Employment Reallocation and
Unemployment Revisited: A Quantile
Regression Approach
Theodore Panagiotidis
Department of Economics, University of Macedonia, Greece
and
Rimini Centre for Economic Analysis, Italy.
Gianluigi Pelloni
Department of Economics, University of Bologna, Italy;
Department of Economics, Wilfrid Laurier University, Canada;
and
Rimini Centre for Economic Analysis, Italy.
1
Introduction
• Intersectoral labour reallocation as a triggering force of
aggregate unemployment fluctuations.
• An aggregate shock → firms to lay off workers temporarily →
changes in aggregate employment and unemployment.
• Sector-specific shocks, affecting the allocation of demand
across sectors, → intersectoral movements of workers → the
time-consuming processes of searching, retraining and
relocating → could also alter the levels of (un) employment
(Lilien, 1982a).
2
Introduction
• Up to 1980’s aggregate shocks seen the driving force of
unemployment cycles.
• Lilien(1982a) Sect. Shifts Hypothesis. : reallocation shocks
→macroeconomic effects.
• Changes in demand composition operate as the driving
force of unemployment fluctuations. Idiosyncratic shocks
bring flows of job reallocation from declining sectors to
expanding ones
3
Literature
• Lilien (1982a): reduced form equation with
dispersion index:
σt = [j (N j,t / N t) ( Δ ln N j,t - Δln Nt)2]1/2
• Criticism: Lilien (1982b, WP); Abraham and Katz
(1986).
• Literature Review: Gallipoli & Pelloni (2008)
4
Methodology
• Most of the existing literature focuses on the
conditional mean response (LRM). The latter
assumes symmetry and linearity.
• Literature approached the issues by employing
nonlinear models both at univeriate and multivariate
level.
• This paper is the first attempt to investigate this
issue by quantile regression (QR): assymetry
5
• QR (Koenker and Basset, 1978) is a tool that
allows us to model distributions.
• Starting point for QRM → conditional quantile
function (CDF).
• The CDF of Yi at quantile τ given a vector of
covariates Xi is given by:
1
y
Q (Yi / X i )  F
( / X i )
6
• Where F ( / X ) is the distribution function of Yi at
y, conditional on X . When τ=0.10 Q (Yi / X i )
describes the lower decile of Yi given X .
• Reduced form of the estimated model:
1
y
i
i
i
Q (ui / X i )  0 ( )  1 ( )s  2 ( )D  3 ( )LM   4( )LE
• ut = ln(Ut/(1- Ut)) logistic transfromation
7
.030
.025
.020
.015
.010
.005
.12
.000
.10
.08
.06
.04
.02
50
55
60
65
70
75
80
85
Unemployment rate
90
95
00
05
10
σ
8
UNRATE
LOGISUNRATE
30
1.6
1.4
25
1.2
1.0
Density
Density
20
15
0.8
0.6
10
0.4
5
0.2
0
.01
.02
.03
.04
.05
.06
.07
.08
.09
.10
.11
.12
0.0
-4.0
-3.8
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
-1.8
9
Quantile Process Estimates (95% CI)
C
SIGMA_PURGED2
-2.7
80
-2.8
60
-2.9
40
-3.0
20
-3.1
0
-3.2
-20
-3.3
-40
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
Quantile
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Quantile
FEDERALDEFICIT
DLAMBSL
-7
4
-8
2
-9
0
-10
-2
-11
-4
-12
-13
-6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
DLCPI_ENERGY
1
0
-1
-2
-3
-4
-5
0.0
0.1
0.2
0.3
0.4
0.5
Quantile
0.6
0.7
0.8
0.9
1.0
10
Quantile Process Estimates (95% CI)
C
SIGMA_PURGED2(-6)
-2.6
80
-2.7
60
-2.8
-2.9
40
-3.0
20
-3.1
0
-3.2
-3.3
-20
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
Quantile
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Quantile
FEDERALDEFICIT(-6)
DLAMBSL(-6)
-5
4
-6
3
-7
2
-8
1
-9
0
-10
-1
-11
-2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
DLCPI_ENERGY(-6)
2
1
0
-1
-2
-3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
11
Quantile Process Estimates (95% CI)
C
SIGMA_PURGED2(-12)
-2.4
50
40
-2.6
30
-2.8
20
-3.0
10
0
-3.2
-10
-3.4
-20
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
Quantile
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Quantile
FEDERALDEFICIT(-12)
DLAMBSL(-12)
-2
6
-4
4
-6
2
-8
0
-10
-12
-2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
DLCPI_ENERGY(-12)
5
4
3
2
1
0
-1
0.0
0.1
0.2
0.3
0.4
0.5
Quantile
0.6
0.7
0.8
0.9
1.0
12
What happens if we replace the logistic transformation with unemployment rate?
Quantile Process Estimates (95% CI)
C
SIGMA_PURGED2
.065
4
.060
3
.055
2
.050
1
.045
0
.040
-1
.035
.030
-2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
Quantile
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Quantile
FEDERALDEFICIT
DLAMBSL
-.3
.2
-.4
.1
-.5
.0
-.6
-.1
-.7
-.8
-.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
DLCPI_ENERGY
.05
.00
-.05
-.10
-.15
-.20
0.0
0.1
0.2
0.3
0.4
0.5
Quantile
0.6
0.7
0.8
0.9
1.0
13
Quantile Process Estimates (95% CI)
C
SIGMA_PURGED2(-6)
.07
5
4
.06
3
.05
2
1
.04
0
.03
-1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
Quantile
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Quantile
FEDERALDEFICIT(-6)
DLAMBSL(-6)
-.35
.24
.20
-.40
.16
.12
-.45
.08
-.50
.04
.00
-.55
-.04
-.60
-.08
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
DLCPI_ENERGY(-6)
.10
.05
.00
-.05
-.10
-.15
0.0
0.1
0.2
0.3
0.4
0.5
Quantile
0.6
0.7
0.8
0.9
1.0
14
Quantile Process Estimates (95% CI)
C
SIGMA_PURGED2(-12)
.08
4
.07
3
.06
2
.05
1
.04
0
.03
-1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
Quantile
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Quantile
FEDERALDEFICIT(-12)
DLAMBSL(-12)
-.2
.4
-.3
.3
-.4
.2
-.5
.1
-.6
.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
DLCPI_ENERGY(-12)
.4
.3
.2
.1
.0
-.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Quantile
15
Conclusions
• Assymetry in the relationship revealed.
• The higher the unemploeyment the more
reallocation is taking place.
• Deficit: upward sloping, negative and
significant
• Money: singificant at the 12 month lag only
when unemployment is high.
• Energy: not singificant
16