Sectoral Shifts or Aggregate Sectoral Shifts or Aggregate Shocks?Shocks?

A New Test of Sectoral Shifts HypothesisA New Test of Sectoral Shifts Hypothesis

Yanggyu ByunYanggyu ByunKorea Economic Research InstituteKorea Economic Research Institute

Hae-shin HwangHae-shin HwangTexas A&M UniversityTexas A&M University

Sectoral Shifts HypothesisSectoral Shifts Hypothesis

Two components of unemploymentTwo components of unemployment

- unemployment caused by aggregate - unemployment caused by aggregate shocksshocks

- unemployment caused by sectoral - unemployment caused by sectoral shocksshocks

Hypothesis: sectoral shifts of labor Hypothesis: sectoral shifts of labor demand havedemand have

- a significant effect on aggregate - a significant effect on aggregate unemployment rateunemployment rate

- and frictional U-rate (NRU) fluctuates - and frictional U-rate (NRU) fluctuates significantlysignificantly

Empirical TestsEmpirical Tests

Past empirical studiesPast empirical studies– Contradicting results: depend on the Contradicting results: depend on the

model specificationmodel specification

– Two types of modelTwo types of model•Lilien type - supports the hypothesisLilien type - supports the hypothesis•Abraham & Katz type - rejects the Abraham & Katz type - rejects the

hypothesishypothesis

Empirical Models and TestsEmpirical Models and Tests

Major empirical issuesMajor empirical issues

– How to separate the effects of How to separate the effects of aggregate shocks and sectoral aggregate shocks and sectoral shocks - most controversial issue in shocks - most controversial issue in past studiespast studies

– How to measure the size of layoffs How to measure the size of layoffs caused by sectoral shockscaused by sectoral shocks

Measure of Average Layoff RateMeasure of Average Layoff Rate

Employment growth of sector Employment growth of sector jj

: sector specific shocks: sector specific shocks

: effect of aggregate shocks: effect of aggregate shocks

additive and commonadditive and common

Layoffs caused by a large negative Layoffs caused by a large negative sectoral shockssectoral shocks

– for which for which

h tj

h h AStj t tj ( )

tj

tj th AS ( )

h AS t( )

h tj

Measure of Average Layoff RateMeasure of Average Layoff Rate

Average Layoff RateAverage Layoff Rate

This depends on the properties of This depends on the properties of distribution function of sectoral shocks - distribution function of sectoral shocks - How do we capture themHow do we capture them??

L E h h AS p h E h h

F h AS h AS E h AS

L h AS

t tj t tj tj tj

t t t tj tj t

t t

[m ax ( , ) | ( )] ( ) ( | )

( ( ) ; )[ ( ) ( | ( ))]

( ( ) , )

0 0 0

h h AS ftj t tj tj tj t ( ) , ~ ( ; )

Measure of Average Layoff Rate Measure of Average Layoff Rate (ALR)(ALR)

Lilien proposed the Lilien proposed the dispersion dispersion of the of the distributiondistribution

– Lilien's example of symmetric MPS of Lilien's example of symmetric MPS of ff1 1 to fto f22

– ff1 1 : both sectors grow at 2%, ALR=0%: both sectors grow at 2%, ALR=0%

– ff2 2 : -4% and +8%, average=2%, : -4% and +8%, average=2%, ALR=2%, higher unemployment rateALR=2%, higher unemployment rate

0

0.5

1

f2 ( =6) (ALR=2)

f1 ( =0) (ALR=0)

-4 2 14-10 8

Measure of Average Layoff RateMeasure of Average Layoff RateDispersion & SkewnessDispersion & Skewness

• Dispersion Dispersion σσ may be sufficient for may be sufficient for symmetric location-scale distributions. symmetric location-scale distributions. But it may not be sufficient for But it may not be sufficient for asymmetric distribution.asymmetric distribution.

• Example: Mean-Variance Preserving Example: Mean-Variance Preserving TransformationTransformation

-4 2 8 140

0.5

1

f1 ( =sk=0)

f2 ( =6, sk=0) (ALR=2)

f3 ( =6, sk=0.75) (ALR=1.5)

MVPT

Effects of Skewness on Approximation of LEffects of Skewness on Approximation of L

-1.6 -0.8 0 0.8 1.60

0.01

0.02

0.03

0.04

0.05

True ALR

H, SD

H, SD, SK (0.09)

2=0.5

-4 -2 0 2 40.05

0.1

0.15

0.2

0.25

True ALR

H, SD

H, SD, SK (0.07)

skewness

2=1.0

-0.09 -0.07 -0.05 -0.03 -0.01-0.05

0

0.05

0.1

0.15

True ALR

H, SD

H, SD, SK (0.11)

=-0.01

0.45 1.45 2.45 3.45-0.02

0.03

0.08True ALR

H, SD

H, SD, SK (0.07)

=0.5

skewness

Three-equation empirical modelsThree-equation empirical models

• Purging equationPurging equation → estimate sectoral → estimate sectoral shifts variables fromshifts variables from

– most controversial specificationmost controversial specification

– ASAStt include monetary variables include monetary variables (anticipated & unanticipated), time (anticipated & unanticipated), time trend, and 'unobservable' aggregate trend, and 'unobservable' aggregate non-monetary factors (AK)non-monetary factors (AK)

• Monetary equation Monetary equation → estimate → estimate unanticipated (DMR) and anticipated unanticipated (DMR) and anticipated (DMF) monetary factors(DMF) monetary factors

• Unemployment rate equation Unemployment rate equation → test → test hypothesis and compute NRUhypothesis and compute NRU

h h AStj t tj ( )

Purging EquationPurging Equation

• Lilien TypeLilien Type

• Abraham-Katz typeAbraham-Katz type

h = + a + a + + c +tj j0 j1 t j2s = 0

4

t -ss = 4

4

t -s j t -1 , j tja H t b DM R b DM F hjsr

jsf

h = + a + a + +tj j0 j1 t j2s = 0

4

t -ss = 0

4

t -s tja g t b DM R b DM Fjsr

jsf

tj j t -1 , j u tj

Purging EquationPurging Equation

• Lilien TypeLilien Type

• Abraham-Katz typeAbraham-Katz type

h = + a + a + + c +tj j0 j1 t j2s = 0

4

t -ss = 4

4

t -s j t -1 , j tja H t b DM R b DM F hjsr

jsf

h = + a + a + +tj j0 j1 t j2s = 0

4

t -ss = 0

4

t -s tja g t b DM R b DM Fjsr

jsf

tj j t -1 , j u tj

Purging EquationPurging Equation

• Estimation of dispersion and skewnessEstimation of dispersion and skewness– Lilien Type: from Lilien Type: from – Abraham-Katz type: fromAbraham-Katz type: from

• Theoretically, estimates of sectoral Theoretically, estimates of sectoral shocks are more compatible with the shocks are more compatible with the purpose than the innovation termspurpose than the innovation terms– because we wish to capture the because we wish to capture the

relationship between average layoff relationship between average layoff rate (ALR) and distributional rate (ALR) and distributional properties of sectoral shocksproperties of sectoral shocks

tj

u tj

tj

u tj

Monetary EquationsMonetary Equations

DMFDMFtt=predicted value of DM=predicted value of DMtt

DMRDMRtt=residuals=residuals

L ilien : D M = + + + e

A K : D M = + a + + e

t 0 ss=1

8

t - s ss=1

3

t - s ss=1

4

t - s t

t 0 1 ss=1

4

t - s ss=1

4

t - s t

a b DM c FEDV d UN

a t b DM c TB

UN UR URt t t ln ( / ( ))1

Unemployment Rates EquationUnemployment Rates Equation

• Lilien - ARDL model; AK - DL model Lilien - ARDL model; AK - DL model with AR(1) error termwith AR(1) error term

• Different number of lags (4 vs 8) for Different number of lags (4 vs 8) for σ σ and skand sk

• Coefficient of time trend is Coefficient of time trend is predetermined in AK model from a predetermined in AK model from a linear detrendinglinear detrending

L ilien : U R = + + + + +

A K : U R = + + + +

t 0 1 ss = 0

4

t -s ss = 0

4

t -s ss = 0

8

t -s ss = 0

4

t -s t

t 0 1 ss = 0

8

t -s ss = 0

8

t -s ss = 0

8

t -s t

t ss = 0

4

t -s t

t sk DM R UR

t sk DM R

r

Estimation of in AK ModelEstimation of in AK Model• AK's purging equationAK's purging equation

• AK's estimator of AK's estimator of – Estimate the purging equation by Estimate the purging equation by

OLS withoutOLS without– Let be the OLS residuals. AK's Let be the OLS residuals. AK's

estimator isestimator is

g t

e tj

g w et tjj

n

tj

1

h = + a + a + +tj j0 j1 t j2s = 0

4

t -ss = 0

4

t -s tj

tj j t -1 , j

a g t b DM R b DM F

u

jsr

jsf

tj

g t

g t

Estimation of in AK ModelEstimation of in AK Model• Alternative EstimatorAlternative Estimator

• The estimator of The estimator of gg is the first principal is the first principal component of the least squares component of the least squares residual matrix residual matrix

• The estimator isThe estimator is

g t

m in ( ) ( ), ,

j j g

j j j j j jj

n

h X g h X g

1

( )e tj

,g epc t jj

n

tj

1

Table 2. Estimates and Tests of Table 2. Estimates and Tests of Sectoral ShiftsSectoral Shifts

(1955Q1 – 2011Q1)(1955Q1 – 2011Q1)ModeModell

VariablVariablee

sum of sum of coefscoefs SDSD p-valuep-value

joint joint

p-valuep-value

LilieLilienn

σσ onlyonly

0.2570.257 0.1050.105 0.0150.015 n.a.n.a.

σσ

sksk

0.2060.206 0.1040.104 0.0500.0500.0000.000

-0.310-0.310 0.0870.087 0.0000.000

AKAK

(g(gakak))

σσuu onlyonly

0.8580.858 0.8250.825 0.3000.300 n.a.n.a.

σσuu

skskuu

0.6750.675 0.8030.803 0.4020.4020.0020.002

-2.241-2.241 0.6710.671 0.0010.001

σ and skin Lilien and σσu u and sku in AK

AK ModelAK Model((σσu, u, skskuu) vs () vs (σσsksk

ModeModell

VariablVariablee

sum of sum of coefscoefs SDSD p-valuep-value

joint joint

p-valuep-value

AKAK

(g(gakak))

σσuu onlyonly

0.8580.858 0.8250.825 0.3000.300 n.a.n.a.

σσuu

skskuu

0.6750.675 0.8030.803 0.4020.4020.0020.002

-2.241-2.241 0.6710.671 0.0010.001

AKAK

(g(gakak))

σσ onlyonly

1.7001.700 0.7450.745 0.0240.024 n.a.n.a.

σσ

sksk

1.4011.401 0.6970.697 0.0460.0460.0000.000

-1.502-1.502 0.3680.368 0.0000.000

Comparison of Lilien and AKComparison of Lilien and AKσσ and sk and skin both modelsin both models

p-values are p-values are very similarvery similar

ModeModell

VariablVariablee

sum of sum of coefscoefs SDSD p-valuep-value

joint joint

p-valuep-value

LilieLilienn

σσ onlyonly

0.2570.257 0.1050.105 0.0150.015 n.a.n.a.

σσ

sksk

0.2060.206 0.1040.104 0.0500.0500.0000.000

-0.310-0.310 0.0870.087 0.0000.000

AKAK

(g(gakak))

σσ onlyonly

1.7001.700 0.7450.745 0.0240.024 n.a.n.a.

σσ

sksk

1.4011.401 0.6970.697 0.0460.0460.0000.000

-1.502-1.502 0.3680.368 0.0000.000

Table 3. Various Results of AK(gTable 3. Various Results of AK(gakak) ) ModelModel

p-values of the hypothesis testsp-values of the hypothesis tests

1955-1982: AK's sample period, 1955-2003: no adjustment of data1955-1982: AK's sample period, 1955-2003: no adjustment of data

DMF is not included in AK's original purging equationDMF is not included in AK's original purging equation

SamSample ple PerioPeriodd DMFDMF

estimate from estimate from estimate from estimate from uu

σσ & sk & skσσ onlyonly σσ & sk & sk σσ onlyonly

1955Q1955Q1-1-2011Q2011Q11

includincludeded 0.0000.000 0.0240.024 0.0020.002 0.3000.300

excludexcludeded 0.0000.000 0.0050.005 0.0080.008 0.0370.037

1955Q1955Q1-1-2003Q2003Q11

includincludeded 0.0000.000 0.0060.006 0.0120.012 0.1760.176

excludexcludeded 0.0000.000 0.0040.004 0.0150.015 0.0380.038

1955Q1955Q1-1-1982Q1982Q11

includincludeded 0.0000.000 0.1370.137 0.0130.013 0.2500.250

excludexcludeded 0.0000.000 0.0580.058 0.0260.026 0.0920.092

Unemployment Rates EquationUnemployment Rates Equation

L ilien : U R = + + + + +

A K : U R = + + + +

t 0 1 ss = 0

4

t -s ss = 0

4

t -s ss = 0

8

t -s ss = 0

4

t -s t

t 0 1 ss = 0

8

t -s ss = 0

8

t -s ss = 0

8

t -s t

t ss = 0

4

t -s t

t sk DM R UR

t sk DM R

r

ConclusionConclusion

• Hypothesis: sectoral shifts of labor Hypothesis: sectoral shifts of labor demand causedemand cause– layoffs → job Search → frictional U layoffs → job Search → frictional U

(NRU)(NRU)– a significant effect on aggregate a significant effect on aggregate

unemployment rateunemployment rate– Natural (frictional) unemplyment Natural (frictional) unemplyment

rate fluctuates significantlyrate fluctuates significantly

• Macro-policy implication of the Macro-policy implication of the hypothesis: hypothesis: – if a large portion of the UR is if a large portion of the UR is

frictional rate, aggregate demand frictional rate, aggregate demand management policy may be management policy may be ineffective.ineffective.

ConclusionConclusion

• Empirical TestsEmpirical Tests– conflicting resultsconflicting results– Lilien type models support the Lilien type models support the

hypothesis and Abraham-Katz type hypothesis and Abraham-Katz type models reject it.models reject it.

• Past studies used the cross-sectional Past studies used the cross-sectional dispersiondispersion of net employment growth of net employment growth rates as the proxy for sectoral shifts rates as the proxy for sectoral shifts (size of layoffs).(size of layoffs).

• But, the skewness plays an important But, the skewness plays an important role.role.

ConclusionConclusion

• When both dispersion and skewness of When both dispersion and skewness of the distribution of sectoral shifts are the distribution of sectoral shifts are usedused

– the sectoral shifts hypothesis is the sectoral shifts hypothesis is supported strongly in both Lilien supported strongly in both Lilien type and Abraham-Katz type modelstype and Abraham-Katz type models

– supports are robust to sample period supports are robust to sample period and other model differencesand other model differences

ConclusionConclusion

• Estimates of NRUEstimates of NRU– fluctuates significantly in Lilien type fluctuates significantly in Lilien type

modelmodel– almost flat in AK type modelsalmost flat in AK type models

• The difference in the estimates of NRUThe difference in the estimates of NRU– is not due to the difference in the is not due to the difference in the

estimates of dispersion or/and estimates of dispersion or/and skewnessskewness

– is due to the difference in the is due to the difference in the specification of UR equationspecification of UR equation

– disappears almost when the same disappears almost when the same structure of UR equation is used.structure of UR equation is used.