**1. Introduction**

Economic recessions are events that seriously affect employment and output. Since the early 1990s, recoveries from recessions in the United States were followed by persistently weak employment growth (Galí et al. 2012). Policymakers and economists refer to this phenomenon as jobless recovery and it remains a puzzle to experts. In this article, we examine if there are behavioral traits among employers or employees that have the potential to be managed so that some of the detrimental effects of recessions can be abated. We do this by examining the employment and output in the context of Okun's law.

Okun's law depicts an empirically observed relation between the gross domestic product (GDP) and unemployment (UE), which is specified as:

$$\frac{\left(\overline{\text{GDP}} - \text{GDP}\right)}{\overline{\text{GDP}}} = \beta \left(\text{UE} - \text{UE}\right) \tag{1}$$

where GDP − GDP is the output, GDP, gap and UE − UE is the unemployment (UE) gap. In short, β = GDP gap/UE gap. The β is Okun's coefficient or Okun's elasticity coefficient.

Recently, Hamilton (2018, p. 838) showed that the cyclical component of employment (EM) started to decline significantly before the NBER business cycle peak for essentially every recession. Thus, lead-lag (LL) relations and LL (GDP, EM) show that EM is leading

**Citation:** Seip, Knut Lehre, and Dan Zhang. 2022. A High-Resolution Lead-Lag Analysis of US GDP, Employment, and Unemployment 1977–2021: Okun's Law and the Puzzle of Jobless Recovery. *Economies* 10: 260. https://doi.org/10.3390/ economies10100260

Academic Editors: Ralf Fendel, Robert Czudaj and Sajid Anwar

Received: 7 September 2022 Accepted: 12 October 2022 Published: 20 October 2022

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GDP before a recession. Inspired by Hamilton (2018)'s results, we study GDP versus EM and examine the relation β<sup>E</sup> = GDP/EM and its relation to jobless recovery following a recession. Both EM and UE are often included in forecasting algorithms for GDP (Camacho and Perez-Quiros 2010; Hamilton 2018) and thus their detailed behavior is an important issue in applied economics. Our findings provide insights into the relationship between GDP and employment as well as jobless recovery.

For four recessions, we found that employment is a leading variable of GDP, and labor productivity decreases or levels off relative to its potential growth. The leading role of employment ceases after the recessions, and the change in LL relations causes spikes in β<sup>E</sup> = GDP/EM. There are 34 months out of 547 where EM leads GDP and β<sup>E</sup> shows peaks at the same time, and these 34 months partly precede and partly follow the beginning of the NBER recessions, except the last COVID-19 recession in 2020.

The present study differs from other studies in that we examine (i) the ordinary linear regression (OLR) β coefficients for GDP/UE and GDP/EM over running time windows (9 months) and we study (ii) the LL relations between GDP, EM, and UE over very short time horizons (9 months). Most other studies restrict their study to GDP and UE, and they use longer time windows, e.g., decades, (Cazes et al. 2013; Donayre and Panovska 2021). We also calculate labor productivity with a running time window of 9 months, and lastly, we embed the LL results in a principal component analysis (PCA) "map" of the US economy to place the LL results into a wider context.
