okun’s macroscope: changes in the cyclical behavior of productivity … · 2013-07-15 · percent...

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Okun’s Macroscope: Changes in the Cyclical Behavior of Productivity and the Comovement between Output and Unemployment

Mary C. Daly, John G. Fernald, Òscar Jordà and Fernanda Nechio1

Federal Reserve Bank of San Francisco

Abstract We document sizeable changes over time and across countries in the

comovement of output and unemployment over the business cycle. To a large extent, these changes reflect the evolving cyclical behavior of labor productivity (output per hour worked). For the typical country, productivity shifted from procyclical to countercyclical in the decades prior to 2007, but has since become procyclical once again. We also find, in general, that productivity is more procyclical during recessions than in normal times. We develop a production-theory framework to interpret these empirical results. The theory, together with the empirical results, sheds light on the similarities and differences over time and across countries in the underlying dynamics of how firms and households use various margins of adjustment. For the United States, much of the time-series variation in the cyclicality of productivity reflects variation in the use of the “utilization” margin (e.g., labor hoarding). Our results provide insight into desirable features of macro models that seek to match labor-market facts.

Keywords: Output and employment fluctuations, cyclical productivity, labor-

market institutions, Okun’s Law JEL-codes: E24, E23, J20

1We thank Bart Hobijn, Ron Smith, and seminar participants at the Bank of England for helpful comments. We thank Israel Malkin for excellent research assistance. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of San Francisco or the Federal Reserve System. E-mails: [email protected]; [email protected]; [email protected] ; [email protected]. Corresponding author: Fernanda Nechio, email: [email protected]..

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1 Introduction

Between 2007:Q4 and 2009:Q4, the collapse in GDP was larger in United Kingdom and Germany

than in the United States.2 Yet the unemployment rate rose by more than 5 percentage points over this period

in the United States, compared with only 2-1/2 percentage points in the U.K. And the unemployment rate

actually fell in Germany. Clearly, though the shock or shocks that caused the so-called Great Recession were

presumably similar (or, at least, related) across countries, firms and households in different places used

different margins of adjustment.

In this paper, we take a broad perspective and study changes in the output-unemployment

relationship for 14 OECD countries over 40 years. We develop a growth-accounting/ production-theory

framework to interpret the comovement. This framework highlights which margins of adjustment should

matter for the relationship. Although most countries lack the data to implement the framework fully, it helps

guide our interpretation of the evidence.

Specifically, we find notable changes over time in the output-unemployment relationship which, it

turns out, mainly reflects changes over time in the cyclicality of productivity across OECD economies.3 In

the decades prior to the Great Recession, productivity shifted from procyclical to (slightly) countercyclical in

the typical country.4 Since the onset of the global financial crisis and Great Recession that started in 2007,

productivity has once again been procyclical in most countries.

We also find that productivity is always more procyclical in recessions than in normal times. This

greater procyclicality could reflect greater variation in factor utilization around these times. However, the

changes during and since the Great Depression are larger than can be explained by the typical “recession”

2 In OECD data, the decline over this period was 3.4 percent in the United States, 4.1 percent in Germany, and 5.4 percent in the United Kingdom.

3 For these purposes, we define cyclicality with respect to unemployment, so that “procyclical” productivity means that output per hour tends to rise when the unemployment rate falls (i.e., in a boom).

4 Several papers have highlighted the changing cyclicality of productivity for the United States. For discussion, see Gali and van Rens (2010).

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pattern. Finally, we explore the extent to which the cross-country results are explained by differences in

labor market institutions.5

To gain further insight, we dig more deeply into the reasons for changes in comovement among

output, unemployment, and productivity in the United States, where more detailed data are available.

Specifically, we use a relatively new quarterly growth-accounting dataset from Fernald (2012). These data

include an empirical measure of factor utilization (i.e., labor effort and the workweek of capital) and

technology (i.e. total factor productivity controlling for utilization), which allows us to be more precise in

our decompositions. Indeed, preliminary results in the U.S. data point to changes over time in the

importance in the utilization margin as the reason for changing cyclicality of productivity. In addition, these

data allow us to better identify adjustments conditional on particular shocks, e.g., technology versus

government spending shocks. These results allow us to go beyond reduced-form correlations in the data.

The relationship we focus on, between output growth and unemployment changes, has a long history

in macroeconomics. Half a century ago, Arthur Okun (1962) found a consistent and predictable relationship

between these variables. The reduced-form empirical relationship between these variables has been a key

economic regularity used by monetary policymakers and economic forecasters.

In this paper, we interpret Okun’s relationship as a “macroscope” (not a “law”) through which to

view changes in aggregate patterns. The relationship can provide insight into the similarities and differences

in the underlying dynamics of advanced industrial economies.

More generally, the relationship can provide insight into desirable features of macro models. The

output-unemployment relationship is not a typical “moment” that macro models have sought to match.

Indeed, for a non-technology shock, off-the-shelf macro models will not typically match it. The obvious

challenge comes from the production side of the economy. Suppose the unemployment rate falls 1

percentage point, then the direct effect is that employment rises by 1 percent. With a standard constant

returns production function, output should rise about 2/3 percentage point (1 percent times labor’s share).

5 Admittedly,preliminary results find surprisingly little clear relationship with existing measures of labor-market institutions or frictions.

3

For the typical country, however, a reduced-form regression of output growth on unemployment change

yields a coefficient that substantially exceeds 1 in magnitude and, recently, has been closer to 2.

There are a number of channels that potentially reconcile macro models with the reduced-form

relationship in the data. One channel could be the importance of different shocks. For example, in most

models, the covariance between input and output differs for demand versus technology shocks since, in

general equilibrium, technology shocks can amplify or dampen the input response.6 A second channel is the

margins for adjustment. In the data, the intensive as well as extensive margins are clearly important—such

as hours per worker, labor effort, and the workweek of capital. Many of these margins have been studied,

but our empirical results provide a lens to examine and assess their practical importance.

The remainder of the paper proceeds as follows. Section 2 discusses some of the related literature and

tylized facts. Section 3 describes the data and present the time-series and business-cycle properties of the

Okun “coefficient”—a simple summary statistic for the comovement of output and unemployment. Section

4 provides a simple theoretical framework for thinking about the drivers of Okun’s law and presents an

empirically tractable decomposition of the Okun’s coefficient into aggregate hours and productivity

components. The results of the decomposition are also described and discussed. Section 5 dives more deeply

into the U.S. data, where identification is clearer. Section 6 discusses the post-financial crisis period in light

of the historical findings from our analysis. Section 7 concludes.

2 Okun’s Law? Previous Literature on the Output-Unemployment Relationship

This section reviews some of the recent literature that followed Okun’s (1962) original work. Much

of this work is very reduced-form, and at best only loosely related to modern macroeconomic theory.

However, it points to margins of adjustment that are relevant for macro modeling.

Okun reported several interesting stylized facts. First, “…each extra percentage point in the

unemployment rate…has been associated with about a three percent decrement in real GNP”. Second, a one-

6 Real-business-cycle models typically have an amplified response. Empirically, Gali (1999) and Basu, Fernald, and Kimball (2006) find a dampened response, since inputs fall when technology improves.

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percent decline in output relative to trend during a recession was divided up approximately into a response of

1/3 in the employment rate, 1/6 in hours per employee, 1/6 in labor force participation (LFPR), and 1/3 of

productivity. In other words, 2/3 of the effect is in aggregate hours and 1/3 is in productivity.

Both of these regularities have been investigated by subsequent researchers using data for the U.S.

and other OECD nations. The results of this research, which largely predate the recent financial crisis, can be

summarized as follows. In the U.S. the three to one output-unemployment relationship noted by Okun in

1962 (and again in 1970) appears to have attenuated over time. More recent estimates of the empirical

relationship suggest that Okun’s rule of thumb is closer to two than to three (Attfield and Silverstone 1997,

Gordon 1998 and 2011, Mankiw 1994). The attenuation of the tradeoff in the U.S. may reflect increased

responsiveness of aggregate labor hours and decreased responsiveness of productivity to changes in output

associated with increased labor market flexibility which allows firms to adjust aggregate hours in response to

declining demand (Gordon 2011). Relatedly, the declines may reflect structural and institutional changes in

the labor market, which affect how firms and households adjust to economic shocks. For example, Lee

(2000) discusses how the Okun coefficient might be affected by rising female labor force participation, the

decline of unions, changing productivity trends, and corporate restructuring.

Research has also found marked variation across countries in the magnitude of the relationship

between changes in unemployment and output (Gordon 2011; Freeman 2001; Lee 2000; Moosa, 1997;

Paldam 1987; and Knoester 1986). In general these studies find that the Okun coefficient is lowest in the

U.S. and Canada (around 2), highest in Japan (around 10), and in the range of 3 to 5 in Europe, although like

the U.S., varying over time (Lee 2000; Freeman 2001).7

Policymakers charged with making real time decisions about appropriate fiscal and monetary policy

have often taken Okun’s Law as a benchmark for gauging excess capacity in the economy. Against this

backdrop, recent departures from Okun’s law associated with the financial crisis, ensuing deep recession, and

prolonged and gradual recovery have left some policymakers and researchers questioning the continuing

7 Overall, there has been much less systematic research on changes in Okun’s coefficient over time for countries other than the U.S.

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relevance of Okun’s Law. Figure 1 illustrates some of the challenges. The figure plots the coefficient of a

simple OLS regression of real output growth on unemployment since the 2000s (the blue bars), along with

the coefficient estimated using data since the crisis, that is, from the first quarter of 2007 to the first quarter

of 2012 (the red squares).8 The findings show that for a given increase in unemployment, the decrease in

output has been much larger since the financial crisis than in the beginning of the 2000s. With few

exceptions where the changes were more muted, the increases in “Okun’s coefficient”t ranged from just over

50 percent (France) to close to 300 percent (Finland). The size and breadth of the increases across a range of

industrialized nations is intriguing.

In later sections of this paper, we ask whether the changes depicted in Figure 1 might reflect ongoing

time-variation in the relationship, a normal response of Okun’s coefficient to a business cycle downturn, or

an unusual feature of the shocks that hit the economies.

Figure 1 - Okun's coefficient and the Great Recession

8 The window is selected to account for the conclusion in the literature that the Okun’s coefficient has been declining over time. As we will show later in the paper, using a longer time period would result in larger Okun’s coefficients for most countries.

0.280.46

0.981.20

1.51

0.92

1.67

2.44

0.13

1.38

0.29

1.17 1.23

1.50

0.810.94

1.52 1.52 1.53 1.59

2.04

2.26

2.30

2.59

2.86

3.49 3.57

3.96

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

2000-2006

2007-2012

Source: OECD, Authors' Calculations

2000Q1-2006Q4 versus 2007Q1-2012Q1Okun's coefficient across countries

Absolute Value

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3 Data and Simple First Difference Estimates

To begin our analysis of how Okun’s coefficient has changed over time and over the business cycle

we consider a basic reduced-form formulation of Okun’s law that relates growth in output to changes in the

unemployment rate in the following manner:

(1)

where is the growth rate of real output growth, is the change in unemployment rate. We

estimate this first difference formulation of Okun’s law for a balanced panel of 14 OECD economies,

namely: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Italy, Netherlands, New Zealand,

Norway, Sweden, United Kingdom, and the United States. 9

As a first pass at the data we estimate the relation described in equation (1) for each country using

rolling windows of 40 quarters from the first quarter of 1970 to the first quarter of 2012. More specifically,

for each country we estimate:

(2)

where is the 4-quarter (log) change in real output, and is the 4-quarter change in the rate of

unemployment.10

Figure 2 summarizes these regressions by plotting the time series of the cross-country 50th (median),

25th and the 75th percentiles of the estimated Okun’s coefficient, , from equation (2). The plot shows that

from the mid-1980s through about 2003 the median Okun’s coefficient nearly continuously declined in

absolute value. This decline began to slow and even reverse somewhat in the mid 2000s but even so the

median Okun coefficient in the years preceding the financial crisis was a little less than half as large as it had

been in the early 1980s. In the 1980’s the median Okun’s coefficient ranged around -2 reaching -1.2 by the

9 We refer the reader to the Appendix for data details. 10 Throughout the paper, lower case variables correspond to their respective logarithmic versions.

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2000s. Following the financial crisis, the Okun coefficients in most OECD nations have risen sharply such

that the median value hovers around -1.7. In the aftermath of the global recession then, the relationships

between output growth and unemployment across OECD nations look more similar to the 1980s than to the

early 2000s. This basic pattern for the median mostly holds for the 25th and 75th percentiles.

Figure 2 - Okun's coefficient - sample median and percentiles

The results in Figure 2 suggest that at least some of the characterization of Okun’s coefficients as

“departing from their historical values” (e.g., Okun’s law is broken) depends on a fairly short sense of

history. Compared to the early 1980s, the current values of Okun’s coefficients displayed in Figure 2 seem

plausible and more in line with expectations. That said, the question remains: why have Okun’s coefficients

retraced part of their secular decline during this most recent recession.

An obvious starting point is to consider whether Okun’s coefficients change over the business cycle.

For most countries in our sample, both the early 1980s and the past five years have marked periods of

recession. This suggests that part of the recent increase in Okun’s coefficients across countries might be

cyclical.

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

1981

1982

1983

1984

1985

1986

1988

1989

1990

1991

1992

1993

1995

1996

1997

1998

1999

2000

2002

2003

2004

2005

2006

2007

2009

2010

2011

Source: OECD, Authors' CalculationsNote: sample consists of 14-country balanced panel

40-quarter rolling windowOkun's coefficient over time

Okun's Coefficient

Median

75th Percentile

25th Percentile

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To examine this possibility we return to our benchmark Okun equation. We expand the Okun’s law

shown in equation (2) to include dummy variables meant to capture recessionary periods. In particular, we

estimate:

(3)

where, again, is the 4-quarter log change in real output growth, is the 4-quarter change in

unemployment, is a dummy for recession quarters which attains value of 1 in recessionary quarters and

zero otherwise. Departing from a by-country regression, we instead explore the panel dimension of our data

by pooling our panel of countries and adding controls for time and country fixed effects.11 The sample

includes the 14 countries listed earlier in this section.

A challenge to this type of analysis is to identify recession quarters for each country in our panel. In

our benchmark analysis, we date recessions in accordance with the OECD Composite Leading Indicators,

which provides coverage for all 14 countries in our panel.12 We also consider two alternative methods for

identifying recessions: recession dates provided by Economic Cycle Research Institute (ECRI), and recession

dates gained by applying Harding and Pagan (2002) method to identify turning points.13 The first of these

alternatives has the disadvantage of being limited to a much smaller set of countries than our panel.

Nonetheless, irrespective of the recession identification method, our panel regressions results are

qualitatively unchanged.14 For brevity, we only report results associated with the OECD recession dating,

and the alternative estimations are available upon request.

Table 1 summarizes the main regression results. To interpret the results, one should read the

estimated as the relation between output growth and unemployment during normal periods (or expansions)

and the estimated as the additional wedge to during recessionary periods, that is, the relation between

output growth and unemployment during recessions is given by .

11 Results for a by-country estimation of equation (3) are provided in the Appendix in the first column of Table 7. 12 A table with data coverage and recession dates is provided in the Appendix. 13 We apply Harding and Pagan (2002) using employment data to identify turning points (peaks and troughs). 14 Our preferred method to identify recession accords with ECRI 71% of the time, and with Harding and Pagan (2002) method 61% of the

time.

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The first column of Table 1 presents the regression results controlling for country fixed effects, the

second column controls for time fixed effects and the last column controls for both country and time fixed

effects. For convenience, the table includes the estimated coefficients , , and , and the sum of

which captures the relation between output and unemployment in recession periods. As such, the results

reported in the row labeled “Unemployment ” refer to the Okun’s coefficient under normal times (or

expansions) and the results reported in the row labeled “Unemployment under recession ” refer to the

Okun’s coefficient during recessions.

The findings in Table 1 show that irrespective of the regression controls (time, country or both fixed

effects), in recession periods, the Okun coefficient is larger in absolute value than during expansions.

Focusing on the last column where both country and time fixed effects are included, during expansions, a

one percentage point increase in unemployment leads to a less than one percent decrease in output growth.

During recessions, this number increases and a one percentage point increase in unemployment leads to a 1.3

percent decrease in output growth. The same pattern holds for the other reported regressions.

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Table 1 - Regression results - Okun's Law estimates

Regression Estimates

(1) (2) (3)

Dependent variables:

Constant 3.1*** 4.1*** 4.1***

(0.0) (0.5) (0.5)

Recession dummy ( ) -1.1*** -1.0*** -1.0***

(0.071) (0.086) (0.1)

Unemployment -1.1*** -0.8*** -0.8***

(0.1) (0.1) (0.0)

Unemployment under recession

-1.6*** -1.2*** -1.3***

(0.1)a (0.1)a (0.0)a

Country fixed effects yes no yes

Time fixed effects no yes yes

0.4 0.6 0.6

Note: The table reports estimated coefficients and standard errors from equation (3). Coefficients followed by

*** are significant at 1%, ** are significant at 5%, and * are significant at 10%.

a Statistical significance and standard deviations for estimated .

The results in this section suggest that the recent divergences in Okun’s coefficients thought by many

to reflect a breakdown in Okun’s law do not seem as large when viewed in the context of a longer history or

with understanding the cyclicality of the output and unemployment relationship. That said, as we will show

later in the paper, this context cannot account for the entire divergence in coefficients displayed in Figure 1.

There remains something special about the financial crisis and its aftermath that warrants further study.

Before turning to that however, we complete our analysis of what drives the secular and cyclical movements

in Okun’s law over time.

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4 A Decomposition of Okun’s coefficient

So far, we have looked at the simplest formulation of the Okun relationship. In this section we

provide some additional structure around which to organize a discussion about the key factors affecting the

changes in Okun coefficients described in the previous section. This structure allows us to discuss how

institutional or other features of labor markets might affect estimates of Okun’s law across countries or over

time. In addition, it naturally links discussions of Okun’s law to the broader literature on the cyclicality of

productivity.

As described in equation (2), the simplest reduced-form Okun regression relates output growth (the

log change) to the percentage-point change in the unemployment rate. A useful identity recalls that output

growth equals the sum of growth in hours and labor productivity:

(4)

where is the 4-quarter log change in real output, is the 4-quarter log change in total labor

hours. Comparing (4) and (2), the OLS estimate of β can be expressed in terms of the linear (reduced form)

projection of hours growth on unemployment, and of labor-productivity growth on unemployment:15

(5)

where the coefficients are from the regressions:

(6)

(7)

4.1 The Changing Cyclicality of Productivity

The above framework helps interpret the sign, and also the time series and business cycle properties

of the Okun’s coefficient as described in Section 3. Hence, in this section, we move in two directions: (1) we

first study the time series response of hours and labor productivity for our sample of countries; (2) next we

analyze the role of each component in recessionary periods.

15 This follows from standard economic reasoning that considers equation (2) as an omitted-variable estimation of equation (4). We also confirmed that the identity below is numerically true in our data.

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To explore the time series properties of , and , we begin by estimating, for each country,

the relationships expressed in equations (6) and (7) using rolling windows of 40 quarters. To perform these

two additional regressions, we use OECD data on total hours worked and output per hour for the panel of

countries in our sample.16 These new regression results, along with the regression results obtained from the

reduced-form Okun’s law estimated in equation (2) shed light on what drives the time series movement of

the Okun coefficients.

Figure 3 summarizes the results obtained from estimating equations (2), (6), and (7). The figure plots

that the median Okun coefficient ( ) (previously depicted in Figure 2) and the new and . The

findings show that the Okun’s coefficient ( ) mainly reflects the projection of hours growth on

unemployment changes. Productivity, on the other hand, seems to be a much smaller component of the low

frequency movements of the change in the Okun’s coefficient. Looking beyond these broad patterns, casual

observation also suggests that productivity growth might play a larger role in the cyclicality of the Okun

coefficient than it does in the secular movements.

16 The OECD data provides real GDP, hours per worker and number of employees. We use the last two series to build total hours as described in equation (10).

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Figure 3 - Estimated decomposition of the Okun's coefficient

To more formally address this possibility we return to regressions on our pooled sample of countries

that include dummy variables for recessionary periods. Specifically, we augment our regression equations (6)

and (7) to isolate for the effects of recessions in our decomposition as follows:

(8)

(9)

These equations are analogous to (6) and (7) in Section 2. Recall the results from equation (3)

displayed in Table 1 showed that the Okun’s coefficient becomes larger in absolute value during recessions

relative to other periods. The results from equations (6) and (7) tell us whether this cyclical behavior of the

Okun coefficient relates to the aggregate hours or productivity margin.

Table 2 provides the estimation results for regressions (3), (8) and (9). The first column reestimates

equation (3),17 the second column provides the estimation results for equation (8), and the last column shows

17 The small discrepancies in estimated coefficients of equation (3) reported in Table 1 and Table 2 are due to sample differences. For estimating regressions (8) and (9) we make use of labor hours and productivity data which have a smaller coverage than the time series

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.519

8119

8219

8319

8419

8519

8719

8819

8919

9019

9119

9219

9419

9519

9619

9719

9819

9920

0120

0220

0320

0420

0520

0620

0820

0920

1020

11

Source: OECD, Authors' Calculations Note: Sample consists of 14-country balanced panel

β=βhours +βLPEstimated Decomposing Okun's Coefficient

Median of Coefficient

Median of Okun's Coefficient, β

Median of Total Hours Coefficient, βhours

Median of Productivity Coefficient, βLP

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the estimation results for equation (9). As in Table 1, for each regression, the results reported under the row

labeled “Unemployment ” can be interpreted as the effects of unemployment on output growth, total hours

and productivity, respectively, during non-recessionary periods. During recessions, the relationship between

unemployment and those same three variables is moved up or down by , such that the coefficient in

recessions equals . For convenience we report the sum for recessions under the label “Unemployment

under recessions ”.

Beginning with the first column of Table 2, we simply confirm that during recessions the Okun’s

coefficient becomes larger. In the second column, the row “Unemployment ”shows that in normal times,

the relation between unemployment and hours worked is negative, that is, when unemployment increases

(decreases), total hours worked decreases (increases). In other words, the intensive (hours) and extensive

(workers) margins move together. This effect is amplified in recessions as shown in the row labeled

“Unemployment under recessions ”.

Turning to productivity, the third column shows that in normal times, productivity is positively

correlated with unemployment, and hence, is countercyclical. During recessionary times, however, this

positive correlation decreases substantially. The declining positive correlation between unemployment and

productivity during recessions makes the coefficients during recessions, much smaller than the

coefficient during normal times, .

From equation (5) we know that by definition the Okun’s coefficient is the sum of its hours and

productivity component. This allows us to add up all these effects and say something about how aggregate

hours and productivity influence the Okun coefficient over the business cycle. Focusing on the row labeled

“Unemployment ” one sees that in normal periods, the counter-cyclicality of productivity provides an

attenuation on the level of the Okun’s coefficient, since it enters with a positive effect and partly offsets the

negative effect of hours. In recessionary times (the row labeled “Unemployment under recessions ”)

we use for the estimation of equation (3) as reported in Table 1. So, the estimation results for equation (3) have a smaller coverage that is consistent with the hours and productivity data. For details about labor data coverage see Table 5 in the Appendix.

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productivity loses part of its attenuation property and hours become even more negative, which together

make the Okun’s coefficient in recessions larger.

Table 2 – Decomposition regression results – Okun’s coefficient, total hours and labor

productivity estimates

Independent variables:

Output growth (equation (3))

Labor hours ( ) (equation (8))

Productivity ( ) (equation (9))


Constant 4.8*** -0.4 5.2***

(0.7) (0.4) (0.8)

Recession dummy ( ) -1.0*** 0.165 -1.2***

(0.1) (0.2) (0.1)

Unemployment -0.8*** -1.1*** 0.4**

(0.072) (0.162) (0.158)


-1.3*** -1.3 0.1**

(0.1)a (0.1)a (0.1)a

Country and time fixed effects

yes yes yes

0.6 0.6 0.3

Note: The table reports estimated coefficients and standard errors from equations (3), (8) and (9). Coefficients

followed by *** are significant at 1%, ** are significant at 5%, and * are significant at 10%.


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4.2 Interpreting the decomposition

In this section we begin to interpret the results from the regressions just presented. To do this we go

back and expand our simple theoretical framework.

To understand consider the relationship between labor hours, L, and the unemployment rate,

U. The first step is that labor hours depend on the number of workers, N , and hours per worker, H=L/N:

(10)

The link between the unemployment rate and hours worked comes most directly from the fact that

variations in unemployment are naturally related to variations in the number of workers. There are several

links in this chain which are easily seen in the following identity:18

(11)

where N is the number of workers, Emp is the number of people employed, LabForce is the labor

force, and Pop is the overall working-age population. The first term on the right-hand side,

reflects the fact that the number of workers is potentially different from the number of people employed,

Emp. One person employed might have two or more jobs, and thus count as more than one worker. In U.S.

data, this term reflects the gap between the payroll and household surveys.19 The second term is employment

as a share of the labor force, which is by definition equal to (1-U). Lastly, the third is the labor-force

participation rate, LFPR.

Note that the log of (1-U) is (approximately) –U, hence, combining (10) and (11), and taking log-

differences:

(12)

18 Gordon (2011) uses a similar, somewhat expanded, identity. 19 In practice, there are also coverage differences between the payroll and household surveys. The identity abstracts from that issue.

17

Other things equal, a one percentage point increase in the unemployment rate reduces hours worked

by one percent. In the data, however, we would not expect other factors on the right-hand-side to be

invariant. For example, when unemployment rises, we would expect that hours per worker fall, the gap term

falls (as workers lose second or third jobs), and labor-force participation might fall (reflecting a shift towards

home production or, for other reasons, a reduction in labor force attachment). So we expect the OLS

coefficient to exceed unity in absolute value.

Now consider the projection of labor productivity growth on unemployment change, as reflected in

. Suppose aggregate output is approximated by a constant-return production function, which in growth

rates, it takes the form:20

(13)

where a is technology; k is capital; and lq is labor quality/composition, which reflects the education

and age composition of the labor force. The workweek of capital, w, and effort per hour, e, represent

(typically unobserved) intensity or utilization margins. Labor hoarding, for example, would show up in the

production function as variation in effort.

Rearranging (13), labor productivity can change because of capital-deepening, , labor

quality, cyclical variations in utilization, or technology:

(14)

We can use this expression to understand why the sign of the reduced-form in equation (7) is

theoretically ambiguous. Intuitively, is positive if, in recessions, when unemployment rises, productivity

also rises. (In other words, is positive if productivity is countercyclical.) The first two terms in (14)

might push to be positive. Suppose unemployment rises and hours worked fall. Then, since capital is

relatively smooth, capital deepening tends to rise. This capital-deepening effect, which reflects the

20 Suppose the production function takes the translog form, which provides a flexible second-order approximation to any function, then the factor shares/output elasticities α and 1-α are time-varying. In the Cobb-Douglas case, the shares are constant over time. Basu and Fernald (2001) discuss the more general case in which an aggregate constant-returns production function may not exist and how, in practice, the effects are likely to show up as procyclical movements in the cyclicality of the aggregate Solow residual (measured TFP, the empirical counterpart of a).

18

diminishing returns to labor alone, thus tends to push productivity to be countercyclical. Labor quality also

tends to push to be positive, to the extent that low-skilled workers disproportionately tend to lose jobs in

downturns. On the other side, tends to be pushed to be negative by fluctuations in utilization. That is,

utilization falls in recessions, when unemployment is high, as firms hoard labor and reduce the workweek of

capital (e.g., going from two shifts a day to one).21 Finally, the effects of total factor productivity (TFP)

growth, aΔ , on could go in either a positive or a negative direction. In real-business-cycle models,

positive technology shocks raise labor productivity and would typically reduce unemployment (though many

models do not explicitly model unemployment as distinct from total hours worked). This pro-cyclical

productivity pushes to be negative. Empirically, however, after controlling for utilization, labor

productivity and unemployment appear positively correlated conditional on a technology shock ( pushed

positive; see Gali 1999, and Basu, Fernald, and Kimball, 2006).

With these equations in mind, what do we expect for the Okun coefficient β? In the simplest case,

suppose that when unemployment changes, there are no systematic changes in hours per worker, the

employment-worker gap, labor-force participation, or population (immigration would be the channel for

population to change). Also suppose that technology is not systematically related to unemployment, as would

be the case if most fluctuations reflect demand shocks. In this simple case, and . If at

the same time, capital, labor quality, and utilization do not change systematically with unemployment, then,

from (14) . Hence, . It follows that, in this simple example,

. That is, the Okun coefficient is the negative of labor’s share in income. This result is

intuitive in terms of the production function (13). A one percentage point increase in unemployment reduces

labor hours by one percent, while leaving all other inputs and technology unaffected. So output falls by

labor’s share.

21 See Basu, Fernald, and Kimball (2006) for discussion of the importance of procyclical fluctuations in utilization margins in productivity measurement.

19

As is well known, and as we confirm in our empirical results, in almost all cases the magnitude of

Okun’s coefficient is substantially larger than labor’s share. This larger coefficient necessarily reflects the

systematic cyclicality of other terms in (12) or (14). First, the increase in the unemployment rate is also

associated with other changes that tend to reduce total hours worked by a greater amount. Hours per worker

tend to fall; some people might lose a second or third job, reducing payroll workers relative to number of

people employed in at least one job; eventually, workers might drop out of the labor force. Second, labor

productivity may decline if utilization of capital and labor tends to fall. In sum, the effects on hours and

productivity are such that output falls by more than just the direct effect of the rising unemployment rate

would imply.

5 Applying the Decomposition to U.S. Data

[In process, but utilization appears to have become less important prior to the crisis—but much more

important in explaining productivity movements in the crisis.]

6 What happened in 2007?

Our results so far point to the importance of secular changes and the business cycle in explaining

variations in the Okun’s coefficient. Figure 2 confirms this assertion but also shows that during the most

recent there was a sharp increase in the absolute value of the Okun’s coefficient. In this final section we

consider whether 2007 recession was an aberration from the typical patterns we have described or just a

reflection of usual recessionary effect.

To try to answer this question, we depart from equations (3), (8) and (9), and split the recession

dummy, , into recessions dated before 2007, and recessions dated since 2007, isolating the Great

Recession. We estimate:

(15)

20

(16)

(17)

where , , and are defined as before, is a dummy for recession quarters before 2007,

is a dummy for recession quarters since 2007 (inclusive), and we also include controls for country

fixed effects.

Table 3 provides summarizes the results. The first column provides the estimation results for

equation (15), the second provides the results for equation (16), and the third show the results for equation

(17). Analogous to Table 2, one should interpret as the effect of unemployment on output growth, hours

worked and productivity, respectively, in non-recessionary periods. During recessionary periods before 2007,

the effect of unemployment on those same three variables is given by . And for recessionary periods

since 2007, the overall effect of unemployment becomes . For ease of exposition, the table

provides estimation results for , , and . The table shows that the 2007 recession seems to

be a scaled up version of the previous ones. Focusing on the first column, the results show that when

controlling for country fixed effects, the Okun’s coefficient is not only larger in recessions but even larger

when considering the 2007 Great Recession in isolation. The second column shows that the procyclical

effects of labor hours were also amplified during the latest recession. And finally, the last column shows that

the increase in the Okun’s coefficient can also be explained by the reversal in sign of the effects of

productivity, which has become procyclical in this last recession. This last point can also be seen in Figure 3

which shows that after years of being positive or near zero, the median effect of unemployment on

productivity turned negative.22

22 Note that the differences between the results for the estimated equations (9) and (17) reported in the third column of Table 2 and Table 3, respectively slightly differ because the former includes both country and time fixed effects, while the latter only includes country fixed effects. The pattern is, however, the same. During recessions, productivity tends to become procyclical, or less countercyclical than during non-recessionary periods.

21

These results confirm our assertion that recessions are different from expansions but it also shows

that the latest recession went far deeper than the previous ones. This was visible in Figure 2 which showed

that the median Okun’s coefficient across countries approached its 1980s levels after decades of steady

decline. Unfortunately, it is still too soon to tell if those effects are permanent, temporary, or only the result

of a much deeper and worldwide drop in growth and employment.

7 Conclusion

We interpret Okun’s stylized facts as a “macroscope” to provide insights into macro modeling across

countries. We have found several patterns that call for additional study. [To be completed]

22

Table 3 - Decomposition regression results – Okun’s coefficient, total hours and labor

productivity estimates - The Great Recession


Output growth (equation (15))

Labor hours ( ) (equation (16))

Productivity ( )

(equation (17)) Dependent variables:

Constant 3.1*** 0.7*** 2.4***

(0.0) (0.0) (0.1)

Recession before 2007 dummy

-0.9*** -0.1 -0.8***

(0.1) (0.1) (0.1)

Recession after 2007 dummy

-2.7*** 0.2 -2.9***

(0.3) (0.2) (0.4)

Unemployment -1.1*** -1.2*** 0.1

(0.1) (0.1) (0.1)

Unemployment under recession before 2007

-1.4*** -1.4 -0.1*

(0.1)a (0.1)a (0.1)a

Unemployment under recession after 2007

-2.5*** -1.8*** -0.7**

(0.4)b (0.2)b (0.4)b

Country fixed effects yes yes yes

0.4 0.5 0.1

Tests: P-values

0.016 0.018 0.147

23

0.000 0.238 0.000

Note: The table reports estimated coefficients and standard errors from equations (15), (16), and (17).

Coefficients followed by *** are significant at 1%, ** are significant at 5%, and * are significant at 10%.


b Statistical significance and standard deviation for estimated .

8 Appendix

8.1 Data coverage

Table 4 - Data coverage and OECD recessions

Output and unemployment data coverage and OECD Recessions

Country Data Coverage OECD Recessions

Australia 1970Q1-2011Q4

1970Q2-1972Q3, 1973Q4-1975Q4, 1976Q3-1978Q1, 1981Q3-1983Q2, 1985Q3-1986Q3, 1989Q3-1991Q4, 1994Q2-1997Q1, 2000Q1-2001Q1, 2002Q2-2003Q1,

2005Q3-2006Q2, 2008Q1-2009Q2, 2010Q1-2012Q1

Austria 1970Q1-2011Q4


2008Q1-2009Q2, 2011Q2-2012Q1

Belgium 1970Q1-2011Q4


2008Q1-2009Q2, 2011Q2-2012Q1

Canada 1970Q1-2011Q4


2007Q4-2009Q2

Denmark 1970Q1-2011Q4


2000Q3-2003Q2, 2008Q2-2009Q3

Finland 1970Q1-2011Q4

1970Q3-1971Q4, 1973Q4-1978Q2, 1980Q3-1982Q1, 1982Q4-1986Q2, 1990Q1-1993Q1, 1995Q2-1996Q3, 1997Q4-1999Q3, 2000Q3-2003Q2, 2007Q4-2009Q2

France 1970Q1-2011Q4


Italy 1970Q1-2011Q4


2011Q2-2012Q1

Netherlands 1970Q1-2011Q4


2008Q1-2009Q2, 2011Q2-2012Q1

New Zealand 1970Q1-2011Q4


2007Q3-2009Q1, 2010Q2-2012Q1

Norway 1970Q1-2011Q4


Sweden 1970Q1-2011Q4


United Kingdom 1970Q1- 1970Q1-1971Q1, 1973Q2-1975Q3, 1979Q2-1981Q2, 1983Q4-1985Q4, 1988Q4-

24

2011Q4 1992Q3, 1994Q4-1996Q4, 2000Q2-2002Q4, 2004Q1-2005Q1, 2007Q4-2009Q2

United States 1970Q1-2011Q4

1970Q1-1970Q4, 1973Q2-1975Q2, 1978Q4-1982Q4, 1985Q4-1987Q1, 1990Q1-1991Q3, 1994Q3-1995Q4, 2000Q2-2003Q1, 2007Q4-2009Q2

Table 5 - Data coverage - total hours and labor productivity

Data Coverage for Total Hours and Labor Productivity

Country Total hours Productivity

Australia 1972Q1-2011Q4 1972Q1-2012Q1

Austria 1990Q1-2011Q4 1972Q1-2012Q1

Belgium 1972Q1-2010Q4 1972Q1-2012Q1

Canada 1972Q1-2011Q4 1972Q1-2012Q1

Denmark 1972Q1-2011Q4 1972Q1-2012Q1

Finland 1972Q1-2011Q4 1972Q1-2012Q1

France 1972Q1-2011Q4 1972Q1-2012Q1

Italy 1972Q1-2011Q4 1972Q1-2012Q1

Netherlands 1972Q1-2011Q4 1972Q1-2012Q1

New Zealand 1972Q1-2012Q1 1972Q1-2012Q1

Norway 1972Q1-2011Q2 1972Q1-2012Q1

Sweden 1972Q1-2011Q4 1972Q1-2012Q1

United

Kingdom 1972Q1-2011Q3 1972Q1-2012Q1

United States 1972Q1-2010Q4 1972Q1-2012Q1

Table 4 and Table 5 present details about our data coverage for output growth and unemployment

series, OECD recession dates, and total hours worked and productivity. Table 4 shows that our data consists

of a balanced panel of 14 countries, and our unemployment and output series are at a quarterly frequency,

running from the first quarter of 1970 to the first quarter of 2012. Table 5 shows that the data series for hours

25

worked and productivity, for the same panel of countries are slightly more limited. The source for all data is

the OECD.

For all series except unemployment, we calculate the 4-quarter change in logs and those all feed

regressions described in the paper. The exception, unemployment rate enters all regression as a simple 4-

quarter change.

While the series for unemployment rate and real GDP are obtained directly from OECD, we build

our series for total hours worked and productivity. OECD provides data for hours worked per worker and the

total number of employees, which multiplied gives us our measure for total hours worked. We build our

measure of productivity as output per hour, dividing (or taking the log difference) the real output by the

constructed measure of total hours.

8.2 Robustness

8.2.1 Okun’s Law – gap version

In the above exercises we considered a simple version of the Okun’s Law in which we relate the

change in real GDP growth and the change in unemployment rate. Alternatively, we could explore the

relation between the change in real output gap growth rate and the change in unemployment gap. To explore

this venue, we once more make use of the OECD data which provides their own estimations for both the

output gap and the natural level of unemployment. We estimate the analogous of equation (15), while using

instead the gap variables:

(18)

In analogy with Table 3, Table 6 presents the results of the regressions when including country and or

time fixed effects. The table shows the same patterns obtained in the benchmark analysis.

26

Table 6 - Regression results - Okun's Law estimates using gaps


(1) (2) (3)


Constant 0.6*** 0.8*** 0.8***

(0.0) (0.3) (0.3)

Recession dummy ( )

-1.2*** -0.9*** -0.9***

(0.1) (0.1) (0.1)

Unemployment -1.1*** -0.8*** -0.8***

(0.1) (0.1) (0.1)


-1.6*** -1.2*** -1.2***

(0.1)a (0.1)a (0.1)a

Country fixed effects yes no yes

Time fixed effects no yes yes

0.5 0.7 0.7

Note: The table reports estimated coefficients and standard errors from equation (18). Coefficients followed by

*** are significant at 1%, ** are significant at 5%, and * are significant at 10%.


8.2.2 Additional results

Table 7 and

27

Table 8 complement the panel analysis and provide the regression results by-country. The table

shows that for most countries the patterns remain. During recessions the Okun’s coefficient is edged up and

the 2007 recession came with an even larger increase in the absolute value of the Okun’s coefficient. The

procyclical properties of labor hours and the attenuation effect of productivity also seem to hold in normal

quarters (non-recessionary ones). The recession comes together with an increase in the negative effect

unemployment on labor hours, and the attenuation effect of productivity is reduced or even reversed.

Table 7 - Okun's coefficient decomposition - by-country estimation results

Estimation Results Regression (3) Regression (8) Regression (9)

Countries:

Australia -0.9*** -0.3 -1.4*** 0 0.5** -0.3

Austria -1.5** -0.3 -1*** 0.1 -0.4 -0.4

Belgium -0.7*** -0.3 -0.8*** -0.7*** 0 0.4

Canada -1.4*** -0.2 -1.1*** -0.3** -0.2 0.1

Denmark -1.2*** -0.7*** -1*** -0.6** -0.2 0

Finland -1*** -0.5* -1*** -0.4* 0 -0.1

France -1.3*** 0.1 -0.8*** -0.3 -0.5* 0.3

Italy -0.5 -0.5 -1.1*** 0.4* 0.6* -1*

Netherlands -0.8*** -0.6** -1.2*** -0.1 0.4 -0.4

New Zealand -1.4*** -0.2 -2*** 0.5** 0.5* -0.7

Norway -0.6** -1.5*** -1.6*** 0.5 1*** -2***

Sweden -1.1*** -0.4 -1*** -0.2 -0.1 -0.2

United Kingdom -1.3*** -0.8** -1.9*** -0.1 0.5** -0.7*

United States -1.4*** -0.6*** -1.5*** 0.1 0.1 -0.7***

Note: The table reports estimated coefficients and standard errors from equations (3), (8) and (9). Coefficients followed by *** are significant at 1%, ** are significant at 5%, and * are significant at 10%.

28

Table 8 - Okun's coefficient decomposition - by-country estimation results

Estimation Results

Regression (15) Regression (16) Regression (17)

Countries:

Australia

-0.9*** -0.4 0.2 -1.4*** 0 -0.4 0.5** -0.4 0.7*

Austria

-1.5** 0.5 -2.4** -1*** 0.3 -0.9 -0.4 0.2 -1.6**

Belgium

-0.7*** -0.3 -2.2*** -0.8*** -0.7*** -0.8** 0 0.4 -1.5***

Canada

-1.4*** -0.1 -0.8*** -1.1*** -0.3* -0.8*** -0.2 0.2 0.1

Denmark

-1.2*** -0.4** -0.6 -1*** -0.6** -1.3*** -0.2 0.2 0.8*

Finland

-1*** -0.4 -4*** -1*** -0.4* -0.8* 0 0 -3.1***

France

-1.3*** 0 -0.4 -0.8*** 0.1 -0.9*** -0.5* 0 0.4

Italy

-0.5 -0.1 -3.1** -1.1*** 0.5** -0.6 0.6* -0.7 -2.4***

Netherlands

-0.8*** -0.6** -5.7*** -1.2*** -0.1 -1.7*** 0.4 -0.5 -4***

New Zealand

-1.4*** -0.1 -0.6 -2*** 0.5* 1.3** 0.5* -0.6 -2**

Norway

-0.6** -1.4*** -3.8*** -1.6*** 0.6** -4.8*** 1*** -2*** 1

Sweden

-1.1*** -0.1 -2.5*** -1*** -0.1 -0.9*** -0.1 0 -1.6**

United Kingdom

-1.3*** -0.4* -2.5*** -1.9*** -0.2 0.6* 0.5** -0.3 -3.2***

United States

-1.4*** -0.5** -0.7*** -1.5*** 0.3 0 0.1 -0.7*** -0.8***

Note: The table reports estimated coefficients and standard errors from equations (15), (16), and (17). Coefficients followed by *** are significant at 1%, ** are significant at 5%, and * are significant at 10%.

29

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