*

Observations. First, the leading relations of EM → GDP before five of the six recessions and the leading relation of GDP → EM after recessions provided clear signatures to the Okun's βE(t) signature. Second, periods before recessions were associated with labor productivity that was less than optimal. Third, we found that months where both EM → GDP and Okun's βE(GDP,EM) were less than 0.5 were closely associated with the five recessions before 2010. The COVID-19 recession in 2020 was an exception. Fourth, months that are common for the two events (34 months) precisely identify recessions, and fifth, jobless recoveries were pronounced for all five recessions.

Interpretations. Since EM leads GDP before a recession, it suggests that hiring is made before business increases. This is supported by a decrease, or slowing down, in labor productivity. During economic recovery, hiring is slower, providing a background for the term "jobless recovery".

Diagnostics predictions and abatements. The 34 months where EM → GDP and β<sup>E</sup> < 0.5 matched the recessions, indicating that some of the months precede the recession. Thus, inspecting the two series: (i) LL relations between GDP and EM and (ii) Okun's law in the format β<sup>E</sup> = GDP/EM, may help us to predict a recession or support that a recession is real. However, the COVID-19 recession in 2020 provided an important exception to this "rule", perhaps due to the different nature of this atypical recession that was caused by a pandemic.

We could suggest two abatement measures for jobless recoveries. The first is that management should not hire workers during expansion periods that show a sign of a coming recessions. An assessment of the "natural" rise in labor productivity (the trend) is probably not easy to identify but examining labor productivity anomalies may still offer clues as to when new hirings should be made with care. The second measure is to implement legal procedures that make hiring and firing employees less easy. However, employment policy is a multicriteria question. The utility of being temporarily employed before a recession may be higher than the disutility of not being rehired for several months during a recession recovery (see, e.g., (Ball 2015)).

The results were not realized when EM was replaced by UE and real GDP by GDP. For a rationale, see Appendix A.

#### *5.6. Further Studies*

The present study addresses unemployment issues in terms of LL relations and OLR regressions between GDP/EM and time. Our results refer to the US economy, but a comparison with other countries along the same lines would be interesting, for example, comparing Okun's βE(9) coefficient in the US with the corresponding βE(9) coefficients in

Germany and the Netherlands. Volatilities in employment are largest in the US (0.0389), lower in the Netherlands (0.0232) and the lowest in Germany (0.0115).

We found that UE both leads and lags GDP, which would complicate shifting one series relative to the others to identify LL relations for the whole series (Figure 2d). For example, Obst (2020) includes two quarter delays between GDP and UE in analyzing the relation between GDP and UE. Figure A1a in Appendix A shows that even within time windows where the LL relations are consistent, cycle periods and phase shifts vary.

We also compared the two graphs GDP vs. UE (left in Figure A1) and GDP and EM (right in Figure A1), and it is seen that the graph for GDP and UE shows the overall "traditional" inverse relation between GDP and UE, whereas the GDP and EM graph does not directly reflect that UE and EM should be inverse measures of the same phenomenon. However, a contributing factor may be that if unemployed persons drop out of the labor force, they are no longer counted as unemployed in the unemployment statistics (Elhorst and Emili 2022). Thus, replacing UE with EM in Okun's law appears to change the overall relation beyond the fact that the two variables EU and EM express inverse characteristics of labor participation. However, a discussion of these results is beyond the scope of the present study.

#### **6. Conclusions**

Loss of jobs is an important issue and optimum employment is among the three most important goals for the US federal reserve. Okun's law, as expressed by its β coefficient, is traditionally formulated by the ratio between GDP and the UE gap, and over the whole period of study or for decennial time scales. Inspired by the results of Hamilton (2018), we replaced the normal measure of unemployment (UE) with employment (EM) and calculated a βE(9) = real GDP/EM. We found that EM became a leading variable to GDP before a recession, whereas GDP became a leading variable to EM after a recession. The shifts in the leading relation between GDP and EM around a recession also create peaks in the βE(9) coefficient around most "classical" recessions (the 2020 recession caused by the COVID-19 pandemic was an exception). All the recessions were also characterized by a decrease in labor productivity relative to an "optimal" but realized 1997–2010 value. Our findings of the leading role of EM to GDP before a recession and the loss in labor productivity suggest that hiring employees during periods with a heated economy may cause subsequent jobless recovery. To alleviate jobless recoveries, one should make hiring decisions with caution when there is a sign of a coming decision or labor productivity anomalies.

**Author Contributions:** Conceptualization, K.L.S., Methodology, K.L.S.; software, K.L.S.; validation K.L.S. and D.Z., Formal analysis, K.L.S. and D.Z., Investigation, K.L.S. and D.Z.; Resources, K.L.S. and D.Z.; Data curation, K.L.S. and D.Z.; Writing original draft, K.L.S. Review and Editing D.Z.; Visualization, K.L.S., Supervision, K.L.S. and D.Z.; Project administration, K.L.S. and D.Z.; calculations, K.L.S. and D.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Oslo Metropolitan University.

**Data Availability Statement:** All data and all calculations are available from the author.

**Conflicts of Interest:** The author declare no conflict of interest.

#### **Appendix A**

The appendix contains: Comparing rGDP to EM and UE.

#### *Comparing rGDP to EM and UE*

The EM were significantly shifted 1.6 time steps backward relative to rGDP in 16\*% of the time, and EM was significantly shifted forward 1.7 time steps relative to rGDP 33 % of the time.

**Figure A1.** GDP and unemployment. (**a**) time series in bold shows part of the series where UE leads GDP. Distance between the two first peaks (red and blue dropdown lines) are 86 months and distance between the two next peaks are 47 months. (**b**) GDP versus UE and GDP versus EM. Green circles show NBER recessions.

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