Unboxing Okun's relation between economic growth and unemployment rate: Evidence from the United States, 1948-2024

Peláez-Herreros, Óscar Article Unboxing Okun's relation between economic growth and unemployment rate: Evidence from the United States, 1948-2024 Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Peláez-Herreros, Óscar (2025) : Unboxing Okun's relation between economic growth and unemployment rate: Evidence from the United States, 1948-2024, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 3, pp. 1-21, https://doi.org/10.3390/economies13030059 This Version is available at: https://hdl.handle.net/10419/329339 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Academic Editor: Adolfo Maza Received: 13 January 2025 Revised: 10 February 2025 Accepted: 12 February 2025 Published: 20 February 2025 Citation: Peláez-Herreros, Ó. (2025). Unboxing Okun’s Relation Between Economic Growth and Unemployment Rate: Evidence from the United States, 1948–2024. Economies,13(3), 59. https://doi.org/10.3390/ economies13030059 Copyright: © 2025 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Unboxing Okun’s Relation Between Economic Growth and Unemployment Rate: Evidence from the United States, 1948–2024 Óscar Peláez-Herreros Department of Economics, El Colegio de la Frontera Norte, Tijuana 22560, Baja California, Mexico; [email protected] Abstract: We develop the first disaggregation of Okun’s law that quantifies all of the information that is subsumed within its coefficients. The proposed method decomposes the coefficients into the sum of the direct effect of the change in output upon the unemployment rate, plus the indirect effects of the variations in the output per hour worked, the hours worked per employed person, the participation rate, and the size of the working-age population. With quarterly data for the United States from 1948 to 2024, we found that the value of the intercept in Okun’s relation is determined by the increases in working-age population and output per hour of work, along with the decrease in the number of hours worked per employed person, plus the growth of the participation rate until the 1990s and its subsequent decline. For its part, the slope, that is, the value of Okun’s coefficient, depends mainly upon the variations in output per hour of work and the hours per employed person. The other factors were scarcely relevant. Changes in these components caused the Okun’s relation to vary over time, showing a greater sensitivity of the unemployment rate to variations in production since the 2008 crisis. Keywords: Okun’s law; factor decomposition; unemployment rate; labor productivity; hours worked; participation rate; working age population 1. Introduction Early in the 1960s, Arthur Okun described the relation between unemployment and economic growth as simply as possible. His purpose was, indeed, to provide a “simple and direct” formula (Okun,1962, p. 2). The result, which he obtained by examining quarterly data from the United States for the years 1947–1960, was that “on the average, each extra percentage point in the unemployment rate above four percent has been associated with about a three percent decrement in real GNP [gross national product]” (Okun,1962, p. 2). Thirlwall (1969) soon gave the name “Okun’s law” to this relationship of interchange of three percent of real GNP for each additional percentage point in the unemployment rate. Gordon (1984, p. 539) argues that Okun’s law owes its popularity both to the stability of that relationship during the space of two decades, and to the fact that “it short–circuits the rather complex identity that links output and unemployment”. Similarly, Anderton et al. (2014, p. 6) noted that the “elegance and simplicity” of Okun’s approach is an important reason why Okun’s law is still a recurrent theme half a century after its first formulation. In recent years, several authors have discussed the precision and temporal stability of Okun’s rule of thumb. For example, Ball et al. (2017, p. 1439) conclude that Okun’s law “is strong and stable by the standards of macroeconomics”. Similarly, Daly et al. (2017, p. 18) advise us that in the United States, “the Okun coefficient is relatively stable over time”. However, Huang and Lin (2008) observe that a fixed coefficient may be inappropriate, Economies 2025,13, 59 https://doi.org/10.3390/economies13030059 Economies 2025,13, 59 2 of 21 and Grant (2018) finds that the coefficient changed after the 1980s. Other authors who have examined the temporal stability of Okun’s law include Aguiar-Conraria et al. (2020), Karlsson and Österholm (2020), and Krüger and Neugart (2021). Also, some analyses of Okun’s law compare various countries (Furceri et al.,2020;Fontanari et al.,2022;PorrasArena & Martín-Román,2023) or regions (Guisinger et al.,2018;Maza,2022;Porras-Arena et al.,2024). In addition, the variation in Okun’s coefficient has been analyzed according to the phase of the economic cycle (Nebot et al.,2019;Benos & Stavrakoudis,2022;Donayre, 2022) and the type of shock that produced each economic crisis (Anderton et al.,2014; Gelfer,2020;Ziegenbein,2021). In general, such investigations of Okun’s law have modified it by including additional or lagged variables, or by using other functional forms and techniques for estimation. These modifications were attempts to improve fits to the cases that were studied, but have moved away from the essence of Okun’s problem and do not take advantage of information that is contained in Okun’s original formulation. To understand this point, please recall that Okun (1962) described the relation between the unemployment rate and increase in production via “reduced form” equations (Mairesse,1984). Okun was aware that other factors affect this relation, but assumed that the unemployment rate is a satisfactory proxy for them. In the last pages of his 1962 article, Okun attempted to separate the effects of each factor, but described only their influence, in hopes that future advances in analytical techniques and availability of data would allow a more systematic study. Along those lines, later authors (e.g., Hamada & Kurosaka,1984; Sögner & Stiassny,2002;Ismihan,2016) attempted to disaggregate Okun’s coefficients into structural parameters that complete the output–unemployment relation. However, the results were only approximate. The principal contribution of the present article is the development of a procedure that disaggregates the slope and intercept of Okun’s law into an exact sum of the direct effect of variations in production upon the unemployment rate, and the indirect effects of variations in output per hour worked, hours worked per employed person, participation rate, and working-age population. This procedure recovers the information that is implicit in Okun’s equation and quantifies the contribution of each factor to the value of Okun’s coefficients. The present article will limit itself to the case of the United States during 1948–2024. However, the proposed disaggregation enables investigators to study how each factor’s contribution varies with time, as well as among countries and regions. This markedly enriches the possibilities for performing systematic multivariate analyses based on Okun’s law. An initial and much shorter version of this article, published as a letter (PeláezHerreros,2025), only decomposes the slope of the Okun relationship from a different conceptual basis. That earlier version does not analyze the intercept, nor the inverse relationship, nor does it use quarterly data or rolling regressions; it only divides the period 1970–2021 into two subperiods and notes that there are differences between them, but it does not analyze the evolution of the parameters over time, which will be performed in the following pages. The causes of geographic and temporal variations in Okun’s coefficients have been analyzed previously by authors such as Blackley (1991), Herwartz and Niebuhr (2011), and Kraim et al. (2023). These authors used a two-step analysis. First, they estimated Okun’s coefficients for the time periods, countries, or regions that were being compared. Then, the authors explained the differences via cross-sectional or panel data regression models. They included regressor variables such as the industrial structure (Gonzalez-Prieto et al.,2018), the percentage of public employment (Binet & Facchini,2013;Furceri et al.,2020), or the percentage of women and youths in the employed population (Maza,2022), among other variables that can affect the Okun’s coefficient. Economies 2025,13, 59 3 of 21 Those earlier investigations analyzed a wide range of secondary variables. Here, we analyze only those which, by definition, generate the value of the coefficients in Okun’s law. Our objective is to estimate the Okun’s law coefficients for the United States during distinct time periods, so that we can determine not only whether the values of these coefficients are stable over time, but also identify, precisely, which intrinsic factors give rise to those values and associated dynamics. Our analyses include data from quarters that fall within the period of the COVID-19 pandemic, so that we may examine whether the associated variation in production affected the employment rate differently during that time, as has been indicated by Barisic and Kovac (2022), and Porras-Arena et al. (2024). The hypothesis is that the intensity and composition of the relation between economic growth and unemployment rate changed over time. The proposed method allows us to detect and analyze the intrinsic causes of these changes. The structure of this article is as follows. Section 2reviews Okun’s approach, including its bases and implications. Section 3develops the procedure for decomposing the Okun’s law coefficients into their intrinsic factors. Section 4shows the results of analyses for the United States, after which Section 5presents conclusions. 2. The Essence of Okun’s Proposal Okun (1962, p. 1) sought to answer the question, “How much output can the economy produce under conditions of full employment?” To that end, he analyzed the relation between variations in production and unemployment. Although Okun recognized that other factors affect this relation, for simplicity, he assumed the following: whatever the influence of slack economic activity on average hours, labor force participation, and manhour productivity, the magnitudes of all these effects are related to the unemployment rate. With this assumption, the unemployment rate can be viewed as a proxy variable for all the ways in which output is affected by idle resources. (Okun,1962, p. 2) This simplification allowed Okun to model the relation between the two principal variables (production and unemployment) as follows: ∆Ut=α0+α1yt+ε0(1) where U t is the unemployment rate for the year t, and Y t is the real gross domestic product (GDP). 1 Thus, ∆ U t =U t− U t−1 is the change in unemployment rate between t − 1 and t, and y t = ∆ Y t /Y t−1 is the percentage change in real GDP. The symbols α0 and α1 are model parameters, and ε0is the error term. Okun (1962) estimated that for 55 quarterly variations from 1947 to 1960, α0 = 0.30 and α1 = − 0.30, with a correlation of r= 0.79. Okun confirmed these results by analyzing the same data according to two other models. Okun’s second model explained the unemployment rate by means of a constant term (which represents the natural unemployment rate) and the gap between observed and potential output. Okun (1962) found that the constant term was equal to 3.72, and the slope of the model was 0.36. The latter value indicated that an increase of 1% in the difference between the real and potential output is associated with an increase of 0.36 points in the unemployment rate. Ball et al. (2017) explain that this second model is more general than the first. When the natural unemployment rate is constant and the potential output grows at a constant rate, this second model expressed in differences yields Equation (1). Therefore, Equation (1) assumes the constancy of these elements. The third model related the logarithm of the employment rate to the logarithm of output, a time trend, and a constant. Okun (1962, p. 3) found that, depending upon the Economies 2025,13, 59 4 of 21 selected time period, “the estimated elasticity coefficient ran 0.35 to 0.40, suggesting that each one percentage point reduction in unemployment means slightly less than a 3 percent increment in output”. As Okun (1962, p. 3) notes, “The uniformity that emerged from these various techniques was the approximate 3–to–1 link between output and the unemployment rate”. This three-to-one ratio (Okun’s law) had a great impact upon national politics and economics because it showed that the link between the growth in production and decrease in unemployment was stronger than was commonly accepted. Okun (1962, p. 5) explains that “the simple addition of one percent of a given labor force to the ranks of the employed would increase employment by only slightly more than one percent: 100/100–Upercent to be exact. If the workweek and productivity were unchanged, the increment to output would be only that one + percent. The three percent result implies that considerable output gains in a period of rising utilization rates stem from some or all of the following: induced increases in the size of the labor force; longer average weekly hours; and greater productivity”. Okun cautions that the coefficients of approximately one-third that derive from his models do not reflect a ceteris paribus relation between changes in output and the unemployment rate. The ceteris paribus Okun coefficient for an unemployment rate of (for example) 6% would be approximately (1 + 0.06) −1 = 0.94. As Okun was aware, his coefficients capture not only this direct effect, but also the indirect effects of other variables that do not appear explicitly in his model, but do affect ∆ Uthrough their correlations with y. The value of Okun’s coefficient, α1 , indicates the amount by which ∆ Uwill change for each unit change in y, when all of the implicit variables co-evolve as they did, on the average, during the period analyzed. In contrast, α1 will change, and cease to be stable, if the correlations between the implicit variables and ychange; for example, if the decrease in production that occurs during one recession is due more to the reduction in hours worked, than was the case during other recessions.2 The technique that will be developed in the next section allows an analysis of the changes in the values and content of Okun’s coefficients. 3. Analysis Techniques and Data Sources Okun proposed Equation (1) in order to summarize as simply as possible the relation between changes in output and the unemployment rate. For that reason, Okun omitted some variables that affect that relation. However, these variables are known. Okun himself mentions them, and Gordon (1973)—for example—has used them to define a complete relation between changes in output and the employment rate. Gordon’s most recent attempt along those lines (Gordon,2010a) decomposes the real GDP into the product of five factors: Yt≡Yt Ht ·Ht Et ·Et At ·At Nt ·Nt(2) where H t is the number of hours worked during the period t,E t is the number of workers, A t is the number of active persons (employed and unemployed), and N t is the working-age population. Each ratio has a specific interpretation: Y t /H t represents the output per hour worked (productivity), H t /E t is the number of hours worked per employed person, E t /A t is the proportion of workers in the active population (the employment rate), and At/Ntis the proportion of active persons in that population (the participation rate). Gordon (2010a) takes logarithms in Equation (2), proposes that the tendencies of the variables have the same structural decomposition as the observed values, and analyzes the responses of the components to variations in the output gap. However, Gordon (2010a) Economies 2025,13, 59 5 of 21 does not directly link changes in output and the unemployment rate, as Okun (1962) had. Perhaps that is why few subsequent analyses have incorporated Gordon’s (2010a) methodological approach. Here, we will show how Equation (2) can indeed be transformed to relate ∆ Uto y, and to express Gordon’s identity in terms of Okun’s (1962) equations, thus allowing analysts to decompose the coefficients α0and α1. The transformation consists of several steps. First, the notation in Equation (2) is simplified by letting Y t /H t =X 2t ,H t /E t =X 3t , E t /A t =L t ,A t /N t =X 4t , and N t =X 5t . Then, we divide Equation (2) by itself, evaluated at t − 1. (For example, the left-hand side becomes Y t /Y t−1 ). After this, we take logarithms and replace the logarithm of each quotient by the percentage change in the corresponding variable. Rearranging terms, the result is written as follows: yt∼ =lt+ 5 ∑ j=2 xjt (3) where lower-case letters denote percentage changes. Equation (3) indicates that the percentage change in the real GDP (y) is approximately equal to the sum of the percentage changes in the employment rate (l), the output per hour worked (x 2 ), the hours worked per employed person (x 3 ), the participation rate (x 4 ), and the working-age population (x 5 ). This identity is not exact because the percentage changes have been approximated by logarithms. Because Equation (3) does not include the unemployment rate explicitly, the next step in the transformation is to recognize that the unemployment rate is the complement of the employment rate: U t = 1 − L t . Therefore, the relation between the variations of these two rates is ∆ U t = −∆ L t . Using this result, and recognizing that the percentage change in the employment rate is l t = ∆ L t /L t−1 , we see that l t = −∆ U t /L t−1 . Now, after substituting that expression in Equation (3) and solving for ∆Ut, we obtain the following: ∆Ut∼ =Lt−1 −yt+ 5 ∑ j=2 xjt!(4) Like Equation (1) (Okun’s first differences model), Equation (4) relates ∆ Uto ydirectly, but also relates ∆ Uto all of the other factors that affect that relation. If we include these other factors in Equation (1), we obtain a relation that is almost deterministic because Equation (4) is an approximate identity. Concretely, if we estimate the regression ∆Ut=β0+β1yt+ 5 ∑ j=2 βjxjt +ε1(5) we would expect that β0≈ 0, β1≈ − L t−1 , and βj≈ L t−1 , with R 2≈ 1. Thus, these parameters are practically predetermined. For that reason, Equation (5) provides little information. However, that information is important because it allows the analyst to estimate the parameters by ordinary least squares (OLS), thus avoiding the imprecision that arises in Ismihan’s (2016) decomposition of Okun’s coefficient.3 As the next step, we follow Johnston (1984, p. 260) to extract the information that is available via Equation (5). According to the properties of OLS estimators, the coefficients α0 and α1 in Equation (1) (a reduced-form relation between ∆ Uand y) are linked to the parameters in Equation (5) (an extended version) as follows: α0=β0+ 5 ∑ j=2 βjλj(6) Economies 2025,13, 59 6 of 21 α1=β1+ 5 ∑ j=2 βjγj(7) where β0 through β5 are the parameters in Equation (5), and λj and γj are the parameters of the auxiliary regressions: xjt =λj+γjyt+εj(8) The εjterms are error terms, and j= 2, . . ., 5.4 Kmenta (1997, p. 443) explains that these auxiliary regressions are not regression equations in the usual sense; instead, they are used as an artifice to facilitate interpretation. Ismihan (2016, p. 182) interprets these auxiliary parameters within the framework of Okun’s law, pointing out that γj “represent the effect of a one–percentage–point change in output growth on [x j ]”, while λj “represent the growth rate of [X j ] independent of the growth rate of output demand”. These effects are implicit in Okun’s reduced-form equation, as Gordon (1984) and Prachowny (1993) recognized. It should be pointed out that Gordon (1984) used similar auxiliary equations to explain the employment rate (rather than the unemployment rate) as a function of output. Daly et al. (2017), for their part, disaggregated Okun’s coefficient for the inverse relation by decomposing the covariance through the use of accounting identities. Kaufman (1988) decomposed the elasticity of the employment rate with respect to real production (i.e., the coefficient in Okun’s third model). And, from the perspective of production functions, Prachowny (1993) as well as Huang and Lin (2006,2008) disaggregated Okun’s coefficient, but did not specify completely the relationship between growth and unemployment. 5 Other partial disaggregations of Okun’s coefficient were derived by Favereau and Mouillart (1981), Hamada and Kurosaka (1984), and Sögner and Stiassny (2002). The most complete disaggregation was that of Ismihan (2016). Equations (6) and (7) completely disaggregate the intercept and slope of Equation (1). Specifically, Equation (7) decomposes the original Okun coefficient, α1, into the following: • The direct effect of yupon ∆ U. This effect is captured by the coefficient β1 , which is interpreted in ceteris paribus terms because it no longer includes other influences. • The indirect effect of other factors (not made explicit in Equation (1)) whose variations affect ∆Uvia y. These factors are as follows: #the output per hour of work, β2γ2; #the hours worked per employed person, β3γ3; #the participation rate, β4γ4; #and the working-age population, β5γ5. The decomposition of the intercept, α0 , is analogous to that for Okun’s coefficient: Equation (6) disaggregates the constant contribution of each factor to ∆U. Alternatively, the parameters in Equation (1) tend to be estimated via the inversion of causality. Okun (1962) estimated his equations with unemployment as the dependent variable, although he interpreted the reciprocals of the coefficients to explain the evolution of GDP as a function of unemployment. The detail is that Equation (1) is “a reduced–form relationship between two endogenous variables” (Ball et al.,2017, p. 1416), and the cause– effect relationship to be specified depends on the question to be answered. Therefore, it is also possible to write yt=α′ 0+α′ 1∆Ut+ε′ 0(9) In this case, the equation that includes all of the factors is yt=β′ 0+β′ 1∆Ut+ 5 ∑ j=2 β′ jxjt +ε′ 1(10) Economies 2025,13, 59 7 of 21 From Equation (4), it would be expected that the parameters in Equation (10) take the values β′0≈0, β′1≈ −1/Lt−1,β′j≈1, and R2≈1. The parameter β′1 indicates the percentage increase in production that occurs when the unemployment rate falls by one percentage point, ceteris paribus. This is because the value of L t−1 tends to be about 0.94, β′1≈ − 1.06, which is the figure posited by Okun (1962, p. 5): “slightly more than one percent: 100/100–Upercent to be exact [ . . . ] the increment to output would be only that 1 + percent”. Moreover, this case is not susceptible to the criticism that various authors (Plosser & Schwert,1979;Barreto & Howland,1993) directed at the way in which Okun (1962) interpreted the reciprocals of his estimations. Specifically, because β1β′1≈ 1 in the extended equations, the reciprocal of β1 effectively approaches β′1 . In contrast, 1/ α1=α′1 in Okun’s equations, because r 2= 1, as Okun himself noted in the “general discussion” of Perry (1971, p. 578). The relation between the coefficients in Equations (9) and (10) can be understood by following the same logic as was described earlier for Equations (1) and (5). The intercept and slope are disaggregated into the coefficient of the pure direct relation, plus the indirect effects of the variables that are not specified: α′ 0=β′ 0+ 5 ∑ j=2 β′ jλ′ j(11) α′ 1=β′ 1+ 5 ∑ j=2 β′ jγ′ j(12) The auxiliary regressions are as follows: xjt =λ′ j+γ′ j∆Ut+ε′ j(13) In this case, because β′0≈ 0 and β′j≈ 1, the α′0 and α′1 in Equations (11) and (12) can be approximated as α′ 0≈ 5 ∑ j=2 λ′ j(14) α′ 1≈β′ 1+ 5 ∑ j=2 γ′ j(15) Next, we apply the resulting equations to a data set that is basically the same as used by Gordon (2010b), but updated to include the latest available figures. Data for real GDP of the United States are from the Bureau of Economic Analysis (BEA,2024), and span the period from the first quarter of 1947 to the first quarter of 2024 (1947Q1–2024Q1). Values of H t ,E t ,A t and N t are from the Bureau of Labor Statistics (BLS,2024) for the period 1948Q1 to 2024Q1. 6 This data set limits the analysis to 1948Q1–2024Q1, for which a total of 305 quarterly observations are available for each variable. These data allow us to calculate the ratios that appear in Equation (2), as well as the unemployment rates and their changes, plus the percentage changes of the ratios, Y t , and N t , as can be seen in the Supplementary Materials. We did not use quarterly variations; instead, we followed Zanin and Marra (2012, p. 97) and used interannual variations “in order to reduce the variability and autocorrelation in the data”. From the 301 interannual variations that were available for each series, we calculated Regressions (1), (5), and (8), which provide coefficients for performing the disaggregations in Equations (6) and (7). Similarly, we calculated Regressions (9), (10), and (13) (which are for the inverse relation) in order to perform the disaggregations that are proposed in Equations (11) and (12). Economies 2025,13, 59 8 of 21 We calculated the estimates for the entire 1948Q1–2024Q1 period and various subperiods, as well as via rolling regressions. For the latter, we followed Knotek (2007) in using a window size of 13 years. This size ensured that each regression contained at least one recession, as was also the case for the analyses published by Owyang and Sekhposyan (2012) and Mussida and Zanin (2023). The first of the rolling regressions was for the window of 52 interannual variations from 1949Q1 to 1961Q4—practically the same period that Okun treated in his seminal 1962 article. The second regression omitted the 1949Q1 variations and added those of 1962Q1. This pattern of advancing the window one quarter at a time continued until the last regression, which treated the variations from 2011Q2 to 2024Q1. In the section that follows, the estimates for each window are associated with the last date of each window. In total, we estimated 250 rolling regressions for the principal and auxiliary equations. From these results, it was possible to discern how the values of Okun’s coefficients and their components evolved through time, and thus to note the changes that have occurred over the last 76 years. 4. Results and Discussion 4.1. Correlations and Evolutions The strongest correlation was the one between yand ∆ U(= − 0.789; Table 1). These are the only two variables that Okun (1962) specified in his models. The second strongest (= − 0.501) was between ∆ Uand the hours worked per employed person (x 3 ). These results indicate that although the variables share a common evolution, they also provide differentiated information. Table 1. Coefficients of the correlation among variables in Equation (5) during 1948Q1–2024Q1. Change in the Unemployment Rate ∆U Percentage Change Real GDP y Output per Hour Worked x2 Hours Worked per Employed Person x3 Participation Rate x4 Working-Age Population x5 y−0.789 1 x20.171 0.291 1 x3−0.501 0.455 −0.471 1 x4−0.371 0.279 −0.452 0.192 1 x50.083 0.030 −0.163 −0.099 0.236 1 Source: prepared by authors with data from BEA (2024) and BLS (2024). Figure 1shows the evolution of the six variables that are involved in the relation between output and unemployment rate. All six of these vary, but around distinct levels and with distinct amplitudes. The variations in unemployment rate and participation rate oscillate around 0, as would be expected because neither can increase or decrease indefinitely: both rates are bounded by 0 and 1. For both variables, the positive changes tend to be compensated by the negative ones. The same is not true of the other variables. For the GDP, productivity, and working-age population, the positive variations outweigh the negative ones. Therefore, all three factors increased over the long run. This behavior is reflected in the fact that the values of these variables fluctuated around positive numbers (3.1%, 1.8%, and 1.3%, respectively). For that reason, these variables contributed to making the Okun equation’s intercept positive, as we will see in the next section. However, the output per hour worked also has an important impact on the slope due to its wide variation around its average. Economies 2025,13, 59 15 of 21 0.583 in 1974Q4. Since then, β2γ2 has decreased, becoming negative as a result of the 2008 crisis, and reaching its historic minimum of − 0.542 in 2022Q2 after falling abruptly during the COVID-19 pandemic. In the most recent decades, reductions in production correspond to increases in productivity, which has now become counter-cyclical. For that reason, a larger part of the adjustment is achieved via the unemployment rate, and the absolute value of Okun’s coefficient is greater. In fact, the α1 coefficients for periods that include quarters during which COVID-19 was most widespread are almost equal to the direct effect β1 . For such periods, the indirect effects βjγj compensated each other. Concretely, the effect of the variation in output per hour of work ( β2γ2 ) compensated for the variations in the participation rate (β4γ4) and the hours worked per employed person (β3γ3). Economies 2025, 13, x FOR PEER REVIEW 17 of 23 the productive dynamic and the labor market was distinct; compared to earlier crisis periods, the rates of unemployment and participation overreacted. However, that atypical period should not cause us to overlook the changes that took place during previous decades. In 2001Q2, the absolute value of the Okun coefficient for the rolling regressions reached a minimum of 0.289. The coefficient then remained stable for a few years before beginning to rise sharply after the 2008 crisis. In 2020Q1, just before the emergence of COVID-19, the coefficient had already reached −0.637. The intercept (which represents the long-term effect of all of the other factors) took positive values between its minimum of 0.827 (2001Q2; Figure 4) and its maximum of 1.687 (1962Q1). The elements that contributed to increasing the intercept were the variations in working-age population, the output per hour of work, and (until 1995Q2) the participation rate. The value of the intercept was decreased by variations in the participation rate (after 1995Q3) and the hours worked per employed person. Figure 4. Values of the intercept and its component factors: rolling regression estimates. Notes: α 0 is the intercept from Equation (1), β 0 is the direct effect, and the β j λ j are the indirect effects through the variations in output per hour of work (β 2 λ 2 ), hours worked per employed person (β 3 λ 3 ), the participation rate (β 4 λ 4 ), and the working-age population (β 5 λ 5 ). The sum of these five factors is exactly equal to α 0 . Figure 4 reveals that these factors did not remain stable. Instead, the effects of their intensities changed, thus causing a tendency for the intercept to decrease from 1.5 during the first decades to values nearer to 1 in the recent ones. Estimates from the rolling regressions show that during the crises of 2008 and 2020, the intercept rose again to 1.5. However, these increases could be due to the fact that we are confounding part of the cycle with the trend, because each regression covers only 52 quarters. In that regard, it should be noted that Huang and Lin (2008), as well as other regressions that used longer periods, such as those in Table 2, also show an evolution towards a decreasing intercept. The key factor in this dynamic was the slower growth of the working-age population. The impact of that factor was strengthened by the decline in the participation rate, but compensated by the positive (and rising) contribution of the output per hour of work. The Figure 4. Values of the intercept and its component factors: rolling regression estimates. Notes: α0 is the intercept from Equation (1), β0 is the direct effect, and the βjλj are the indirect effects through the variations in output per hour of work ( β2λ2 ), hours worked per employed person ( β3λ3 ), the participation rate ( β4λ4 ), and the working-age population ( β5λ5 ). The sum of these five factors is exactly equal to α0. The value of β3γ3 was quite stable (between 0.119 and 0.288) until 2007, when it began a progressive rise, reaching a maximum of 0.454 in 2019Q2. That increase compensated in part for the evolution in the production per hour of work. The quarters of the COVID19 pandemic, during which the decline in output mainly affected unemployment and participation rates, reduced the contribution of this factor to 0.270 in 2024Q1. The variation in the participation rate had little effect until the end of the 1970s, after which it became another pro-cyclical production–adjustment mechanism. The predominance of the discouraged worker effect over the added worker effect meant that the variations in the participation rate left less room for adjustment via the unemployment rate (Lee & Parasnis,2014). In times of economic crisis, some potential workers dropped out of the labor market rather than remain unemployed. The COVID-19 pandemic was an extreme case, in which the impossibility of seeking work made many people inactive. The effect of this factor ( β4γ4 ) upon the Okun coefficient rose from 0.042 in 2020Q1 to 0.138 in 2020Q2, then rose further to 0.250 in 2024Q1. Economies 2025,13, 59 16 of 21 As pointed out previously by Barisic and Kovac (2022) and Porras-Arena et al. (2024), estimates of Okun’s coefficients change substantially when the analyses include quarters in which production fell because of COVID-19. During the pandemic, the relation between the productive dynamic and the labor market was distinct; compared to earlier crisis periods, the rates of unemployment and participation overreacted. However, that atypical period should not cause us to overlook the changes that took place during previous decades. In 2001Q2, the absolute value of the Okun coefficient for the rolling regressions reached a minimum of 0.289. The coefficient then remained stable for a few years before beginning to rise sharply after the 2008 crisis. In 2020Q1, just before the emergence of COVID-19, the coefficient had already reached −0.637. The intercept (which represents the long-term effect of all of the other factors) took positive values between its minimum of 0.827 (2001Q2; Figure 4) and its maximum of 1.687 (1962Q1). The elements that contributed to increasing the intercept were the variations in working-age population, the output per hour of work, and (until 1995Q2) the participation rate. The value of the intercept was decreased by variations in the participation rate (after 1995Q3) and the hours worked per employed person. Figure 4reveals that these factors did not remain stable. Instead, the effects of their intensities changed, thus causing a tendency for the intercept to decrease from 1.5 during the first decades to values nearer to 1 in the recent ones. Estimates from the rolling regressions show that during the crises of 2008 and 2020, the intercept rose again to 1.5. However, these increases could be due to the fact that we are confounding part of the cycle with the trend, because each regression covers only 52 quarters. In that regard, it should be noted that Huang and Lin (2008), as well as other regressions that used longer periods, such as those in Table 2, also show an evolution towards a decreasing intercept. The key factor in this dynamic was the slower growth of the working-age population. The impact of that factor was strengthened by the decline in the participation rate, but compensated by the positive (and rising) contribution of the output per hour of work. The contribution of the change in working-age population to the value of the intercept increased (reaching a maximum of 1.939 in 1974Q3) as the baby-boom generation entered the workforce, but then decreased slowly until the beginning of the 1980s, after which it fell more rapidly to about 1 during 1995–2010. It has continued to fall during recent years, reaching 0.784 in 2024Q1. Similar dynamics, but weaker ones, can be seen in the effect of the participation rate ( β4λ4 ). Its value increased during the first years, reaching a maximum of 0.616 in 1974Q3. It then entered a decline that has lasted to the present. It has been negative since 1995Q3, and fell to its minimum of −0.930 in 2022Q3. The number of hours worked per employed person declined throughout 1948Q1– 2024Q1. Therefore, the contribution of this factor to the intercept’s value is negative. Until 1982, and from 2006 to 2020, β3λ3 was close to − 1, while the rest of the time it was nearer to −0.5. In contrast, the output per hour of work tended to increase. Therefore, β2λ2 made a positive contribution to the value of the intercept. Until 1967Q2, and after 2002Q1, β2λ2 was greater than 1. However, it was near zero during the period 1971Q3–1991Q1, which coincides with the years when the contributions of participation rate and working-age population were greatest. 5. Conclusions Okun (1962) summarized the relation between economic growth and the labor market in a single number: the ratio of exchange between real GNP and the unemployment rate. In doing so, Okun noted that this coefficient subsumes the effects of other variables that are not Economies 2025,13, 59 17 of 21 explicit in his model, but do affect the output–unemployment relation. Several subsequent investigations attempted to recover information about effects of those other variables in order to offer a more complete interpretation of the relation, but did so only approximately. The disaggregation proposed in the present article allows economists to identify all of the factors that affect Okun’s relation, and to quantify their effects with precision. This is achieved by unpacking the contents of Okun’s relation, specifically the structure of long-term growth and its cyclical variations. By applying this method to the case of the United States during the period 1948Q1–2024Q1, we found that the value of the intercept in Okun’s relation is determined by the increases in working-age population and output per hour of work, along with the decrease in the number of hours worked per employed person, plus the growth of the participation rate until the 1990s and its subsequent decline. For its part, the value of Okun’s coefficient depends mainly upon the variations in output per hour of work and the hours per employed person, which together reduce by half the direct effect of the variation in production upon the unemployment rate. The output per hour of work had the greatest impact during the first decades of the analyzed period, while hours per employed person were more important in recent decades. The other factors were scarcely relevant. Changes in the above-mentioned components caused Okun’s relation to vary over time: the intercept tended to decrease, and the slope increased. These trends indicate a greater sensitivity of the unemployment rate to variations in production, even before the COVID-19 pandemic. Compared to their behavior during previous economic crises, the post-2020Q2 rates of unemployment and participation reacted more strongly to adjustments in production. In essence, the evolution of Okun’s coefficient that we report here is similar to that described by Huang and Lin (2008), Grant (2018), and Aguiar-Conraria et al. (2020), even though those researchers used other estimation techniques. In this article, we have provided the inter-relations and dynamics of all of the factors that contribute to that evolution, thereby markedly enriching the possibilities for performing systematic multivariate analyses of the bases of Okun’s law. Among the limitations of the analysis developed, it can be mentioned that the most recent data are still preliminary and could change. In addition, we have only used a window size of 13 years in the rolling regressions. Other window sizes would yield somewhat different results. Moreover, the disaggregation of the coefficients has only been formulated for Okun’s first differences model. Ismihan (2016) extends his approach to the gap version, so a similar adaptation could be attempted. Other future work could include integrating this article’s decompositions into other developments that have been taking place, such as the differentiated analysis of expansive and recessive phases of production, plus comparisons among countries and regions. Supplementary Materials: The following supplementary material contains the dataset used for analysis in this manuscript: https://www.mdpi.com/article/10.3390/economies13030059/s1. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The article uses publicly available data. The sources and data are defined in Section 3. Conflicts of Interest: The author declares no conflicts of interest. Economies 2025,13, 59 18 of 21 Abbreviations The following abbreviations are used in this manuscript: BEA Bureau of Economic Analysis BLS Bureau of Labor Statistics GDP Gross domestic product GNP Gross national product OLS Ordinary least squares Appendix A Table A1. Estimations of Equation (5) for various time periods. Period β0β1β2β3β4β5R2 1948Q1–2024Q1 −0.013 (0.012) −0.898 (0.003) *** 0.907 (0.004) *** 0.912 (0.006) *** 0.920 (0.009) *** 0.913 (0.009) *** 0.998 1948Q1–2001Q2 −0.005 (0.017) −0.902 (0.005) *** 0.911 (0.007) *** 0.916 (0.009) *** 0.914 (0.012) *** 0.914 (0.011) *** 0.997 2001Q3–2020Q1 0.009 (0.015) −0.920 (0.005) *** 0.911 (0.006) *** 0.927 (0.010) *** 0.936 (0.010) *** 0.932 (0.014) *** 0.999 2001Q3–2024Q1 −0.002 (0.029) −0.896 (0.007) *** 0.906 (0.009) *** 0.910 (0.017) *** 0.925 (0.020) *** 0.893 (0.026) *** 0.999 Notes: standard errors are in parenthesis. *** denotes statistical significance at the 0.1% level. Source: prepared by authors with data from BEA (2024) and BLS (2024). Table A2. Estimations of Equation (8) for various time periods. Equation x2t=λ2+γ2∆Ut+ε2Equation x3t=λ3+γ3∆Ut+ε3 Period λ2γ2r2λ3γ3r2 1948Q1–2024Q1 1.1365 (0.1752) *** 0.2246 (0.0427) *** 0.085 −0.7870 (0.1025) *** 0.2205 (0.0250) *** 0.207 1948Q1–2001Q2 0.6535 (0.2068) ** 0.3757 (0.0459) 0.244 −0.8275 (0.1470) *** 0.2056 (0.0326) *** 0.160 2001Q3–2020Q1 1.6034 (0.2466) *** −0.1121 (0.0957) *** 0.018 −0.9277 (0.1200) *** 0.4156 (0.0466) *** 0.522 2001Q3–2024Q1 2.2554 (0.2592) *** −0.3813 (0.0869) *** 0.178 −0.8324 (0.0949) *** 0.3470 (0.0318) *** 0.572 Equation x4t=λ4+γ4∆Ut+ε4Equation x5t=λ5+γ5∆Ut+ε5 Period λ4γ4r2λ5γ5r2 1948Q1–2024Q1 −0.1470 (0.0607) * 0.0744 (0.0148) *** 0.078 1.2583 (0.0445) *** 0.0056 (0.0108) 0.001 1948Q1–2001Q2 0.1838 (0.0690) ** 0.0180 (0.0153) 0.007 1.4807 (0.0583) *** −0.0222 (0.0129) 0.014 2001Q3–2020Q1 −0.4157 (0.0906) *** 0.0496 (0.0352) 0.027 0.9611 (0.0544) *** 0.0374 (0.0211) 0.041 2001Q3–2024Q1 −0.6757 (0.0993) *** 0.1865 (0.0333) *** 0.261 0.9536 (0.0454) *** 0.0162 (0.0152) 0.012 Notes: standard errors are in parenthesis. The symbols *, **, and *** denote statistical significance at the 5%, 1%, and 0.1% levels, respectively. Source: prepared by authors with data from BEA (2024) and BLS (2024). Notes 1Okun (1962) used the GNP, but the GDP has been used in these analyses since the 1990s (Palley,1993;Guisinger et al.,2018). 2 Similar reasoning applies to comparisons among countries. For example, in Japan, the changes in output are related more closely to changes in output per hour and to hours worked per employed person, than to the evolution in the unemployment rate Economies 2025,13, 59 19 of 21 (Hamada & Kurosaka,1984;Ismihan,2016). The reverse is true in the United States. For that reason, Japan’s Okun coefficient is different from that of the US. Specifically, the absolute value of Japan’s coefficient is smaller (Ball et al.,2019;Furceri et al.,2020; Fontanari et al.,2022). 3 Ismihan (2016) does not estimate the parameters β1 through β5 via regression, as in Equation (5). Instead, Ismihan assigns these parameters “the average value of the employment rate over the time period under consideration” (p. 179). In this way, Ismihan obtains a decomposition of Okun’s coefficient that is very approximate, rather than exact. 4 Equations (6) and (7) can be derived by substituting Equation (8) in Equation (5), reordering the terms, and comparing the intercept and slope to those in Equation (1). 5 Prachowny (1993, p. 332) explains that “Okun’s coefficient of three is derived from a complicated weighted sum of all other changes”. Similarly, our Equation (12) disaggregates Okun’s coefficient (in the relation y=f( ∆ U)) into a “weighted sum of all other changes”. 6 Specifically, the BEA (2024) data correspond to the GDP series in chained millions of dollars (2017), seasonally adjusted at annual rates. The series obtained from BLS (2024) were as follows: LNU02033120Q for H t /E t , LNS12000000Q for E t , LNS11000000Q for At, and LNU00000000Q for Nt. References Aguiar-Conraria, L., Martins, M. M. F., & Soares, M. J. (2020). Okun’s law across time and frequencies. Journal of Economic Dynamics and Control,116, 103897. [CrossRef] Anderton, R., Aranki, T., Bonthuis, B., & Jarvis, V. (2014). Disaggregating Okun’s law: Decomposing the impact of the expenditure components of GDP on euro area unemployment. European Central Bank Working Paper, 1747. Available online: https:// www.ecb.europa.eu/pub/pdf/scpwps/ecbwp1747.en.pdf (accessed on 4 April 2024). Ball, L., Leigh, D., & Loungani, P. (2017). Okun’s law: Fit at 50? Journal of Money, Credit and Banking,49(7), 1413–1441. [CrossRef] Ball, L., Furceri, D., Leigh, D., & Loungani, P. (2019). Does one law fit all? Cross-country evidence on Okun’s law. Open Economies Review,30, 841–874. [CrossRef] Barisic, P., & Kovac, T. (2022). The effectiveness of the fiscal policy response to COVID-19 through the lens of short and long run labor market effects of COVID-19 measures. Public Sector Economics,46(1), 43–81. [CrossRef] Barnichon, R. (2010). Productivity and unemployment over the business cycle. Journal of Monetary Economics,57(8), 1013–1025. [CrossRef] Barreto, H., & Howland, F. (1993). There are two Okun’s law relationships between output and unemployment. Wabash college working paper. Available online: https://www.researchgate.net/publication/228421484 _ There _ Are _ Two _ Okun’s _ Law _ Relationships _ between _Output_and_Unemployment (accessed on 7 March 2022). BEA (Bureau of Economic Analysis). (2024). Table 1.1.6. Real gross domestic product, chained dollars [dataset]. Available online: https://www.bea.gov/itable/national-gdp-and-personal-income (accessed on 21 June 2024). Benos, N., & Stavrakoudis, A. (2022). Okun’s law: Copula-based evidence from G7 countries. Quarterly Review of Economics and Finance, 84, 478–491. [CrossRef] Binet, M. E., & Facchini, F. (2013). Okun’s law in the French regions: A cross-regional comparison. Economics Bulletin,33(1), 420–433. Available online: http://www.accessecon.com/Pubs/EB/2013/Volume33/EB-13-V33-I1-P41.pdf (accessed on 10 August 2024). Blackley, P. R. (1991). The measurement and determination of Okun’s law: Evidence from state economies. Journal of Macroeconomics, 13(4), 641–656. [CrossRef] BLS (Bureau of Labor Statistics). (2024). BLS beta labs [dataset]. Available online: https://beta.bls.gov/dataQuery/search (accessed on 21 June 2024). Daly, M. C., Fernald, J. G., Jordà,Ò., & Nechio, F. (2017). Shocks and adjustments. Federal Reserve Bank of San Francisco Working Paper Series, 2013–32, July 2017 Version. Federal Reserve Bank of San Francisco. [CrossRef] Donayre, L. (2022). On the behavior of Okun’s law across business cycles. Economic Modelling,112, 105858. [CrossRef] Favereau, O., & Mouillart, M. (1981). La stabilité du lien emploi-croissance et la loi d’Okun: Une application àl’économie française. Consommation–Revue de Socio-Économie,28(1), 85–117. Available online: https://www.credoc.fr/download/pdf/Sou/Sou1981-3 281.pdf (accessed on 6 April 2024). Fontanari, C., Palumbo, A., & Salvatori, C. (2022). The updated Okun method for estimation of potential output with alternative measures of labor underutilization. Structural Change and Economic Dynamics,60, 158–178. [CrossRef] Furceri, D., Jalles, J. T., & Loungani, P. (2020). On the determinants of the Okun’s law: New evidence from time-varying estimates. Comparative Economic Studies,62, 661–700. [CrossRef] Galí, J., & Gambetti, L. (2009). On the sources of the great moderation. American Economic Journal: Macroeconomics,1(1), 26–57. [CrossRef] Gelfer, S. (2020). Re-evaluating Okun’s Law: Why all recessions and recoveries are “different”. Economics Letters,196, 109497. [CrossRef] Economies 2025,13, 59 20 of 21 Gonzalez-Prieto, N., Loungani, P., & Mishra, S. (2018). What lies beneath? A sub-national look at Okun’s law in the United States. Open Economies Review,29, 835–852. [CrossRef] Gordon, R. J. (1973). The welfare cost of higher unemployment. Brookings Papers on Economic Activity,1973(1), 133–205. [CrossRef] Gordon, R. J. (1984). Unemployment and potential output in the 1980’s. Brookings Papers on Economic Activity,1984(2), 537–568. [CrossRef] Gordon, R. J. (2010a). Okun’s law and productivity innovations. The American Economic Review,100(2), 11–15. Available online: https://www.jstor.org/stable/27804954 (accessed on 4 April 2024). [CrossRef] Gordon, R. J. (2010b, November 5). The demise of Okun’s law and of procyclical fluctuations in conventional and unconventional measures of productivity. CREI/CEPR Macro-Labor Conference, Barcelona, Spain. Available online: https://www.crei.cat/wp-content/ uploads/2016/09/Gordon.pdf (accessed on 4 April 2024). Grant, A. L. (2018). The Great Recession and Okun’s law. Economic Modelling,69, 291–300. [CrossRef] Guisinger, A. Y., Hernández-Murillo, R., Owyang, M. T., & Sinclair, T. M. (2018). A state-level analysis of Okun’s law. Regional Science and Urban Economics,68, 239–248. [CrossRef] Hamada, K., & Kurosaka, Y. (1984). The relationship between production and unemployment in Japan: Okun’s law in comparative perspective. European Economic Review,25(1), 71–94. [CrossRef] Herwartz, H., & Niebuhr, A. (2011). Growth, unemployment and labour market institutions: Evidence from a cross-section of EU regions. Applied Economics,43(30), 4663–4676. [CrossRef] Huang, H. C., & Lin, S. C. (2006). A flexible nonlinear inference to Okun’s relationship. Applied Economics Letters,13(5), 325–331. [CrossRef] Huang, H. C., & Lin, S. C. (2008). Smooth-time-varying Okun’s coefficients. Economic Modelling,25(2), 363–375. [CrossRef] Ismihan, M. (2016). A useful framework for linking labor and goods markets: Okun’s law and its stability revisited. Review of Keynesian Economics,4(2), 175–192. [CrossRef] Johnston, J. (1984). Econometric methods (3rd ed.). McGraw-Hill. Karlsson, S., & Österholm, P. (2020). A hybrid time-varying parameter Bayesian VAR analysis of Okun’s law in the United States. Economics Letters,197, 109622. [CrossRef] Kaufman, R. T. (1988). An international comparison of Okun’s laws. Journal of Comparative Economics,12(2), 182–203. [CrossRef] Kmenta, J. (1997). Elements of econometrics (2nd ed.). The University of Michigan Press. Knotek, E. S. (2007). How useful is Okun’s law? Federal Reserve Bank of Kansas City Economic Review,92(4), 73–103. Available online: https://www.kansascityfed.org/documents/955/2007-How%20Useful%20is%20Okun’s%20Law?.pdf (accessed on 7 April 2024). Kraim, M., Sarmidi, T., Faizah, F., & Khalid, N. (2023). The determinants of Okun’s coefficients in oil-producing countries: New evidence from quantile regression. International Journal of Economics and Management,17(3), 305–319. [CrossRef] Krüger, J. J., & Neugart, M. (2021). Dissecting Okun’s law beyond time and frequency. Applied Economics Letters,28(20), 1744–1749. [CrossRef] Lee, G. H. Y., & Parasnis, J. (2014). Discouraged workers in developed countries and added workers in developing countries? Unemployment rate and labour force participation. Economic Modelling,41, 90–98. [CrossRef] Mairesse, J. (1984). Comment on ‘The relationship between production and unemployment in Japan: Okun’s law in comparative perspective’ by K. Hamada and Y. Kurosaka. European Economic Review,25(1), 99–105. [CrossRef] Mankiw, N. G. (1994). Macroeconomics (2nd ed.). Worth Publishers. Maza, A. (2022). Regional differences in Okun’s law and explanatory factors: Some insights from Europe. International Regional Science Review,45(5), 555–580. [CrossRef] Monhollon, J. R., & Cullison, W. E. (1970). Okun’s law and the natural rate of growth: Comment. Southern Economic Journal,37(2), 231–232. [CrossRef] Moosa, I. A. (1997). A cross-country comparison of Okun’s coefficient. Journal of Comparative Economics,24(3), 335–356. [CrossRef] Mussida, C., & Zanin, L. (2023). Asymmetry and (in-)stability of Okun’s coefficients in nine European countries. The Journal of Economic Asymmetries,28, e00313. [CrossRef] Nebot, C., Beyaert, A., & García-Solanes, J. (2019). New insights into non-linearity of Okun’s law. Economic Modelling,82, 202–210. [CrossRef] Okun, A. M. (1962). Potential GNP: Its measurement and significance. Proceedings of the Business and Economic Statistics Section, 98–104. Reprinted as Cowles Foundation Paper, 190. Available online: https://milescorak.files.wordpress.com/2016/01/okun-potential -gnp-its-measurement-and-significance-p0190.pdf (accessed on 7 August 2023). Owyang, M. T., & Sekhposyan, T. (2012). Okun’s law over the business cycle: Was the great recession all that different? Federal Reserve Bank of St. Louis Review,5(94), 399–418. Available online: https://files.stlouisfed.org/files/htdocs/publications/review/12/09/ 399-418Owyang_rev.pdf (accessed on 17 June 2024). [CrossRef] Economies 2025,13, 59 21 of 21 Palley, T. I. (1993). Okun’s law and the asymmetric and changing cyclical behaviour of the USA economy. International Review of Applied Economics,7(2), 144–162. [CrossRef] Peláez-Herreros, O. (2025). Decomposing Okun’s law: Evidence for the United States, 1970–2021. Applied Economics Letters,32(1), 121–124. [CrossRef] Perry, G. L. (1971). Labor force structure, potential output, and productivity. Brookings Papers on Economic Activity,1971(3), 533–578. Available online: https://www.brookings.edu/wp-content/uploads/1971/12/1971c _ bpea _ perry _ denison _ solow.pdf (accessed on 12 March 2022). [CrossRef] Plosser, C. I., & Schwert, G. W. (1979). Potential GNP: Its measurement and significance: A dissenting opinion. Carnegie-Rochester Conference Series on Public Policy,10, 179–186. [CrossRef] Porras-Arena, M. S., & Martín-Román, Á. L. (2023). The correlation between unemployment and economic growth in Latin America– Okun’s law estimates by country. International Labour Review,162(2), 171–198. [CrossRef] Porras-Arena, M. S., Martín-Román, Á. L., Dueñas-Fernández, D., & Llorente-Heras, R. (2024). Okun’s law: The effects of the COVID-19 pandemic and the temporary layoffs procedures (ERTEs) on Spanish regions. Investigaciones Regionales–Journal of Regional Research, 59(2), 105–125. [CrossRef] Prachowny, M. F. J. (1993). Okun’s law: Theoretical foundations and revised estimates. The Review of Economics and Statistics,75(2), 331–336. [CrossRef] Sögner, L., & Stiassny, A. (2002). An analysis on the structural stability of Okun’s law: A cross-country study. Applied Economics,34(14), 1775–1787. [CrossRef] Thirlwall, A. P. (1969). Okun’s law and the natural rate of growth. Southern Economic Journal,36(1), 87–89. [CrossRef] Valadkhani, A., & Smyth, R. (2015). Switching and asymmetric behaviour of the Okun coefficient in the US: Evidence for the 1948–2015 period. Economic Modelling,50, 281–290. [CrossRef] Zanin, L., & Marra, G. (2012). Rolling regression versus time-varying coefficient modelling: An empirical investigation of the Okun’s law in some Euro area countries. Bulletin of Economic Review,64(1), 91–108. [CrossRef] Ziegenbein, A. (2021). Macroeconomic shocks and Okun’s Law. Economics Letters,202, 109826. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.