Longitudinal Data Analysis

hardtofindcurtainΠολεοδομικά Έργα

16 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

90 εμφανίσεις

CIRCLE, Lund University, Sweden

CENTER FOR INNOVATION, RESEARCH AND
COMPETENCE
IN THE LEARNING ECONOMY

Longitudinal Data Analysis




methods and applications in Innovation Studies


Martin Andersson


CIRCLE, Lund university


CIRCLE, Lund University, Sweden

OUTLINE



Part I:
WHY?
-

identification problems in Innovation Studies and
social sciences more broadly



Part II:
WHAT?

-

introducing panel data analysis



Part II:
HOW?

-

lab session on panel data


CIRCLE, Lund University, Sweden


Part I


Identification problems in Innovation
Studies and social sciences more broadly

CIRCLE, Lund University, Sweden

Identification


Main goal in regression analysis is often
to learn about causal
relationships from micro
-
data
capturing

non
-
experimental
economic

behavior
.



Studies ask "
treatment effect
" questions of the form: what is the
effect of X on Y?



What

is the
effect

of R&D investment on a
firm’s

productivity
?


Does the
the

local

milieu

of a
firm

affects

its

innovativeness
?


What

is the
effect

of general
purpose

technologies

in
growth
?


What

is the
effect

of a
a

local

university

on new
firm

formation?


Does
entrepreneurship

influence

regional
economic

growth
?



CIRCLE, Lund University, Sweden

Identification





Does the
estimated

-

parameter
reflect

a
causal

effect

of
X

on
Y?



How

to ”
isolate
” the
effect

of X on Y?






i
i
i
i
X
Y







CIRCLE, Lund University, Sweden

Identification


Identification is closely linked to consistency:




is the ”true” parameter




is our estimate



Ideally, we choose a model (right technique, right
variables and right assumptions) whichs means that
is consistent, such that it converges to when
N

is
large



This is essentially what identification is all about




true


ˆ
true


ˆ
CIRCLE, Lund University, Sweden

Identification


Manski (2003): the selection problem



The researcher wants to compare the outcomes that people would experience if
they were to receive alternative treatments. However, treatments are mutually
exclusive. At most, the researcher can observe the outcome that each person
experiences under the treatment that this person actually receives. The
researcher cannot observe the outcomes that people would have experienced
under other treatments. These other outcomes are counterfactual. Hence, data
on treatments and outcomes cannot by themselves reveal treatment effects.”



IDEAL: “treated” individuals selected randomly


When is random treatment selection appropriate?


in the analysis of data from classical randomized experiments. This is the
main reason why randomized experiments are valued so highly.


The assumption of random treatment selection is usually suspect in non
-
experimental settings, where observed treatments may be self
-
selected or
otherwise chosen purposefully.

CIRCLE, Lund University, Sweden

Identification


Example

1.1 in
Jurada

(2007):



Suppose that you are interested in the effect of military
service on subsequent earnings. You can look at the mean
difference in the outcome between veterans and non
-
vets.



…. but, inside this number hides not only a causal effect of
the service, but also the composition of other causal
variables in each group, both observed and unobserved.



Are there variables that affect both participation in the
program and the outcome? Are the vets earning more
because of the military service or are the high
-
earners more
likely to enroll in the army?

CIRCLE, Lund University, Sweden

Identification


One solution is to
control

for
factors

that
may

drive
selection
.




Typical procedure in most empirical papers

»
we are interested in
x
but to isolate its effect we control for
z
.



when is controlling for observable factors enough to identify a causal effect ?
=> when is “selection on observables plausible”?



When is it plausible that conditional on Z, assignment to treatment is “ideal”,
i.e. as good as random?


If applicants to a college are screened based on Z, but conditional on passing the
Z test, they are accepted based on a random draw.



IMPORTANT TO THINK ABOUT THE DATA GENERATING PROCESS (DGP)

CIRCLE, Lund University, Sweden

Identification


An
issue

of

selection

vs.

learning




Applies

to
several

different
topics

in Innovation Studies


Roles

of
selection

and
learning

is
typically

of great
conceptual

interest

and
policy relevant



usually

we

think

of ”
learning
” as
reflecting

a
causal

effect
:



Three
examples

from the
literature
:



Persistence

of Innovation


Exporting

and
productivity


Urban
Wage

Premium


CIRCLE, Lund University, Sweden

Example

1:
Persistence

of Innovation


Bettina Peters:


Persistence of Innovation:
stylised

facts and panel data evidence,
Journal of Technology Transfer
, 2009



German
manufacturing

and services
firms

1994
-
2002:


Is innovation persistent? =>
Yes
!



What

drives this?



CIRCLE, Lund University, Sweden

Example

1:
Persistence

of Innovation


1: “True” state dependence.



a causal behavioral effect:
the decision to innovate in one period in
itself enhances the probability to innovate in the subsequent period
.



(
i
) success breeds success (Mansfield 1968)



(ii) innovations involve dynamic increasing returns (Nelson and
Winter 1982 and
Malerba

and
Orsenigo

1993)



(iii) sunk costs in R&D investments (Sutton 1991)

CIRCLE, Lund University, Sweden

Example

1:
Persistence

of Innovation


2: Selection on time
-
invariant characteristics



Innovating firms may have characteristics which make them
particularly ”innovation
-
prone”



If these characteristics themselves show persistence over time,
they will induce persistence in innovation behavior.



If these are not appropriately controlled for, past innovation may
appear to affect future innovation merely because it picks up the
effect of the persistent characteristics.



In contrast to true state dependence this phenomenon is therefore
called
spurious state dependence

CIRCLE, Lund University, Sweden

Example

2:
Exporting

and
Productivity


Stylized fact that exporters are more productive


In Sweden, persistent exporters are about 20 % more productive than are non
-
exporters (
Andersson

et al 2008)



Why?



Learning
-
by
-
exporting
:


Causal effect from exporting on productivity


Knowledge accumulation through interaction with foreign customers may stimulate
innovation and productivity


Export markets more competitive and stimulate reduction of X
-
inefficiencies and adoption
of ‘best
-
practice’ routines



Self
-
selection:


Exports associated with entry costs, implying productivity thresholds that only more
productive firms can overcome (Bernard and Jensen 2004, Greenaway and Kneller
2007, Wagner 2007)



Simply

analzying

the
relationship

between

exports and
productivity

withouth

further

controls

and/or
study

of time
sequences

(ex post // ex ante)
tells

us

nothing

about

the
relevance

of the different
explanations
.



CIRCLE, Lund University, Sweden

Example

3: Urban
Productivity

Premium


Wages (and productivity) generally higher in larger regions



Figure
1
.
The relationship between mean wages (log) and accessibility to total
e
conomic activity

(log) acr
oss
Swedish municipalities in 2008.

Log access
ibility to wages

Log mean wage

CIRCLE, Lund University, Sweden

Example

3: Urban
Productivity

Premium



Selection


the “best” and the “brightest” move to the cities



Learning


Causal effect “from the environment” on productivity


operating
in a
dense
agglomeration stimulate a
worker’s productivity



CIRCLE, Lund University, Sweden

Example

3: Urban
Productivity

Premium

Alfred Marshall on
selection

in 1890:


”In almost all countries there is constant migration towards the
towns. The large towns and especially London absorb the very best
blood from all the rest of England: the most enterprising, the most
highly gifted, those with the highest physique and the strongest
characters go there to find scope for their abilities”

CIRCLE, Lund University, Sweden

Example

3: Urban
Productivity

Premium


Learning relates to
‘pure’ agglomeration effects and is
conceptually rooted in the literature on agglomeration economies
and localized human capital spillovers (Rauch 1993,
Glaeser

2008
).



Agglomerations as “innovation environments” (
Glaeser

1999)



CIRCLE, Lund University, Sweden

Example

3: Urban
Productivity

Premium


Big
literature

focused

on
untangling

the relative
roles

of
selection

and
learning

in
explaining

the UWP.



Risk of
overestimating

learning

(
causal

effect

from agglomeration
on
productivity
)
if

not
appropriately

controlling

for
selection






CIRCLE, Lund University, Sweden

Identification


Thinking

in terms of ”
selection
” and ”
learning

important

for
identification



but
,




selection

and
learning

effects

are, at
least

conceptually
,
seldom
mutually

exclusive




and,



their

relative
roles

often

bear

on
theory

as
well

as policy





CIRCLE, Lund University, Sweden

Identification


Example

UWP:



Theory and conceptualizations:


if selection is the dominant source of the city productivity premium, then
theory should focus on why cities attract more productive workers rather
than why cities are more productive (
Glaeser

and
Maré

2001)



Policy


learning effects provides support for policies stimulating the growth of large
city agglomerations.


CIRCLE, Lund University, Sweden

Identification


Example

persistence

of innovation:



Theory and conceptualizations:



Endogenous
growth models:



Romer

(1990
)
assumes that innovation
behaviour

is persistent at
the firm
level to a very large
extent.


Aghion

and
Howitt

(1982) suggest that
the process of creative destruction
leads to a
perpetual renewal
of
innovators.



Empirical knowledge
about the dynamics in firms’ innovation
behaviour

is a tool to assess
different endogenous
growth
models


CIRCLE, Lund University, Sweden

Identification


Policy



If
innovation is state dependent, innovation

stimulating policy measures such as
government support
programmes

are supposed to have a more profound effect
because they do not only affect current innovation activities but are also likely to
induce a permanent change in
favour

of innovation.



If
, on the other hand, individual heterogeneity induces persistent
behaviour
,
support
programmes

are unlikely to have long

lasting effects and policy should
concentrate more on measures which have the potential to improve innovation

relevant firm

specific factors.


CIRCLE, Lund University, Sweden

Identification


SUMMARY:




For identification of the effect of X on Y, accounting for selection
is imperative.



Selection vs. learning a key issue in many lines of inquiry in
Innovation Studies, as well as in the social sciences more
broadly



But how to account for selection?


CIRCLE, Lund University, Sweden

Identification


Selection on observables:



Estimate
effect of X on Y, while controlling for observable
characteristics of the ”observational units”, such as individuals or
firms.



Firms:
productiviy, employment size, location, capital stock, human
capital, industry affliation ownership structure



Individuals:
age, gender, education, place of residence, tenure, etc.



NOTE: one reason for the growing popularity of using micro
-
level datasets on
individuals and firms is the potential for accounting for selection on observables




CIRCLE, Lund University, Sweden

Identification


Problem!



We do not observe all relevant attributes of firms and
individuals that may be of importance in explaining the
phenomena we are interested in.



Firms:

managerial abilities, organizational routines,
attitudes towards risk, technological opportunities, etc



Individuals:
IQ, skills, creativity, risk attitudes and all other
sorts of innate abilities




What to do?






CIRCLE, Lund University, Sweden

Identification


One option is selection on “
unobservables




We can do this with panel data.



Many researchers maintain that the main advantage of panel
data is that one can get rid of unobserved heterogeneity,
since unobserved heterogeneity is
considered as ‘
the

problem
of non
-
experimental
research.






CIRCLE, Lund University, Sweden

Part II


Introducing panel data analysis

CIRCLE, Lund University, Sweden

What is panel data?


Panel data are a form of longitudinal data,
involving
regularly
repeated observations on the same
individuals



Individuals
may be people, households, firms, areas,
etc



Repeated
observations
over time



repeated cross
-
sectional time
-
series

CIRCLE, Lund University, Sweden

Typical data structure

Id

Year

y

x

z

1

t1

y11

x11

z11

1

t2

y12

x12

z12

2

t1

y21

x21

z21

2

t2

y22

x22

z22

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

N

t1

yN1

xN1

zN1

N

t2

yN2

xN2

zN2

CIRCLE, Lund University, Sweden

Terminology in panel data applications


A
balanced panel
has the same number of time observations (
T
) for
each of the
n
individuals



An
unbalanced panel
has different numbers of time
observations
(
Ti
) on each
individual



A
compact panel
covers only consecutive time periods for
each individual


there are no “gaps”



Attrition
is the process of drop
-
out of individuals from the
panel, leading
to an
unbalanced (and possibly non
-
compact) panel



A
short panel
has a large number of individuals but few
time observations
on
each



A
long panel
has a long run of time observations on
each individual
, permitting
separate
time
-
series analysis for each

CIRCLE, Lund University, Sweden

Benefits of panel data


They are more informative (more variability, less
collinearity
, more
degrees
of freedom
), estimates are more efficient.



They
allow to study individual
dynamics



Some
phenomena are inherently longitudinal (
e.g.
poverty
persistence;
unstable employment
)



The ability to make causal inference is enhanced
by
temporal
ordering



They
allow to control for individual unobserved heterogeneity

CIRCLE, Lund University, Sweden

A note on casual inference and panel data


This example is based on Brüderl (2005)



Let
i
denote an individual,
t
time,
T

treatment and
C

non
-
treatment.
Y
is the
outcome we are interested in.



Optimal identification is: => impossible! (clones not available)



Cross
-
sectional data: => compare treated with untreated



This only provides the
“true
causal
effect”
if
the assumption of unit homogeneity
(no
unobserved heterogeneity) holds. Requires ’perfect’ controls



With panel data:


=> ’within estimation’



We observe the same indiviual before and after treatment.
Unit
homogeneity here is needed only in an intrapersonal
sense!!



C
t
i
T
t
i
Y
Y
0
,
0
,

C
t
j
T
t
i
Y
Y
0
,
0
,

C
t
i
T
t
i
Y
Y
0
,
1
,

CIRCLE, Lund University, Sweden

The issue with not accounting for
unobserved ability


We want to analyze the effect of human capital
x
on a firm
i
’s innovation output,
y
.



We have panel data and set up the following model:






Despite panel data, all issues of selection is at work
here as well.



It may be the managerial ability of the firms that
matters. The effect of
x

on
y
may be biased because
more high
-
ability managers tend to recruit more human
capital. (
omitted variable bias
)


it
it
it
x
y






CIRCLE, Lund University, Sweden

The issue with not accounting for
unobserved ability


Unobserved heterogeneity, such as managerial ability, end
up in the error term .



But if high
-
ability managers hire more human capital, then
this means that and are correlated.


This violates the assumption of exogenity



Endogeneity

(X
-
variable correlates with
the error term)
results
in biased regression estimates.



Endogeneity

can be
a
consequence
of
unobserved
heterogeneity.

it

it
x
it

CIRCLE, Lund University, Sweden

How panel data can take care of
unobserved heterogeneity


Panel
data
in itself do
not remedy the problem of
unobserved
heterogeneity


but one can apply techniques using panel data that do
that.



Within transformation does the trick.



Panel data:


Variance across individuals (between variance)


Variance within individuals over time (within variance)


CIRCLE, Lund University, Sweden

How panel data can take care of
unobserved heterogeneity


Suppose the managerial ability of each firm
i
is time
-
invariant.


Denote this by (firm
-
specific fixed effects)


A model including (unobserved) managerial ability would read:




(1)



Take the average value of each
i
:



(2)


We have ”taken away” the time dimension and have a cross
-
section with
average values of the time periods. (between variation)







it
i
it
it
x
y






i

i
i
i
i
x
y






CIRCLE, Lund University, Sweden

How panel data can take care of
unobserved heterogeneity


Now substract the second equation from the first:







is gone!



Why? => it is constant over time, so its mean value over
the periods for each
i
is the same:



Time
-
constant unobserved
heterogeneity is
no longer a
problem







i
it
i
it
i
it
x
x
y
y








)
(
0




i
i
i
i




i

CIRCLE, Lund University, Sweden

How panel data can take care of
unobserved heterogeneity


Within transformation means that the data is "time
-
demeaned".



Only
the within variation
is left
, because we subtract the
between variation.



The within
-
transformation made possible by panel data
allows researchers to account for time
-
invariant
unobserved heterogeneity


Better identification






CIRCLE, Lund University, Sweden

Is unobserved heterogeneity empirically
important?


Yes!


in many research papers the magnitude of the estimated
effects of
x
on
y

depends to large extent on whether one
accounts for unobserved heterogeneity or not



Example:


Andersson, Klaesson and Larsson (2012),



”Selection and Learning of Workers in Cities”




CIRCLE, Lund University, Sweden

Is unobserved heterogeneity empirically
important?


Main question:



How important is selection and learning, repectively, in
explaining the urban wage premium?



Panel
data of private sector workers 2001
-
2010

CIRCLE, Lund University, Sweden

Identification of selection


Workers are heterogeneous:


eduction, age, gender:
observed


innate ’abilities’:
unobserved



Suppose wages are10% higher in cities



how much of this is due to workers in cities being better
educated and older?



how much of the wage diffence remains
after
controlling
education and age?



if
selection is important, we should observe that the
wage premium drops as we account for worker
heterogeneity
.



CIRCLE, Lund University, Sweden

Identification of selection




We
run different models and test how sensitve the
city wage
premium
is to observed and unobserved worker heterogeneity


CIRCLE, Lund University, Sweden

Identificatin of learning


1: indirectly quantified while accounting for selection


remainder wage gap after controlling for spatial sorting of
workers



2: identification of workers that move from urban to rural regions.



faster human capital accumulation in cities => the
advantages of having worked in a larger dense city should
remain while moving away.



we estimate the wage premium for workers that move
away from dense agglomerations and test if their wage
drops or remains upon moving.


CIRCLE, Lund University, Sweden

Wages, education levels and skills in the
Swedish economic geography


Table 3.
Key figures divided by fraction of non
-
routine work tasks.

Jo
b type

Mean wage
(EUR)

Graduate
share

Mean
experience

Metropolitan
share

All types of professions

High fraction non
-
routine tasks

29 698

36 683

15%

28%

22

23

27%

36%

Low fraction non
-
routine tasks

23 088

3%

21

19%

Note:

Graduate share is the fraction of

workers with a university education of at least three years. Metropolitan
share is the fraction of workers that work in three biggest labor market regions: Stockholm, Göteborg and
Malmö. Wages converted to EUR using the 2008 exchange rate between SEK and
EUR of 9.68. High
(low) fraction non
-
routine jobs are those with fraction non
-
routine tasks above (below) the mean fraction
across all occupations (see Table 2).

CIRCLE, Lund University, Sweden

Wages, education levels and skills in the
Swedish economic geography


Table 4
. Mean wages (2008) and unadjusted wage gap between metropolitan and non
-
metropolitan workers.

Job type

Metropolitan
wag
e (EUR)

Non metropolitan
wage (EUR)

Wage
differential

All types of professions

34 417

27 926

23%

High fraction non
-
routine tasks

41 024

34 245

20%

Low fraction non
-
routine tasks

22 634

23 195

-
2%

Note:

The metropolitan areas are defined as the three bi
ggest labor market regions: Stockholm, Göteborg and
Malmö. Wages converted to EUR using the 2008 exchange rate between SEK and EUR of 9.68.

High
(low) fraction non
-
routine jobs are those
with fraction non
-
routine tasks

above (below) the mean fraction
acros
s all occupations (see Table 2).

How much of the wage premium in larger cities is due to
selection?

CIRCLE, Lund University, Sweden

Empirical model



...
ln
ln
ln
ln
3
2
1





E
rt
R
rt
M
rt
irt
De
De
De
w





(3)




irt
TR
tR
R
t
tR
T
t
t
t
R
R
R
D
D
D
D

















γ
Z
1
1
81
1
...

De = market potential measures
(Harris 1954)



In red:
time effects, regional effects, region
-
specific ”shocks”


In green:
worker characteristics

CIRCLE, Lund University, Sweden

Table 6.
The relationship between spatial economic density and wages
, all private sector workers.


Raw OLS

Mincerian
OLS

Full OLS

Raw with
worker FE

Full with
worker F
E

Municipal density
(log)

0.0326***

0.0218***

0.0205***

0.00773***

0.00538***

(0.00322)

(0.00224)

(0.00123)

(0.000242)

(0.000242)

Regional density
(log)

0.0335***

0.0218***

0.0195***

0.00790***

0.00522***

(0.00777)

(0.00425)

(0.00641)

(0.000518)

(0.0
00514)

Extra
-
regional
density (log)

-
0.0323*

-
0.0221

-
0.0248***

-
0.0127***

-
0.00797***

(0.0185)

(0.0139)

(0.00788)

(0.000679)

(0.000674)

Years of schooling


0.0930***

0.0823***


0.117***


(0.00468)

(0.00300)


(0.0190)

Experience


0.0503***

0.0408***


0.0587***


(0.00326)

(0.00279)


(0.0190)

Experience^2


-
0.000781***

-
0.000635***


-
0.000745***


(5.42e
-
05)

(4.64e
-
05)


(2.84e
-
06)

Immigrant (dummy)


-
0.136***

-
0.108***




(0.00737)

(0.00409)



Male (dummy)


0.351***

0.330***




(0.00947)

(0.0
0425)



Tenure



0.0176***


-
0.0109***



(0.000458)


(0.000127)

Number of prior
employees



-
0.0120***


-
0.0189***



(0.00286)


(0.000176)

New occupation
(dummy)



-
0.0930***


-
0.0268***



(0.00222)


(0.000366)

Employer size (log)



0.0257***


0.
0183***



(0.00225)


(0.000175)

Year dummies

Yes

Yes

Yes

Yes

Yes

Region dummies

Yes

Yes

Yes

Yes

Yes

Region*Year effects

Yes

Yes

Yes

Yes

Yes

Education type
dummies

No

Yes

Yes

No

Yes

Industry dummies

No

No

Yes

No

Yes

Observations

12,367,700

12,367,70
0

12,367,700

12,367,700

12,367,700

Individuals

2,681,164

2,681,164

2,681,164

2,681,164

2,681,164

R
-
squared

0.031

0.248

0.288

0.059

0.078

Note:
The table reports

estimates of wage
-
density elasticities for private sector workers in Sweden 2002
-
2008.
Raw r
efers to the
wage equation in
e
quation (3)

without any further controls
.
The Mincerian model adds
years of schooling, experience and its squared value as well as dummies for immigrant
s
,
males

and
education specialization. The full specification further add
s variables reflecting labor market status and
employer characteristics of each worker. OLS refers to the pooled OLS estimator and FE to a panel
estimator

with worker fixed effects
. All v
ariables are defined in Table 1.
The full FE model excludes
immigrant

and sex dummies as these reflect time
-
invariant worker characteristics.
All models include
year and region dummies as well as

region
-
year dummies, where the latter account for any region
-
specific
time
-
varying shocks shared by all workers in the same local

labor market region
.

The dependent variable
is the nat
ural logarithm of wage earnings
. Robust standard errors are presented in brackets.
*** p<0.01,
** p<0.05, * p<0.1
.

CIRCLE, Lund University, Sweden

Is unobserved heterogeneity empirically
important?



The wage
-
density elasticity drops from 3.3% to 0.8% when
accounting for worker fixed effects (within transformation)!!



Selection on observables relatively unimportant.




CIRCLE, Lund University, Sweden

Table 7.
The relationship between spatial econ
omic density and wages for workers with occupations associated
with high fractions of non
-
routine job tasks.


Raw OLS

Mincerian
OLS

Full OLS

Raw with
worker FE

Full with
worker FE

Municipal density
(log)

0.0317***

0.0253***

0.0250***

0.00810***

0.00655***

(0.00206)

(0.00260)

(0.00141)

(0.000345)

(0.000346)

Regional density
(log)

0.0364***

0.0263***

0.0240***

0.00868***

0.00618***

(0.00734)

(0.00523)

(0.00829)

(0.000772)

(0.000769)

Extra
-
regional
density (log)

-
0.0271

-
0.0231

-
0.0253**

-
0.0124***

-
0.0
0834***

(0.0232)

(0.0183)

(0.0114)

(0.00105)

(0.00105)

Years of schooling


0.0797***

0.0766***


0.133*


(0.00312)

(0.00289)


(0.0691)

Experience


0.0556***

0.0513***


0.0926


(0.00204)

(0.00185)


(0.0691)

Experience^2


-
0.000862***

-
0.000794***


-
0.000737***


(3.95e
-
05)

(3.54e
-
05)


(4.05e
-
06)

Immigrant (dummy)


-
0.0419***

-
0.0371***




(0.00285)

(0.00260)



Male (dummy)


0.353***

0.351***




(0.00319)

(0.00306)



Tenure



0.0105***


-
0.00644***



(0.000400)


(0.000172)

Number of prior
e
mployees



0.000754


-
0.00741***



(0.000741)


(0.000237)

New occupation
(dummy)



-
0.0703***


-
0.0151***



(0.00209)


(0.000502)

Employer size (log)



0.0259***


0.0149***



(0.00314)


(0.000236)

Year dummies

Yes

Yes

Yes

Yes

Yes

Region dummies

Y
es

Yes

Yes

Yes

Yes

Region*Year effects

Yes

Yes

Yes

Yes

Yes

Education type
dummies

No

Yes

Yes

No

Yes

Industry dummies

No

No

Yes

No

Yes

Observations

5,986,454

5,986,454

5,986,454

5,986,454

5,986,454

Individuals

0.038

0.258

0.280

0.061

0.074

R
-
squared

1
,388,166

1,388,166

1,388,166

1,388,166

1,388,166

Note:
The table reports estimates of wage
-
density elasticities for private sector workers in Sweden 2002
-
2008
with occupations associated with high fractions of non
-
routine job tasks (see Table 2).
Raw refe
rs to the
wage equation in equation (3) without any further controls. The Mincerian model adds years of schooling,
experience and its squared value as well as dummies for immigrant
s
,
males

and education specialization.
The full specification further adds v
ariables reflecting labor market status and employer characteristics of
each worker. OLS refers to the pooled OLS estimator and FE
to a panel estimator with worker fixed
effects
. All variables are defined in Table 1. The full FE model excludes immigrant an
d sex dummies as
these reflect time
-
invariant worker characteristics. All models include
year and region dummies as well as

region
-
year dummies, where the latter account for any region
-
specific time
-
varying shocks shared by all
workers in the same local la
bor market region
.

The dependent variable is the natural logarithm of wage
earnings. Robust standard errors are presented in brackets.
*** p<0.01, ** p<0.05, * p<0.1

Non
-
routine
workers

CIRCLE, Lund University, Sweden

Table 9.
Wage premium for workers moving away from a metropolitan region to
the rest of the country, by
fraction of non
-
routine job tasks.


All private sector
workers

High fraction non
-
routine tasks

Low fraction non
-
routine tasks

Dummy
for
moving away
from metropolitan region

0.00286 ***

(0.0014)

0.01085***

(0.0020)

-
0.00055

(0.
0021)

Model

Full with worker fixed
effects

Full with worker fixed
effects

Full with worker fixed
effects

Note:
The table reports the coefficient estimate of a dummy variable reflecting a move from
any of Sweden’s
three metropolitan labor market regions (
Stockholm, Göteborg and Malmö)

to anywhere else in Sweden
.


The underlying model is a panel estimator with worker fix effects including the full set of additional
control variables report
ed

in

the ‘Full with worker FE’ specification in Tables 6
-
7.

Complete

estimation
results are obtained from the authors upon request.

The dependent variable is the natural logarithm of
wage earnings. Robust standard errors are presented in brackets.
*** p<0.01, ** p<0.05, * p<0.1

RESULTS FOR ”MOVERS” (from urban to rural)


CIRCLE, Lund University, Sweden

CONCLUSIONS


Who
you are and the kind of job you have are more
important than where you live in explaining spatial wage
disparities.



The
main reason why workers in denser regions earn more
is simply that they are different from the workers in more
rural regions.



Learning
effects (or pure agglomeration economies) are
not zero but are quantitatively of smaller importance than
spatial sorting.

CIRCLE, Lund University, Sweden

Some issues


Identification of parameters:



In the FE
-
model, parameters are identified from changes in
indiviuals over time.



Time
-
invariant variables cannot be estimated (gender, race,
education etc......)



Effects of dummy variables is only identified based on those
individuals that change status over time (e.g. from 0 to 1, or 1 to 0)



There
must be some variation in
the variable of interest. Otherwise
,
we cannot estimate
its effect
. This is
potentially a
problem, if only a
few observations show a change
in a variable.



CIRCLE, Lund University, Sweden

An example


Suppose you estimate the effect of a location in a high
-
tech
cluster on firm innovation.


We have a dummy which is 1 for firms in a cluster, and 0 otherwise



Model 1 is a cross
-
section:



Here the is identified from differences between firms ’inside’ and
’outside’ a high
-
tech cluster



Model 2 is a an FE
-
model (within transformation):





Here the is identified from firms that move into (or out from) a high
-
tech
cluster. Captures instantaneous effect on
y
from moving into a cluster.


i
i
i
i
Cluster
x
y








2
1
2

it
i
it
it
it
Cluster
x
y










2
1
2

CIRCLE, Lund University, Sweden

Some issues continued


Fixed and random effects:



An alternative to FE is Random
-
effects (RE).



RE exploits both within and between variation. But, it relies on the
restrictive assumption that the unobserved individual effects are
uncorrelated with the explanatory variable (x). The FE
-
model do
not.



The RE
-
estimator, however, provides estimates for time
-
constant
covariates. Many
researchers want to report effects
of sex, race, etc. Therefore,
they choose
the RE
-
estimator
over the FE
-
estimator.



CIRCLE, Lund University, Sweden

Panel data estimation in practice


Most statistical packages, such as STATA or LIMDEP,
have built
-
in meny
-
based procedures for panel data
analysis



Next class: panel data analysis in practice using STATA


declaring data to be panel


describing datasets


descriptive statistics


estimation of FE, RE and BE models


interpretation of coefficients