Heterogeneous Firms and Substitution by
Tasks: the Productivity Effects of Immigrants
International Workshop
Economic impacts of immigration and
population diversity
University Waikato, 12 April 2012
Anette Haas
Michael Lucht
Agenda
1. Motivation
2. Task approach
3. Preview of the Model: Assumptions and Results
4. Model with Heterogeneous Firms (Melitz 2003)
5. Model Simulation
6. Conclusion
2
Motivation I
” (…) the growing divergence between immigrants
and natives does not lie in which sector of the
economy they are employed. Rather, the
divergence is occurring in the kinds of tasks that
immigrants and natives perform on the job”
Borjas, G. J. (2003): The Labor Demand Curve is Downward Sloping: Reexamining
the Impact of Immigration on the Labor Market. QJoE 118, 1335-1374.
3
Motivation II
What is the impact of immigrants on firm productivity
do migrants and natives differ regarding their skills on the labor market ?
Immigrants lose Human Capital, because it is not fully transferable
Empirical studies
immigration: small wage effects, but no effects to employment rate of
natives
migrants are imperfect substitutes for natives (Ottaviano/Peri 2005)
migrants sort into different occupations (Peri/Sparber 2009)
Strategy here: extend the Melitz (2003) heterogeneous firm
framework
including labor market segmentation
including imperfect substitutability
4
Task approach
Lazear (2009): Human capital include education, manual
and cognitive skills, language and communicative skills
Task based approach: comparative advantage of natives
relative to immigrants in interactive and communication
skills
Peri/Sparber (2009) develop a general equilibrium model
(unskilled) immigrants concentrate in manual and less interactive tasks
with lower wages than natives
Schoellman (2010) for US
D’Amuri/Peri (2011) for Europe without Germany; AmuedoDorantes/de la Rica (2011) for Spain
imperfect substitutes thesis is confirmed, further evidence for changing
task specialization and occupational distribution
5
Main Task by Nationallity in Germany
100
90
80
70
60
Non-Routine
Interactive
Manual
50
40
30
20
10
0
German
Western EU
EU8
Rest of
Europe
Non European
Data Source: BA Employment History 2008, BIBB/IAB data, own calculations
6
Empirical evidence for Germany
Manual and routine tasks dominate for Non-EU immigrants
Only few migrants workin technical occupations, a lot of
migrants in general (personal) services
Migrants work in different occupational segments, even if
formal qualification is similar (see also Steinhardt 2011)
Brücker/Jahn (2011) for Germany imperfect substitution
between natives and migrants even with same work
experience, but “old” migrants with “new” migrants
7
Preview: Assumptions and Results
One region, two labor types: migrants and natives
Migrants cluster in certain labor market segments (task 1)
Imperfect substitutability: High supply in task 1 leads to lower
wages
Firms are heterogeneous with regard to productivity and job
composition: productivity and wage cost (dis-)advantages
In general equilibrium, wage differences increases in the
migrant share of the region
Firms need productivity or wage cost advantages to stay in
the market. A higher migrant share leads to a higher failure
rate of low productive firms. The average productivity of the
firms in the market increases with the migrant share.
8
Model: Worker and Firm Behavior
Assumptions:
Labor force groups: migrants and natives, inelastic supply
There are two kinds of job tasks: Migrants cannot do the
second job task, while natives can do both
certain abilities are necessary for some jobs
discrimination (employer or customer)
human capital sorting
No differences regarding productivity in the job task that both
groups can do
9
Framework following Melitz (2003)
new firms
firms in the
market
idiosyncratic
exit
• Dixit-Stiglitz monopolistic competition:
• CES production technology:
immediate exit
A: Total factor productivity; af : share of migrants;
γ : elasticity of substitution
10
Firm Productivity and Costs
Total factor productivity A may also differ between firms
two levels:
and
drawn at firm founding, independently from the share of job task 1
Marginal costs of the production of a symmetric good for firm f :
af : share of migrants in firm f
wM: wage of migrants; wN: wage of natives
two factors: productivity advantage and wage costs advantage
11
Long-Run Equilibrium I
Free Exit:
every firm with nonnegative profit immediately leaves the market
thus there is a minimum job task 1 share with
(Zero-Cutoff-Point):
every remaining firm has a share of job 1
Free-Entry:
new firms are founded as long as the expected lifetime profit of a firm is
positive
Free-Entry-Condition:
12
Long-Run Equilibrium II
Combining Free Entry and Zero-Cutoff Condition yields:
calculate implicit functions
Corner solution:
< 0 all firms produce;
>1 no firm produces
is always smaller than
13
Wages
Labor demand equation:
Average Wage in West Germany
calculate
using above results
3500
3000
Inverse function
higher migrant share higher wage differences
is increasing:
2500
2000
German
1500
EU15
1000
Rest of the World
500
0
Agglomerations
Districts with
Districts with
higher population lower population
density
density
14
Simulation Parameter Set
6
4
2
0
g (x)
8
10
0.0
0.2
0.4
0.6
0.8
1.0
x
15
0.60
0.55
0.50
share of high productive firms
0.65
Simulation – Average Productivity
0.5
1.0
1.5
L_migrants/L_natives
gamma = 0(black), .5(red), 1(green), 1.5(dark blue), 10(light blue)
Share of high productive firms in the market is increasing
Elasticity of substitution between migrants and natives reduces effect
16
-1.5
-1.0
a2*
0.2
0.1
0.0
-2.0
-0.1
-0.2
a1*
0.3
-0.5
0.4
0.0
0.5
Simulation – Minimum-Share Parameter
0.5
1.0
1.5
L_migrants/L_natives
gamma = 0(black), .5(red), 1(green), 1.5(dark blue), 10(light blue)
0.5
1.0
1.5
L_migrants/L_natives
Less productive firms need wage-cost advantages to stay in the market,
while high productive firms do not
Increased average firm productivity thus is not the result of individual firm
productivity increase, but tougher competition among low productive firms
17
Concluding Results from the Model
Constrained job choice and imperfect substitutability explains
wage differential of migrants
emphasizes the role of tasks
A higher migrant share may lead to higher productivity
increased wage differential leads to more firm failures on low
productive firms
The less productive a firm, the more likely it employs a higher
share of migrants
wage advantages compensate for disadvantages in total factor
productivity
18
Anette Haas
[email protected]
www.iab.de
BACK UP
Nested CES-Production Function
qualification
high
low
medium
…
…
task type
interactive
…
analytical
manual
routine /
nonroutine
migrant/
native
…
migrant/
native
21
Estimation Strategy
Similar: Card/Lemieux (2001), D‘Amuri/Ottaviano/Peri (2011)
Additional CES nest(s): Tasks
Substitution elasticities between migrants and natives heterogenous
across tasks, qualification etc.?
Three levels of aggregation
National (like D‘Amuri/Ottaviano/Peri 2011)
Regional (NUTS3)
Establishment (no experience in qualification/task available)
At regional/establishment level: truncation if
L ijkmo ( ft ) = 0 ⇔ w ijkmo ( ft ) ≤ min{ w ijkmo ( t )}
Two-sided „Tobit“ (numerator and denominator of the log employment
ratios)
Preliminary Results for National Level
Data SIAB (1975-2008), panel data 1992-2008
Tasks classified by occupation according to
Gathman/Schoenberg JoLE, 2010
Homogeneous inverse elasticities:
Qualification:
Task:
Experience:
Migrant/Native:
EU15 – others
0.1359
0.0223
0.1648
0.0194
0.0245
σ
−1
Substitution Migrants/Natives by Tasks and Skills
Analytical
Analytical
Manual
Manual
Interactive
Routine
Non-routine Routine
Non-routine Non-routine
Joint
-.0427**
.0175(a)
-.1018**
-.0439**
.0262(a)
University
degree
-.0426**
-.0310*
-.0165*
.0320(a)
-.0253*
Vocational
training .
-.0326**
-.0582**
-.0582**
-.0264*
-.0569*
Low skilled
-.0524**
-.0033
-.1501**
-.1491**
-.2123**
Inverse negative elasticities: the closer to 0, the better the substitutability.
(a) Estimates outside the definition area but not significantly different from zero
*/** significantly different from zero at the 90/95% confidence level
Estimation strategy
model approach
use the formula from the model to estimate the elasticity of substitution
Simulate a migration shock
calculate General equilibrium results using above formula and results
from the estimated CES-parameters
Compare both results
25
Aggregation
Let
be the long equilibrium number of firms and
the distribution of maximum
migrant shares of firms in the market. Define a weighted average productivity:
nice:
not so nice: labor demand
Every firm that makes positive profit will try to stay in business. So define the
minimum necessary productivity
(and thus a minmax migrant share
) by:
26
Results
A higher share of migrants lead to:
stronger relative difference in wages between natives
and migrants
more competition in terms of firms exits
higher average productivity of firms
Clustering of migrants in certain jobs or tasks
27
Equilibrium
The mean and the minimal productivity are related:
so the average profit level is determined by it too:
The Free-Entry condition:
Both conditions lead to:
right side is decreasing monotonically in
.
28
Aggregate labor demand
Labor demand for migrants
Relative labor demand (excluding fixed and entry costs)
the right side is increasing in
and
.
29
Labor Market Segmentation: Case 1
wM
LD Job 1
LS Migrants
wN
LS Natives
wN*
LD Job 2
wM*
LM
LN
Natives and migrants are separated in different labor market segments
The wage for natives exceeds the wage of migrants
Migrants and natives are no substitutes
High Labor supply of migrants: city case
30
Labor Market Segmentation: Case 2
wM
LS Migrants
w
wN
LS Natives
LS M+N
wN* = wM*
LD Job 1+2
LD Job 2
LD Job 1
LM
LN
L
Natives are drawn in the first job due to higher wage
opportunities: labor market segments merge
Migrants and natives are perfect substitutes
Low labor supply of migrants: periphery case
31