*A Literature and Hypotheses*

Various attributes of Okun's law have been studied extensively in the literature and summaries have been made, for example in Donayre and Panovska (2021) and Obst (2020). Here, we simply summarize attributes assigned to Okun's law with respect to regional differences and differences across business cycle regimes. The latter studies relate to regime shifts, recession and shocks that are identified in the cycles.

Maza (2022) found regional differences across Europe in Okun's law, defined as β = (βUE − ΔUE − α − μ)/ΔGDP, α constant, μ error term. The β-values were clustered geographically and with high values in, e.g., Germany. However, Elhorst and Emili (2022) show for the Netherlands that there are spillover effects among regions, thus a finer spatial solution than nations may be helpful to understand the relation between output and unemployment.

Across business cycles for the US economy from 1949 to 2020, Donayre and Panovska (2021) identify three regimes and thus two structural breaks, and they show that there is an increase (steepening) of Okun's β across expansions, mild recessions, and deep recessions. That is, GDP changes relatively more than the UE during a deep recession than during an expansion. In contrast, Søgner (2001) found no structural breaks in the Austrian economy from 1977 to 1995 and concludes that there is a stable Okun's β coefficient across time in Austria. Ziegenbein (2021) studies the effects of six types of macroeconomic shocks on Okun's β and found that shock type, e.g., financial shocks and government spending shocks, affect both the reaction time and the duration (0 to 20 quarters) of changes in the Okun's β, away from its "neutral" value (zero in Ziegenbein (2021)). A major conclusion is that while GDP and employment declined with similar speed during a recession, output recovered faster than employment, thus giving rise to the term "jobless recovery".

Several studies also offer explanations for the "jobless recoveries", and the mechanisms that could explain jobless recoveries can be divided into six categories: (i) Demographic traits. For example, Maza (2022) found that, across all regions in Europe, the β coefficient significantly depended on the participation of women and youth in the workforce and the industry's contribution to GDP. (ii) Legal factors were found by Maza (2022) to contribute only when the UK was exempted from the sample. However, Vaubel (2008) shows that legislative acts related to social provisions increased in the EU from 1970 to 2003. Cazes et al. (2013) suggests that whereas Okun's β increased sharply in the US, Canada, Spain, and other economies that were severely affected by the Great Recession in 2008, in

countries such as Germany and the Netherlands, with strong (legislative) employment protection, it did not. However, Mukoyama and Sahin (2009) quote studies that show the ratio of benefit claims to total UE in the US has declined over the post-war era, and thus employment protection in terms of unemployment compensation may not play a prominent role for explaining jobless recovery in the US. (iii) Worker behavior may play a role in several respects. With references to Yellen (1991) Mukoyama and Sahin (2009) propose that unemployment may be caused by the unemployed searching for good, rent-paying jobs rather than working at the poor jobs following a recession. Capsada-Munsech and Valiente (2020) examine variations in employee willingness to participate in vocational education and training (VET) and thus to obtain skills that meet demand. Elhorst and Emili (2022) suggest that employed persons may work shorter hours. (iv) Employer behavior will interact with employee behavior. For example, firms in Germany and Austria support more vocational training than southern European countries (Capsada-Munsech and Valiente 2020, p. 171). (v) The mismatch between human resources available and human resources required was studied by Lazear and Spletzer (2012). However, they show that unemployment was a cyclic phenomenon during the 2007–2009 recession rather than due to a mismatch between labor requirements and labor supply. Gimbel and Sinclair (2020), studying the period 2014 to 2019, suggest that a mismatch that may have been an issue around 2014 declined after the Great Recession. However, since Okun's β changes with the development of the GDP, e.g., expansions and recessions, the average β<sup>E</sup> coefficient will also depend on the economic policy, management, and probably luck, in the region studied. (iv) For the present study, we do not believe that the underground economy will have a great influence on employment and its recovery after a recession, but it may be important in countries with a large and established underground economy.

We develop three hypotheses that all relate to US recessions. The first hypothesis, H1, is that employment leads GDP (EM → GDP), and if employment is decreasing faster than GDP before a recession, β(GDP, EM) will tend to increase ↑ (Abel et al. (1998, p. 658 on x/y relations). The rationale for the hypothesis is the results shown by Hamilton (2018) that employment was leading GDP before recession. Our second hypothesis, H2, is that GDP leads employment (GDP → EM), and βE(GDP, EM) decreases↓ after a recession and during an expansion. The rationale is that Cazes et al. (2013, p. 6) show that for many countries, unemployment is likely to rise (and employment to decrease (our interpretation)) during a recession. However, if employment decreases less rapidly than GDP, β<sup>E</sup> (GDP/EM) will tend to increase. Our third hypothesis, H3, is that by embedding the lead-lag results in a "map" of US macroeconomy, we will obtain clues as to which macroeconomic variables determine the LL relations between GDP and EM. The rationale is that Seip et al. (2019), by using the "map" method, found macroeconomic conditions for why leading indexes failed to predict industrial production in Germany.

The rest of the article is organized as follows. In Section 2, we present the data we used, and in Section 3, we outline the methods used with emphasis on the relatively novel LL method. In Section 4, we present the results from the application of the high-resolution LL method and, as far as we know, a novel application of Okun's law to GDP, EM, and UE. The results are discussed in Section 5, and Section 6 summarizes and concludes.

#### **2. Data**

All the following data are retrieved from the St. Louis Federal Reserve database between 14 June 2022 and 10 July 2022. We use two sets of data. The first set is US employment rate, EP, US unemployment rate (UE) and real gross domestic product (GDP). The other set is used to draw a "map" of the US economy. We emphasize variables that may have implications for the interpretation of Okun's law and we include time series that could allow us to examine causal mechanisms for "jobless recovery".

Okun's law data. UE represents the number of unemployed as a percentage of the nonfarm labor force. EM is the number of employed in thousand persons. Real GDP is measured in billions of chained 2012 dollars.

US economy data. The strings of letters following the acronyms we use are the identification code used by St. Louis Fed. We have chosen twelve macroeconomic variables. In addition to real GDP, we chose industrial production (IP); working hours (WH)— HOANBS; inflation (INF) represented by the consumer price index (CPI)-CPI; US government expenditures (EXP)—W068RCQ27SBEA; federal government tax receipts (TRE)— W006RC1Q027SBEA; federal government: current expenditures (CE)—FGEXPND; federal debt as total public debt (PD)—GFDEBTN; federal funds rate (FF); and monetary supply (M2). Data for labor productivity (LP)—OPHNFB is an index for output per hour and were used to compare productivity during recession phases. Data for union affiliation as percentage of employed were only available from 2011 to 2021 and ranged from 10.3 to 11.8% (https://data.bls.gov/cgi-bin/surveymost) accessed on 15 August 2022, and were therefore not used. For wage spread, we used the Gini index, which is only sporadically available for the US before 1991. A high index value suggests a high degree of inequality. Mukoyama and Sahin (2009, p. 203) show a curve for the 90–10% residual wage inequality from 1970 to 2002, and we extended the Gini index to the time window 1977 to 2022 based on the author's figure. We use the recession dating from NBER, and characteristics for the recessions are shown in Table 1.

**Table 1.** Recessions in USA, 1977 to 2022. Beginning, end and duration are NBER data. GDP decline, labor productivity, jobless depth and jobless duration is measured as the anomaly from the linear detrended series.


Number of months EM leads GDP during one years before a NBER recession. Peak value relative to a detrended βE. Deviation from linear trend. Months to pre-recession values. Employment does not recover to pre-recession values before next recession. Duration is the time between the two recessions.
