the motivation

1

Job Chains and Welfare Gains from Employment: Testing an I-O Type

Labor Market Model

Joseph PerskyDaniel Felsenstein

Funded by the W.E. Upjohn Institute for Employment Research

2

The Motivation

• What are the welfare and distributional effects of employment creation?

• What is a job worth?• No policy guidance: what kind of jobs to

promote? High wage or low wage? For locals or commuters? Service sector or manufacturing?

• No adequate model of employment creation in local economic development efforts

3

A Job Chains Model of Local Labor Markets

• Assume unemployment and underemployment – slack in labor market

• Assume rigid wage structure• A new job, if filled by an employed worker,

opens up a chain• Workers move from job to job to improve their

welfare• New perspective on employment ‘multipliers’

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Horizontal Multipliers

Backward LinkagesSuppliers:30 Indirect Jobs

Light Bulbs Inc.

Forward LinkagesHousehold-serving:20 Induced Jobs

Supermarket Stores

Instrument Plant100 Direct Jobs

SciSource

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‘Horizontal’ Multipliers

InducedIndirect

Direct

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Job Chains and Vertical Multipliers

New Job in SciSourceExisting

Similar Job in OptiSourceExisting

Related Job in InstruSource

In-Migrant to LocalArea Ms. Black

Terminates Chain

Job Changer:Mr. Jones

Job Changer:Ms. Dee

Vacancies

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Job Chains and ‘Vertical’ MultipliersInduced

Chain Termination Job ChainsVacancies

IndirectDirect

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Chain Literature• Housing Market Studies—

– Lansing J.B., Clifton C.W. and Morgan J.N. (1969)– Emmi and Magnusson (1994,1995)

• Organizational Studies —– Parishes: White (1970) – Orchestras: Abbot and Hrycak (1990)

• Hermit Crabs– Chase, Weissburg and DeWitt (1988)

• Labor Market Flows– Schettkat (1996)

• Economic Development– Webster (1979)– Robson, Bradford and Daes (1999) – Persky and Felsenstein (1999)

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The Job Chains Model as an I-O Type Model • Job chains = production chains in I-O• Production chains: estimated by average ‘input

vector’ for each industry• Job chains: estimate ‘input vector’ for each

type of new job, by wage group.• Chain length=size of employment multiplier• Chains initiated by indirect and induced

activity, not just direct.

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Leontief Model of Job Chains

• (Q) : A square job flow matrix (origin-destination)

• qij, elements of Q which show the chance that a job vacancy of a j-type position is taken by a worker currently in an i-type position.

• tij elements of T matrix, probabilities that chain will terminate due to (1) unemployed, (2) out of labor force and (3) in-migrants.

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A Job Chains Matrix: Q and T matrices

New Wage Group Origin 1 2 3 4 5

Group 1 q11=41.1% 0.0% 0.0% 0.0% 0.0% Group 2 q21=25.0% q22=52.9% 0.0% 0.0% 0.0% Group 3 q31=4.8% q32=22.1% q33=46.6% 0.0% 0.0% Group 4 q41=2.2% q42=1.5% q43=18.5% q44=47.3% 0.0% Group 5 q51=0.0% q52=0.3% q53=2.4% q54=13.3% q55=34.5%

Column Sum 73.1% 76.8% 67.5% 60.6% 34.5%

New Wage Group

1 2 3 4 5 Unemployed t11=2.9% t12=3.8% t13=9.7% t14=15.8% t15=24.7%

Not-in-Labor Force t21=4.0% t22=3.8% t23=7.5% t24=13.5% t25=30.5% In-Migrant t31=20.1% t32=15.6% t33=15.4% t34=10.0% t35=10.2%

Column Sum 27.0% 23.2% 32.6% 39.3% 65.4%

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A Housing Chains Matrix

Destination: New Home

Origin: Old Home

High Quality Mid Quality Low Quality

High Quality 0.45 0.07 0.01

Mid Quality 0.38 0.39 0.09

Low Quality 0.09 0.35 0.38

Outside 0.08 0.19 0.52

Total 100.0 100.0 100.0

Based on Marullo (1985).

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Chains by Attributes

Attributes

G-Chain(Leontieff – Production)

L-Chain(Labor market)

H-Chain(Housing)

Direction of Movement through chain

Goods – physical transformation (horizontal)

•Workers – moving up

•Vacancies reaching down

• Housing declining

• Households improving

Change in Stock (cohort) over Time

Depreciates Appreciates Depreciates

Driver of Movement Technology Job

OpportunitiesHousing

Opportunities

Stickiness in Movement through Chains

Low High Moderate

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Assumptions of Chain Models Assumptions of

ModelG-Chain

(Leontieff – Production)

L-Chain(Labor market)

H-Chain(Housing)

Model Focus Demand for Goods

Demand for Labor

Supply of Housing

Characteristic of Market

Highly Elastic Short Run Supply

Highly Elastic Short Run Supply

Inelastic Supply in the Short Run

Equilibrium Characteristics Excess Supply Excess Supply Excess Demand

Allocation via Proportions (Technology)

Probabilities (Recruiting Channels)

Proportions (Marketing Channels)

Role of Prices Fixed Fixed Variable

Welfare Gains via Quantity Change Job Change Quality Change and Asset Prices

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Chain Models: the Case Against

• Mechanistic, lacking in theoretical basis• No formal maximizing behavior by firms

and individuals• Little attention to short run price changes

as allocation method• Often assume markets don’t clear, no real

closure

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Chain Models: the Case For

• When markets are connected through institutional and structural links (wage agreements, banking regulations etc) not prices

• In the presence of fixed mark-ups: suppliers working with fixed prices (flat supply curve).

• When quantity changes represent welfare changes (firms receiving fixed mark-up, workers welfare gain through movement). Chains as modeling spread.

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The Job Chains Model

• Mechanics• Data• A supply-side example:

restricting access to employment

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1. Chain Lengths

• Mn = 1/(1- qnn)

• Mn-1 = [1/(1- q(n-1)(n-1))] * [ 1 + qn(n-1) Mn ]

• Mn-2 = [1/(1- q(n-2)(n-2)) * ( 1 + q(n-1)(n-2) Mn-1 + q(n(n-2) Mn )

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2. Welfare Gains (Efficiency Effects)

V/wj = wage gains of job changers + (wage- opportunity cost) of non-employed job recruits, as a share of new wages

Vj = imij [(kqki *(wi-wk ) + hthi *(wi- chi)].

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3. Distributional Effects

• A Rawlsian measure (R/w): gains to lowest groups, as a share of new wages

Rj = mnj h thn *(wn – chn)

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Opportunity Costs (w/c) for Unemployed, Out of Labor Force and In-

Migrants

Opp.Costs

1: $25.50 - $40.00 75%

2: $16.40 - $25.50 75%

3: $10.50 - $16.40 50%

4: $ 6.70 - $10.50 40%

5: $ 4.25 - $ 6.70 31%

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Data

• PSID 1987-1993 (heads and spouses only)

• 3500 distinct year-to-year job changes

• 1992 Real average wage gains for job changers

• Data for four regions and five earnings classes

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Flows into Job VacanciesDestination Job Group

Origin Job Group 1 2 3 4 51: $25.50 - $40.00 41.1% 0.0% 0.0% 0.0% 0.0%

2: $16.40 - $25.50 25.0% 52.9% 0.0% 0.0% 0.0%3: $10.50 - $16.40 4.8% 22.1% 46.6% 0.0% 0.0%4: $ 6.70 - $10.50 2.2% 1.5% 18.5% 47.3% 0.0%5: $ 4.25 - $ 6.70 0.0% 0.3% 2.4% 13.3% 34.5%Unemployed 2.9% 3.8% 9.7% 15.8% 24.7%Out of Labor Force 4.0% 3.8% 7.5% 13.5% 30.5%In-Migrant 20.1% 15.6% 15.4% 10.0% 10.2%Column Sum 100.0% 100.0% 100.0% 100.0% 100.0%

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Multiplier Effect

Class of New JobCreated Vacancies 1 2 3 4 51: $25.50 - $40.00 1.70 0.00 0.00 0.00 0.002: $16.40 - $25.50 0.90 2.12 0.00 0.00 0.003: $10.50 - $16.40 0.52 0.88 1.87 0.00 0.004: $ 6.70 - $10.50 0.28 0.37 0.66 1.90 0.005: $ 4.25 - $ 6.70 0.08 0.12 0.20 0.39 1.53

Total Job Multiplier 3.48 3.48 2.73 2.28 1.53

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Efficiency and Distributional Effects

Wage Group of Initial New Job1 2 3 4 5

V/w 0.43 0.42 0.56 0.62 0.69

Per job

Share to Job Changers 0.52 0.37 0.21 0.10 0

R/w Per initial new job:

Dollars per yr to Lowest-R 397 550 960 1,888 7,202

Dollars per yr to Low 4,654 4,303 6,600 10,582 7,202

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Efficiency Effect: Sensitivity Analysis

1 2 3 4 51 Basic Assumptions 0.43 0.42 0.56 0.62 0.69

2 .75 in-migs; .25 all others 0.41 0.39 0.47 0.54 0.62

3 .75 all in-migrants 0.51 0.51 0.57 0.63 0.67

4 .25 all non job-changers 0.74 0.72 0.74 0.74 0.75

Alternative Opportunity Cost Assumptions

Wage Group of Initial New Job

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A Supply-Side Example of the Job Chains Model

Simulation of three scenarios. New employment created but restricted:

1. Full local restriction: only locals can take jobs: no in-migrants

2. First round local restriction: no in-migrants on first round of hiring

3. First round restriction to local non-employed: only locals (local unemployed or out of labor force) can take jobs on first round

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Base Case Summary

New Wage Group 1 2 3 4 5 Total Job Multiplier 3.48 3.48 2.73 2.28 1.53 V/w 0.43 0.42 0.56 0.62 0.69 R*/w 0.07 0.10 0.22 0.49 0.58

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Case 1: Full Local Restriction

• Exclude in-migrants from T-matrix• Recalibrate Q and T matrix• Recalculate Leontief inverse• Using new multipliers and q’s recalculate

efficiency measure (V/w)• Using new multipliers and q’s recalculate

distributional measure (R/w)

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Case 1: Full Local Restriction – Chain Lengths, Welfare Gains and

Distribution


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Case 2: First Round Local Restriction

• Exclude in-migrants from T-matrix for first round only

• Use Resulting vacancies and Base Q and T matrices

• Recalculate efficiency measure (V/w)• Recalculate distributional measure (R/w)

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Case 2: First Round Local Restriction: – Chain Lengths,

Welfare Gains and Distribution


33

Case 3: First Round Restriction to Local Non-employed

• Limit first and only round to local non-employed

• All chain lengths are thus 1.0• Calculate efficiency measure (V/w)• Calculate distributional measure (R/w)

34

Case 3: First Round Restriction to Local Non-employed – Chain Lengths, Welfare Gains and

Distribution

New Wage Group 1 2 3 4 5

Total Job Multiplier 1.00 1.00 1.00 1.00 1.00 V/w 0.25 0.25 0.50 0.60 0.69 R*/w 0.00 0.00 0.00 0.60 0.69

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Comparing the Results

Compared to the standard case: • Full local restriction: longest chains, greater

efficiency, and more trickle down• First round local restriction: modest increases in

chain length, efficiency and trickle down• First round restriction to local non-employed: no

chains, lower efficiency and some (non-trickle down) distributional gains

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Tentative Policy Conclusions

• Full local restriction: dramatic returns, but unpalatable politically

• First round local restriction: politically feasible, but only modest expected gains

• First round restriction to local non-employed: politically feasible, but low return on high-end placements, and only modest gains on low-end placements

the motivation

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