Selected Issues

Abstract

Selected Issues

Labor Market Slack and the Output Gap in Korea1

A. Introduction

Output gap estimates are needed to inform policy discussions. Given that labor is the most important input into the production, estimates of available capacity on the labor market are in turn informative for output gap estimates. However, the traditional measure of unemployment yields an incomplete picture of the true degree of under-utilized resources on the labor market. This Selection Issues Paper, first formulates a simple multivariate filter, based on Blagrave et al. (2015), with a strong link between labor market slack and the output gap through a production function. We then discuss how the traditional measure of unemployment can broadened to yield a more complete picture of available resources on the labor market in Korea. We use this data to estimate the multivariate filter and show how using broader measures of available labor resources affect the estimated output gap

1. Estimates of output gaps are key inputs into macroeconomic policy making. The output gap denotes the difference between the actual and potential output, where the latter often is defined as the maximum level of output an economy can produce without generating inflationary pressure (Okun, 1962). An estimate of the output gap is thus key for policymakers, as it helps inform their view on the appropriate stance of policy.

2. Output gaps are usually estimated using either a production function or filtering methods. The simplest method relies on a univariate statistical filter, such as the Hodrick-Prescott (HP), which smooth out fluctuations in output at business cycle frequencies (DeMasi, 1997). The production function approach is an alternative. This approach considers all input to the production separately. By combining the smoothed version through a production function one can arrive at a measure of potential output (see e.g. Giorno et al., 1995). Another alternative is a multivariate filter (MVF) approach. This approach works by estimation of a system of economic equations with observed and unobservable variables. For recent examples see Blagrave et al. (2015) or Alichi et al. (2017).

3. The degree of labor market slack is informative for the output gap calculation. The motivating observation, is that information about the degree of under-utilization of labor market resources (slack) is important to appropriately assess whether the economy is operating above or below potential. Economically, a labor market operating above potential will create an upwards pressure on wages which in turn lead to inflationary pressure. Conversely, idle labor market capacity will create downwards pressure on wages, which in turn will cause disinflation.

4. This paper proposes a modified multivariate filter (MVF) with a tight link between labor market slack and the output gap. Generally, lower labor market utilization than potential should be associated with an economy running below capacity, i.e. a negative output gap. This is because 1) labor is the most important input into the production function, and 2) idle workers on the labor market means that the economy could potentially produce a higher level of output if all workers were employed. To capture this basic idea, we modify the MVF by Blagrave et al. (2015) by tying output and labor market slack closer together through a production function.

5. The paper also contributes by discussing how to broaden the measure of labor utilization. Usually labor market utilization is measured through regular unemployment. This concept is well-defined but does not fully capture the degree of under-utilized resources on the labor market. First, it does not include the number of workers outside the labor force who are ready to take employment. Second, it does not contain part-time workers who are willing and able to work longer hours. To partly address these issues, we construct an alternative measure for labor market slack, which augments the traditional measure of unemployment on the extensive margin. We argue that this measure provides a more complete measure of resource utilization on the labor market, e.g. as witnessed by a clearer relationship with inflation (the Phillips Curve).

6. The remainder of the paper is organized as follows. We first formulate a revised multivariate filter (MVF), where labor market slack and the output gap are tied together through a production function (Section B). We then discuss how to augment unemployment to better measure idle resources on the labor market in Korea (Section C). Drawing the method and data presented, Section D presents estimates for labor market slack and output gaps. Finally, Section V concludes.

B. A Multivariate Filter With Labor Market Gaps

7. This section presents a multivariate filter augmented with a tighter link between the output gap and labor market slack. The filter is a modified version of the MVF presented in Blagrave et al. (2015), which we modify in three ways given this paper’s focus on the labor market. First, we introduce an equation that links output, TFP, and employment through a production function. This allows us to write the output gap as a combination of labor market slack and TFP deviations. Second, we introduce a bloc of equations to separate trend and cyclical TFP. Third, we formulate the model such that it allows for a flexible representation of labor market utilization ranging from ordinary unemployment to a broader measures of non-utilized resources on the labor market (empirical measures to be discussed in Section C).

8. The filter takes point of departure in a production function. Specifically, we assume that output can be represented using a Cobb-Douglas production function that takes capital (K), employment (E), and total factor productivity (A) as input.

Y=AKαE1α(1)

This equation can be rewritten using that employment (E) is the product of the potential labor force (PLF) and the non-employed fraction of this potential labor force (u).

Y=AKα[(1U)PLF]1α(2)

Notice, that the definition of both PLF and u will vary below as we use different measures of labor market slack. When regular employment is used, u is measured using regular unemployed workers as percent of PLF which will be measured as the actual labor force. When broader measures are used, u is measured using augmented unemployment in percent of PLF which is the augmented labor force.

9. The output gap can be written as a function of the TFP gap and labor market slackness. Based on equation (2) we can write the output gap (y) as the sum of a the TFP gap (a), and labor market slack (u).2

y=a+(1α)u(3)

Here the output gap (y) is expressed as percent deviation from potential GDP (Y¯t), while the TFP gap (a) is expressed in percent deviation from the structural level of TFP (A¯t). Finally, the labor market gap is expressed as the deviation (in percentage points) of the degree of under-utilization of labor from the structural degree of under-utilization (U¯t). In addition, we allow the output gap to be stochastic shocks. That is, we allow the output gap to change temporary without corresponding change in the TFP or labor market gap.

yt=φyt1+ϵtY(4)

This stochasticity represents the uncertainty surrounding the output gap estimates. Indeed, the actual output gap is not observed why it can only be estimated with a significant degree of uncertainty, which is represented by the error term (ϵtY) in equation (4).

10. Structural TFP is modelled as a stochastic process. This process is governed by a long term deterministic growth rate (Gss), as well as stochastic shocks that can shift both the TFP level (ϵtA¯) or temporary change the growth rate (ϵtG) of TFP.

A¯t=A¯{t1}+Gt+ϵtA¯(5)
Gt=θGSS+(1θ)G{t1}+ϵtG(6)

The stochastic process for TFP is illustrated in Figure 1. Here Gss is the long-term rate that TFP will grow according to absent any stochastic shocks. ϵtA¯ is a stochastic shock that can permanently increase or decrease the level of TFP. Finally, ϵtG is a shock to the growth rate in TFP, which temporarily causes the growth rate of TFP to fall below, or rise above, the long term growth rate Gss.

11. The level of structural under-utilization of labor market resources is modelled as a stochastic proces. The structural level of labor market under-utilization is governed by a long run steady state level, U¯ss, which will materialize absent any stochastic shocks. The structural level of labor market utilizatoin is also affected by (1) transitory shocks to the level (ϵtU¯), and (2) the realization of a stochastic trend (gtU¯). The stochastic trend is added to allow for more permanent deviations from the long run steady state level. Economically, such deviations can be brought about by a demand shock which creates hysteresis effects as unemployed workers skills are depleted after a prolonged period of unemployment (Blanchard and Summers, 1986). The structural level of under-utilization of labor market resources can also increase following a supply shock, which renders the skill set of a certain fraction of the potential labor force obsolute (Braun et al., 2009).

uA03fig01

Stochastic Process for the Structural Level of TFP

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

U¯t=τ4S¯ss+(1τ4)U¯t1+gU¯t+ϵtU¯(7)
gU¯t=(1τ3)gU¯t+ϵtgU¯t(8)

The process for under-utilization of labor market resources is illustrated in Figure 2. Here U¯ss is the steady state level of under-utilization which would materialize in the absence of any shocks. ϵtU¯ is a stochastick shock which temporarily raises the structural level of under-utilization. gU¯t is a stochastic trend, and shocks to this raises the structural level in a more persistent way (Figure 2).

12. The labor market gap is defined as the difference between actual and structural under-utilization of labor market resources.

ut=u¯tut(9)
ut=τ2ut1+ϵtu(10)

This means that a positive gap implies that the labor market operates above potential, while a negative gap means it operates below potential (equation 9).3 In addition, the labor market gap is subject to stochastic shocks representing the uncertainty surrounding the correct level of the gap (equation 10).

13. A Phillip Curve links the output gap to inflation. As a final equation we include a New Keynesian Phillips curve in the filter (Gali, 2015).

πt=λπt+1+(1λ)πt1+βyt+ϵtπ(9)

This equation links current, future, and past inflation with the output gap. This captures the idea that a positive output gap (an economy operating above potential) is expected to generate cost pressures which in turn generates inflation as companies pass on the higher costs to their consumers. The existence of both current, future, and past inflation in the equation captures the inertia in the price setting process. The equation also includes a stochastic shock term (ϵtπ), which allows for inflation to also be affected by other shocks.

uA03fig02

Stochastic Process for Structural Under Utilization of Labor Market Resources

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

C. Measuring Under-Utilization of Labor Market Resources

14. A key empirical input into the output calculation is the degree of under-utilization of labor market resources. To estimate the filter presented in Section B and get measures of the output gap one an empirical measure for Ut. Often this is done by feeding in a measure of unemployment (Blagrave et al, 2015). Empirically, unemployment can be measured either using survey data (from the labor force survey) or register data (on the number of recipients of unemployment benefits). In Korea, only survey base data is published, which shows that the unemployment rate since 1980 has varied around 3–4 percent of the labor force with a spike in 2000 and later in 2009.

uA03fig03

Unemployment Rate

(Percent of labor force)

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Sources: Haver Analytics.

15. However, the regular unemployment rate does not fully capture degree of under-utilization of resources on the labor market. According to the international definition of unemployment, workers are categorized as unemployed if they are (i) without work; (ii) available to start work within two weeks; and (iii) actively engaged in job searching activities (International Labor Organization, 2018). This definition is narrow, however, and does not fully captures the degree of slack on the labor market. Indeed, wider definitions include both an additional external and internal margin (International Labor Organization, 2018). The additional internal margin includes persons that are without work, but are not able to start without two weeks, or are not actively engaged in job searching activities. The additional external margin includes workers that are already employed but want to work more hours. The former group is classified as outside the labor force as per the traditional classification, while the latter group is classified as employed.

16. This is also manifested in a weak relationship between inflation and regular unemployment. Economically, the relationship between inflation and regular unemployment is captured in the Phillips curve (Phillips, 1958). This relationship is expected to be tight and negative, as lower cyclical unemployment creates an upwards pressure on wages. As labor is the most important input into the production function, the higher wages will translate into higher inflation. For most countries the Phillip curve relation is indeed found to be negative (Bhattarai, 2016). However, for Korea the relation is weak, and not negative for all time periods (Bhattarai, 2016). One interpretation of this result is that unemployment in Korea does not fully capture the degree of unutilized labor market resources.

17. We construct broader measures of labor market under-utilization. Both measured are computed by extending the traditional measure for unemployment along the extensive margin. First, we augment the unemployment by including discouraged workers expressed in percent of the labor force (also extended with discouraged workers). Discouraged workers are workers of the legal working age that wants to work, and have been looking for a job over the last year, but are not currently engaged in job search. Second, we augment unemployment with persons that are classified as inactive for unspecified reasons. These are reasons other than childcare, house-keeping, schooling, old age, or disabilities. The alternative measures for labor market slack are depicted below. The levels hovers around 5.5 and 10.5 percent, respectively, and generally shows more volatility on business cycle frequency than the regular unemployment measure. Our measures relate to the Labor Utilization Indicator 2 published by Statistics Korea, which augments regular unemployment with workers that potentially are in the labor force. However, the short time period of this series precludes us from using this as input to the filter. We consider the measure with discouraged workers most relevant as it is confined to workers relatively close to the labor market, while still being broader than the regular unemployment measure.

uA03fig04

Labor Market Slack Measures

(Percent)

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Haver Analytics.
uA03fig05

Labor Market Slack Measures

(Deviation from Average, Perecentage Points)

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Haver Analytics.

18. The broader measure of under-utilization yields a negative Phillips Curve. The figure below shows the relationship between the alternative measure of under-utilization including discouraged workers and inflation. Unlike regular unemployment this measure yields a negative relationship between inflation since 2001. This suggests that this broader measure better measures under-utilization of resources, as a larger degree of under -utilization is associated with a higher value of inflation.

uA03fig06

Phillips Curve, 2001–2018, Korea

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Haver Analytics.
uA03fig07

Modified Phillips Curve, 2001–18. Korea

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Haver Analytics.

19. Below we estimate the output gap using regular unemployment as well as the broader measures of labor market under-utilization. We do this within the multivariate filter framework formulated in Section B. This will allow us to gauge how the chosen measure of underutilization affect the estimated output gap.

D. Results

20. This section provides estimates of the output gap during the period 2007–2023. The model is estimated using annual data from 2001 for the gross domestic product, inflation, employment, TFP, unemployment along with the alternative measures for labor market slack outlined above. Up to 2017 historical data is used, and for 2018–23 forecasts are applied. The parameters in the model are estimated using Bayesian estimation.4

21. The estimated output gap based on regular unemployment. According to this estimation the output gap was around +1 percent in 2007/08 before it turned negative in 2009. It went back to up to slightly below 1 percent in 2010–11, before it turned negative again in 2012. From 2012 to 2014 the gap widened to around -0.8 percent before it started to narrow. The output gap generally has the same sign as the labor market, although 2010, 2012, and 2013 are exceptions. Such exceptions are possible if the TFP gap pull in the opposite direction of the labor market gap. From 2018 and onwards the output gap displays a close correlation with the labor market gap, however, as TFP is projected to evolve according to potential.

uA03fig08

Output and Labor Market Gap Based on Regular Unemployment

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Staff Estimations.

22. The estimated output gap based on unemployment augmented with discouraged workers. Here, we augment our measure of under-utilization from regular unemployment to regular unemployment plus discouraged workers. This produces a more volatile labor market and output gap, and more consistency between the two measures up to 2012. Both the output and labor market gap deteriorate more in 2009, but during 2012–17 the unemployment gap remains positive while the output gap is negative. From 2017 and onwards the two gaps are projected to move in tandem.

uA03fig09

Output and Labor Market Gap Based on Regular Unemployment + Discouraged Workers

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Staff Estimations.
uA03fig10

Output and Labor Market gap Based on Regular Unemployment + Inactive Workers for Unspecified Reasons

Citation: IMF Staff Country Reports 2019, 133; 10.5089/9781498314824.002.A003

Source: Staff Estimations.

23. The estimated output gap when using unemployment augmented with workers classified as inactive for unspecified reasons. This also shows a volatile labor market gap, while the output gap is broadly similar to the gap produced when using regular unemployment. This measure indicates the largest labor market gap in 2017, and produces a consistent labor market and output gap from 2017 onwards.

24. Summarizing the robust findings across all three models. First, up to 2017 the labor market and output gaps display somewhat conflicting signals, with some years of opposite signs. This is because deviations in TFP from trend also contribute to the output gap. Second, from 2017 both the output and labor market gap are projected to be negative across all models. This is because TFP is projected to grow according to trend, why the only factor contributing to the output gap is the labor market gap. Third, the labor market gaps computed using broader measures of under-utilization than regular unemployment display larger fluctuations. The results based on the slack measure with discouraged workers (paragraph 22) may be most relevant for the reasons laid out above (paragraph 17).

E. Conclusion

25. This paper draws on existing MVF literature to formulate a model with a link between the output gap and under-utilization of labor market resources. We do this starting from the basic observation that lower labor market utilization ceteris paribus should be associated with an economy running below capacity. To capture this basic idea, we modify the MVF by Blagrave et al. (2015) by tying output and labor market slack together through a production function.

26. We also discuss how to best measure under-utilization of labor market resources in Korea. Often labor market under-utilization is measured by the unemployment rate. Although well-defined, this measure does not fully capture the amount of under-utilized resources on the labor market. Specifically, it does not capture the workers outside the labor force that are able and willing to work, but are not currently engaged in active job-search. To address this, we construct an alternative measures for under-utilization, which augments regular unemployment with workers outside the labor force that are potentially able to take an incoming job offer. We show that this measure produces a more standard Phillip curve, than when only using unemployment.

27. We feed the revised measure of under-utilization into the revised MVF model to produce estimates for the labor market and output gap. Three robust conclusions across the models emerge. First, up to 2017 the estimated labor market and output gaps display somewhat conflicting signals, with some years of opposite signs. This is because deviations in TFP from trend also contribute to the output gap. Second, from 2017 onwards both the labor market and output gap is projected to be negative across all models, as TFP is projected to grow according to trend. Third, in general the labor market gaps computed using broader measures of utilization display a higher degree of variation on business cycle frequency.

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1

Prepared by Niels-Jakob Harbo Hansen based on the forthcoming working paper “Labor Market Slack and the Output Gap” by Niels-Jakob Harbo Hansen, Gee Hee Hong, Joannes Mongardini, and Fan Zhang. We are grateful to Signe Krogstrup, Tarhan Feyzioglu, Sean Craig, Rui Xu, Sohrab Rafiq, Edda Zoli, Patrick Blagrave, Kadir Tanyeri, and Joannes Mongardini for useful discussions and suggestions. All remaining errors are our own.

2

This equation is derived by logging equation (2) and subtracting the expression for potential GDP. We assume that capital is at its structural level.

3

This formulation is done to make the interpretation of the labor market gap consistent with the interpretation of the output gap.

4

For details on the model estimation see IMF Working Paper “Labor Market Slack and the Output Gap” (forthcoming).

Republic of Korea: Selected Issues
Author: International Monetary Fund. Asia and Pacific Dept