Basic Facts on Reallocation
Transcript of Basic Facts on Reallocation
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Basic Facts on ReallocationBasic Facts on Reallocation
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Introduction• Shocks:
– Business Cycle Shocks “common” to all sectors yalthough not common response.
– Sectoral shocks: Industry and regionIdiosyncratic shocks– Idiosyncratic shocks
• Frictions:– Search/matchingg– Adjustment costs (capital/labor)– Technology adoption costs– Entry/exit
• Importance for macro: Growth vs Fluctuations (Emerging vs Advanced)– Growth vs. Fluctuations (Emerging vs. Advanced)
– Nonlinear micro + Heterogeneity– Non-representative agent approach
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Job Creation and DestructionJob Creation and Destruction• Job Creation: Employment gains from p y g
expanding and new businesses.• Job Destruction: Employment losses from
i d i i b icontracting and exiting businesses.• Job Flows are SUBSET of worker flows!
M i j b fl i l it di l• Measuring job flows requires longitudinal business data – Data infrastructure projects at Census (LBD, LEHD)Data infrastructure projects at Census (LBD, LEHD)
http://lehd.dsd.census.gov/, http://www.bls.gov/bdm/home.htm, http://www bsos umd edu/econ/haltiwanger/downloadhttp://www.bsos.umd.edu/econ/haltiwanger/download.htm, http://www.ces.census.gov/ces.php/home
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jktjktjktjkt XEEg /)( 1 jktjktjkt XaACC /
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jktsktjktskt gXXPOS0
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jktsktjktskt gXXNEG0
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|| jktjktjktjkt gSEPACCEXCESSW
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kkk NEGPOSNET
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sj
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j=firm/establishment, k=worker type, s=sector
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Basic FactsBasic Facts• Magnitudeg
– Relationship to worker flows• Productivity Dynamics?• Concentration• Concentration• Persistence• Idiosyncratic Shocks• Cyclicality• By Plant Characteristics
Along the a U S s E rope s Emerging s• Along the way: U.S. vs. Europe vs. Emerging vs. Transition
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11.0
12.0
14.0
16.0Job Creation Rate (left axis)Job Destruction Rate (left axis)
Excess Reallocation MA(5) (right axis)
9 0
10.012.0
8.0
9.0
8.0
10.0
6.0
7.0
6.0
4 0
5.0
2.0
4.0
3.0
4.0
947
950
953
956
959
962
965
968
971
974
977
980
983
986
989
992
995
998
2001
2004
0.0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
Figure 5. Quarterly Job Flows in Manufacturing, Seasonally Adjusted, 1947-2004
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0.092
0.096 Job Creation RateJob Destruction Rate
0.088
0.080
0.084
0.076
0.068
0.072
0.064
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Quarterly Job Flows in the U.S. Private Sector, Seasonally Adjusted, 1990-2004
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MagnitudeMagnitude• Quarterly: Approximately 6%Quarterly: Approximately 6%• Annual: Approximately 11%• Five-year: Approximately 35%Five-year: Approximately 35%• Ten-year: Approximately 60%• Varies SUBSTANTIALLY by industry and• Varies SUBSTANTIALLY by industry and
plant characteristic• Important transitory and permanent• Important transitory and permanent
components• About 1/3 to 1/2 of Worker FlowsAbout 1/3 to 1/2 of Worker Flows
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A. Job Flow Rates
Data SourceTime Period
Sampling Interval
Job Creation
JobDestruction
JOLTS December 2000 – January JOLTS, continuous units
y2004 Monthly 1.5 1.5
BED March 1990 –
June 2003 Quarterly 8.0 7.7
B. Worker Flow Rates
Hires SeparationsTime Period
Data SourceTime Period Sampling
Interval
JOLTS,continuous units
December 2000 – January 2004 Monthly 3.2 3.1
LEHD, selected states,full-quarter cases
1993:2 to2003:3, Quarterly 13.2 10.7
LEHD l d 1993:2 toLEHD, selected states, cumulative flows
1993:2 to2003:3 Quarterly 25.0 24.0
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Table: Gross Reallocation of Outputs and Inputs in U.S. Manufacturing and Retail Trade
Measure Creation Share of Destruction Share of Fraction ofMeasure Creation(Expansion)Rate
Share ofCreation(Expansion)Due toEntrants
Destruction(Contraction)Rate
Share ofDestruction(Contraction)Due to Exits
Fraction ofExcessReallocationWithin 4-digitIndustryEntrants Industry
Manufacturing, 1977-87
Real GrossO t t
49.4 0.44 34.4 0.61 0.80Output
Employment 39.4 0.58 45.8 0.62 0.75
Capital 46.1 0.42 37.1 0.51 0.71pEquipment
CapitalStructures
44.9 0.44 48.4 0.42 0.69
Retail Trade, 1987-97
Employment 70.3 0.85 55.7 0.83 0.96
Real Output 72.6 0.81 46.6 0.80 0.98
Source: Tabulations from the Census of Retail Trade and Census of Manufacturers
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C ountry Period C overage E m ployer Unit JobCre a-tion
JobD estruc -tion
Net Growth
Austra lia 1984-85 M anufa cturing E sta blishm ents 16.1 13.2 3.9 Ca nada 1974 92 M anufa cturing E sta blishm ents 10 9 11 1 0 2Ca nada 1974-92 M anufa cturing E sta blishm ents 10.9 11.1 -0.2 Ca nada 1983-91 A ll E m ployees Firms 14.5 11.9 2.6 C hile 1976-86 M anufa cturing E sta blishm ents 13.0 13.9 -1.0 C olombia 1977-91 M anufa cturing E sta blishm ents 12.5 12.2 0.3De nma rk 1983-89 Private Sec tor E sta blishm ents 16.0 13.8 2.2 De nma rk 1981-91 M anufa cturing E sta blishm ents 12.0 11.5 0.5 E stonia 1992-94 A ll E m ployees Firms 9.7 12.9 -2.2Finla nd 1986-91 A ll E m ployees E sta blishm ents 10.4 12.0 -1.6 France 1984-92 Private Sec tor E sta blishm ents 13.9 13.2 0.6 France 1985-91 M anufa cturing Firms 10.2 11.0 -0.8France 1 1985-91 N onma nufacturing Firms 14.3 11.8 2.4Ge rm any 1983-90 A ll E m ployees E sta blishm ents 9.0 7.5 1.5 Ge rm any(LowerS axony)
1979-93 M anufa cturing E sta blishm ents 4.5 5.2 -0.7S axony)Ita ly2 1984-93 Private Sec tor Firms 11.9 11.1 0.8 Israe l 1971-72 M anufa cturing E sta blishm ents 9.7 8.2 1.5M orocco 1984-89 M anufa cturing Firms 18.6 12.1 6.5 Ne therla nds 1979-93 M anufa cturing Firms 7.3 8.3 -1.0 Ne w Z ea la nd 1987-92 Private Sec tor E sta blishm ents 15.7 19.8 -4.1 Norwa y 1976-86 M anufa cturing E sta blishm ents 7.1 8.4 -1.2 Swede n 1985-92 A ll E m ployees E sta blishm ents 14.5 14.6 -0.1 USA 1973-93 M anufa cturing E sta blishm ents 8.8 10.2 -1.3 USA 3 1979 83 Private Sec tor E sta blishm ents 11 4 9 9 1 4USA 3 1979-83 Private Sec tor E sta blishm ents 11.4 9.9 1.4 USA c 1979-83 M anufa cturing E sta blishm ents 10.2 11.5 -1.3 Unite d K ingdom 1985-91 A ll E m ployees Firms 8.7 6.6 2.1
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Colombia
0 2
Brazil
0 25
0 05
0.10.15
0.2
Rate pos
neg 0.10.15
0.20.25
Rat
e posneg
00.05
1980 1985 1990 1995 2000 2005
Y
00.05
1991 1993 1995 1997 1999 2001
g
Year
Chile
Year
MexicoChile
0 2
0.3
pos 0 150.2
0.250.3
te pos
0
0.1
0.2
Rate pos
neg0
0.050.1
0.15
1991 1993 1995 1997 1999 2001
Rat
p
neg
1980 1985 1990 1995 2000 2005
Year
1991 1993 1995 1997 1999 2001
Year
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Average Quarterly Job Flow Rates in the BED, 1990:2 – 2003:2
Job Creation Job Destruction Net Growth
T l P i 8 0 7 7 0 3Total Private 8.0 7.7 0.3
Resources 19.7 19.8 -0.1
Construction 14.3 14.0 0.4
f iManufacturing 4.9 5.3 -0.4
Wholesale Trade 6.8 6.7 0.1
Retail Trade 8.1 7.9 0.2
Transportation & Utilities 6.7 6.4 0.3
Information 6.9 6.6 0.3
Financial Activities 6.7 6.4 0.3
Professional & Business Services 9.9 9.1 0.8
Education & Health 5.6 4.9 0.7
Leisure & Hospitality 10.9 10.4 0.5Leisure & Hospitality 10.9 10.4 0.5
Other Services 8.9 8.6 0.3
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Study Coverage EmployerUnit
BetweenRealloca
WithinReallocaUnit Realloca-
tion RateRealloca-tion Rate
Hamermesh et al Netherlands, Firms 6.2 0.8(1996), Table 2
,All Sectors,1988-90
L d t l(1994) F All E t bli h 79 67Largarde et al (1994),Table 1
France, AllSectors, 1984-91
Establish-ments
7.9 6.7
Dunne et al (1997),Table 5
USA,Manufacturing1972-88
Establish-ments
19.2 2.7
97 88
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Slovenia. Total, Within Firm and Between Firm Job Reallocation (By Worker Type)Reallocation (By Worker Type)
0.3
0 2
0.25
0 3
0.15
0.2
Rat
e
TotalBetween
0.05
0.1
R
Within
0Age Educ Gender All ThreeAge Educ Gender All Three
Group Category
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Country/Sta Coverage Sampling Accession Job Separation JobCountry/State
Coverage SamplingFrequency
AccessionRate
JobCreationRate
SeparationRate
JobDestructionRate
USA(Selected
Private Sector Quarterly 22.3 7.1 21.4 6.4(SelectedStates)USA(SelectedStates)
Manufacturing
Quarterly 24.7 5.8 24.6 6.2
)U S A - -Maryland
P r i v a t eSector1
Quarterly 18.4 9.0 18.7 9.3
U S A - -Maryland
Manufacturing
Quarterly 12.9 7.5 14.2 8.8y g
Denmark Manufacturing
Annual 28.5 12.0 28.0 11.5
Netherlands Manufacturing2
Annual 16.3 7.3 15.7 8.3g
Norway Manufacturing
Annual 21.0 11.0 23.0 13.0
Norway Banking andInsurance
Annual 21.0 12.5 22.0 14.5
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Productivity DecompositionProductivity Decomposition
etetit PsPie
etetitie
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Within, Between, Cross, Entry and E i ffExit effects
Ce Ne Xe
kitketketkitetetetetCe Ce
kitketetetketit PPsPPssPPPsPsP )()()(
Key Issues: 1. Longitudinal links2. Horizon3 Measurement3. Measurement
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Decomposition of TFP in U.S. Mfgp g1977-1987
Net Entry (26 00%)
Within Plant (48.00%)
Net Entry (26.00%)
Reallocation (26.00%)
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Contribution of Continuing Establishments vs. Net Entry to U.S. Manufacturing Labor Productivity Growth 1977-87Manufacturing Labor Productivity Growth, 1977 87
0.8
0.60.7
0.40.5
hare
s
0.20.3Sh
00.1
Continuing Establishments Net Entry
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Contribution of Continuing Establishments vs. Net Entry to U.S. Retail Trade Labor Productivity Growth 1987-97Retail Trade Labor Productivity Growth, 1987-97
1.2
1
1.2
0.6
0.8
es
0.4Shar
0
0.2
-0.2 Continuing Establishments Net Entry
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Comments on Decomposition in Literature
• Some question about how to interpret aggregate q p gg gindex defined in this manner– Typical check (e.g., BHC and FHK) to see how this
index performs relative to standard aggregateindex performs relative to standard aggregate measures
• Common result – magnitudes very similar and correlations highhigh
– Not clear what correct aggregate index is• Standard aggregate indexes not well-justified on theoretical
d ( Fi h diti d hi h tgrounds (e.g., Fisher – conditions under which aggregate production function exists are very stringent)
– Standard decomposition summarizes activity weighted micro distribution taking into accountweighted micro distribution taking into account unbalanced panel
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ConcentrationConcentration • For Manufacturing, more than 2/3 of g,
creation/destruction accounted for by large (greater than 25% changers). Births account for 20% of annual creation Deaths account for 25%20% of annual creation, Deaths account for 25% of annual destruction.
• For non-mfg entry/exit play an even larger roleFor non mfg, entry/exit play an even larger role.• Contribution of entry/exit larger over longer
horizons.• Importance:
– Job flows can’t be fully accommodated by attrition/worker flowsattrition/worker flows
– Adjustment costs?
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30.0
Job Flow Concentration Net Density
Job Creation
25.0
Job Creation Mean: 6.4 percent Share with Rate > 10 pct: 0.63Job Destruction
20.0
Job Destruction Mean: 8.0 percent Share with Rate > 10 pct: 0.68
15.0
10.0
5.0
0.0-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0
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Country Percent of Job Creation or Destruction Accounted for by Plants
with Growth Rates in the Indicated Interval
[-2,-1) [-1,-.2) [-0.2,0) (0,0.2] (0.2,1] (1,2]
UnitedStates
32.9 44.0 23.1 30.7 45.1 24.2
Canada 77.7 22.3 24.8 75.2Canada 77.7 22.3 24.8 75.2
Denmark 45.9 33.7 20.4 23.4 37.4 39.1
Israel 84.7 15.3 21.8 78.2
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PersistencePersistence
• Measured as the fraction of the changeMeasured as the fraction of the change that persists for 1 year.
• Roughly 50 percent of quarterly job flows• Roughly 50 percent of quarterly job flows persistentR hl 70 80 t f l j b fl• Roughly 70-80 percent of annual job flows persistent
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Country USA Denmark Netherlands Norway
Period 1973 88 1980 91 1979 93 1977 86Period 1973-88 1980-91 1979-93 1977-86
Horizon OneYear
TwoYears
OneYear
TwoYears
OneYear
TwoYears
OneYear
TwoYears
Job Creation 70.2 54.4 71.0 58.0 77.9 58.8 72.7 65.1
Job Destruction 82.3 73.6 71.0 58.0 92.5 87.3 84.2 79.8
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Between vs. Within Sector Shifts
• Decomposition of Excess Reallocation intoDecomposition of Excess Reallocation into Between/Within Components.
• 4-digit industry accounts for 13% of Mfg.;4 digit industry accounts for 13% of Mfg.; less for other sectors.
• 2-digit, state accounts for 14% of Mfg;2 digit, state accounts for 14% of Mfg;• 2-digit, region, size, age, ownership
(14,400 sectors in Mfg) accounts for only(14,400 sectors in Mfg) accounts for only 39% of Mfg.
• Idiosyncratic Shocks Dominate!Idiosyncratic Shocks Dominate!
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Decomposition of excess job reallocation
)|||)|)/()(/((|)|()( jtjktjtjktstjtststst ggXXXXNETSUMkEXCESSJsj k
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Country Period Unit Number Average FractionCountry Period UnitofAnalysis
NumberofSectors
AverageNumber ofWorkersper Sector(inthousands)
FractionResultingfromShiftsBetweenSectors
USA 1972-88 plant 448/456 39.11 0.13USA 1972-88 plant 980 17.9 0.14Denmark 1983-89 plant 8 196.1 0.00Finland 1986-91 plant 27 48.9 0.06Germany 1983-90 plant 24 1171.2 0.03Italy 1986-91 firm 28 321.5 0.02Netherlands 1979-93 firm 18 10.0 0.20Sweden 1985-91 plant 28 112.4 0.03Norway 1976-86 plant 142 2.4 0.06France 1 1984-88 plant 15 883.3 0.06France 2 1985-91 firm 600 36.6 0.17France 3 1984-91 plant 100 0.12New Zealand 1987-92 plant 28 27.5 0.01Chile 1979-86 plant 69 3.7 12.2Colombia 1977-91 plant 73 6.31 13.2Morocco 1984-89 plant 61 4.0 16.9
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Sectoral Differences in FlowsSectoral Differences in Flows
• Non-manufacturing greater thanNon manufacturing greater than manufacturing.
• Small young single unit low wage• Small, young, single unit, low wage businesses more likely to create and destroy jobsdestroy jobs.
• These factors are highly interrelated!
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Country USA Canada Netherlands Norway
Industry Period 1974-92 1974-92 1979-93 1976-86
Food 17.9 19.5 18.4 15.3
Tobacco 12.7 12.3
Textiles 16.9 21.3 19.1 18.3
Apparel 25.2 27.8 23.4
Lumber 25 8 26 2 20 8 15 7Lumber 25.8 26.2 20.8 15.7
Furniture 20.7 27.7
Paper 12.5 11.1 14.6 12.6
Printing 17.1 22.0 16.3
Chemicals 14.0 18.7 12.1 12.7
Petroleum 14.2 15.6 10.1 13.2
Rubber 20.3 21.5 12.1
Leather 22 4 24 2 17 5Leather 22.4 24.2 17.5
Stone, Clay, Glass 20.4 23.0 15.6
Primary Metals 16.0 13.3 5.2 6.3
Fabricated Metals 20.0 27.7 18.8 18.7
Nonelectric Machinery 20.5 27.8 16.4
Electric Machinery 19.5 24.6 11.3
Transportation 18.4 20.6 14.6
I t t 10 5 19 7Instruments 10.528.1
19.7
Miscellaneous 14.4 28.5 18.3
Total Manufaturing 19.0 21.9 15.6 15.5
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Excess Job Reallocation Rates By Business Age
04
0.3
0.4
01
0.2
0
0.1
1 2 3 4 5 61 2 3 4 5 6
CHL(1980-1999) COL(1977-1999) MEX(1994-2000) BRA(2000)CHL(19801999) COL(19771999) MEX(19942000) BRA (2000)
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NETEmploymentGrowthbyBusinessAge NET Employment Growth by Business Age
0.1
0
0.05
-0.05
01 2 3 4 5 6
-0.1CHL(1980-1999) COL(1977-1999) MEX(1994-2000) BRA (2000)
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NETEmploymentGrowthbyBusinessAge NET Employment Growth by Business Age
0.1
0
0.05
-0.05
01 2 3 4 5 6
-0.1CHL(1980-1999) COL(1977-1999) MEX(1994-2000) BRA (2000)
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CyclicalityCyclicality
• Recessions are times of reorganizationRecessions are times of reorganization especially in manufacturing and especially for large mature businesses infor large, mature businesses in manufacturing.
• Spikes in permanent job destruction are• Spikes in permanent job destruction are key characteristic of recessions in manufacturingmanufacturing– Open question about most recent recession
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11.0
12.0
14.0
16.0Job Creation Rate (left axis)Job Destruction Rate (left axis)
Excess Reallocation MA(5) (right axis)
10.012.0
8.0
9.010.0
7.0
6.0
8.0
5.0
6.0
4.0
4.0 2.0
3.0
1947
1950
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2001
2004
0.0
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0.040 Hires RateSeparations Rate
0.035
0 0300.030
0.0250.025
2000
12
2001
03
2001
06
2001
09
2001
12
2002
03
2002
06
2002
09
2002
12
2003
03
2003
06
2003
09
2003
12
2004
03
2004
06
2004
09
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JobCreat JobDestEST RUS
14.31
.5
SLN
14.31
UKR
Job Flows in Selected Transition Economiesyear
1990 1992 1994 1996 1998 2000.5
1990 1992 1994 1996 1998 2000
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Cyclical Link Between Job and Worker FlowsWorker Flows
Micro Nonlinearity + Heterogeneity = Complex g y
Aggregation
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OverviewOverview
• Caution about drawing inferences forCaution about drawing inferences for representative worker/firm based upon aggregate/industry evidenceaggregate/industry evidence
• Aggregate behavior may reflect micro nonlinearities + heterogeneitynonlinearities + heterogeneity– More than just compositional aggregation
problemsproblems
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(Not Seasonally Adjusted Data)Separation Rates as a Function of NET
1214
(Not Seasonally Adjusted Data)8
10tio
n R
ate
46
Sepa
rat
02
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8NET = Hire - Separation Rate
bandwidth = .8Note: Loess Smoothing Plot using JOLTS Monthly Flows Dec 00 - Oct 04
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Hire Rates as a Function of NET12
14(Not Seasonally Adjusted Data)
810
Rat
e4
6H
ire R
02
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8NET = Hire - Separation Rate
bandwid th = .8Note: Loess Smoothing Plot using JOLTS Monthly Flows Dec 00 - Oct 04
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Worker & Job Flow Relations –Hires and Separations vs NetHires and Separations vs Net
Growth0.35
0.25
0.30Hiring Rate Separations RateH UCl S UClMean = 0.033 Mean = 0.031
0.15
0.20
0.05
0.10
• Strong nonlinear relations of H and S to net growth
0.00-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30
Net Growth Rate
Strong nonlinear relations of H and S to net growth– H rates rise sharply to right of 0, S rates rise sharply to left of 0– Considerable hires at contracting, separations at expanding estabs
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Worker & Job Flow Relations –Excess Worker Flows vs NetExcess Worker Flows vs Net
Growth0.06
0 04
0.05
Excess Worker Flow RateV UClMean = 0.017
0.03
0.04
0.01
0.02
• Excess Flow H – JC = S – JD highlights churning from last figure
0.00-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30
Net Growth Rate
Excess Flow H JC S JD, highlights churning from last figure– Excess flows increase with the magnitude of net growth– Greater excess churning for expanding estabs (~ 4-5 pct vs 2-3 pct)
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Worker & Job Flow Relations –Q i d L ff N G hQuits and Layoffs vs Net Growth
0.35
0.25
0.30Quits Rate Layoffs RateH UCl S UClMean = 0.012Mean = 0.017
0.15
0.20
0.05
0.10
• Quits, Layoffs also exhibit strong nonlinear patterns
0.00-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30
Net Growth Rate
, y g p– Quits dominate separations at expansions– Quits also account for many separations at contractions– Layoff/quit ratio rises as net growth rate becomes more negative
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4.5
4.0
3 0
3.5
2 5
3.0
2.0
2.5
2001
01
2001
04
2001
07
2001
10
2002
01
2002
04
2002
07
2002
10
2003
01
2003
04
2003
07
2003
10
2004
01
Actual Predicted from Growth Distribution Predicted from OLS
Hires
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4.5
4.0
3 0
3.5
2.5
3.0
2.0
2.5
2001
01
2001
04
2001
07
2001
10
2002
01
2002
04
2002
07
2002
10
2003
01
2003
04
2003
07
2003
10
2004
01
Actual Predicted from Growth Distribution Predicted from OLSActual Predicted from Growth Distribution Predicted from OLS
Separations
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Nonlinear aggregation
dnnfnhH )()(
dfS
dnnfnhH
)()(
)()(
dnnfnsS )()(
Cross sectional distribution shape and location mattersConcentration matters!Concentration matters!
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Taking stockTaking stock• Idiosyncratic shocks dominatey
– Technology– Taste– Cost
• Time varying intensity of reallocation shocks vs. changes in incentives?changes in incentives?
• Efficiency? – Is it at least productivity enhancing?s a eas p oduc y e a c g
• Measurement issues for productivity– What market structure/institutions promote efficient
reallocation?reallocation?• Cautions:
– Second Best and Creative Destruction
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Taking stock ContTaking stock Cont...
• Large scale job (and worker flows) driven byLarge scale job (and worker flows) driven by idiosyncratic shocks
• Varies by sector, cyclically, time period, countryy , y y, p , y• From here – two areas of focus:
– Cyclicality:y y• Theory• More structured empirical analysis
P d ti it d ll ti– Productivity and reallocation:• Theory• More structured empirical analysis