Transcript TIME DISTANCE Concept and novel generic statistical measure

SICENTER
Ljubljana, Slovenia
Time Distance Measure for
Analysis and Presentation:
Benchmarking and Monitoring of
Structural Indicators
Professor Pavle Sicherl
Presented at the 2nd Meeting of the EPC Task Force on Structural
Indicators, Brussels, September 7, 2006
SICENTER and University of Ljubljana
Email: [email protected]; www.sicenter.si
Copyright © 1994-2006 P. Sicherl All rights reserved
Three issues in the presentation
1.
S-time-distance is a novel generic statistical
measure (like static difference or growth rate) and
an excellent presentation tool
2.
Application in comparative analysis and in
benchmarking
3.
Application in monitoring implementation of
Lisbon and Growth and Jobs Strategy
SUMMARY: Benefits of immediate operational uses of time
distance methodology for Commission services
Example: A Comparison of European and US
Economies Based on Time Distances
US-EU gaps in GDP per capita:
static index and time distance
100
US GDP per capita (2003=100)
95
90
85
Index
141
80
75
70
S-time-distance 18 years
US
65
60
55
50
EU15
45
EU15
40
US
35
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002
Time
Source: P. Sicherl, A Comparison of European and US Economies Based on Time
Distances, EUROCHAMBRES, Brussels, March 2005
The fact that
comparisons should
be made in two
dimensions has been
verified by the worldwide media interest in
my analysis for the
EUROCHAMBRES
Spring Business
Forum. The static
ratio of 1.41 does not
catch much attention,
while the time gap of
about two decades
obviously produced a
different perception of
reality. The same will
be true for comparing
within the EU.
FURTHER
APPLICATIONS
PERCEPTION OF A SITUATION
A NEW VIEW IN TIME SERIES ANALYSIS
I. DESCRIPTIVE STATISTICAL MEASURE
II. a. CONCEPT OF MULTIDIMENSIONAL
COMPARISON AND EVALUATION
b. PRESENTATION
c. VISUALIZATION
d. SEMANTICS: POLICY, MANAGEMENT
III. STOHASTIC MODELS WITH S-TIME-DISTANCE
-e.g. criterion for evaluating forecasting models
(Granger and Jeon, 2003)
IV. DECISION MAKING MODELS
- extension of decision making models
A new view of the information using levels
of the variable as identifiers and time as the
focus of comparison and numeraire
Time matrix from the inverse relations: time when a specified
level of the variable was achieved in each compared unit
Level
XL1
XL2
XL3
…
XLn
Time
ti (XL)
ti (XL2)
ti (XL3)
…
ti (XLn)
Time
tj (XL)
tj (XL1)
tj (XL2)
tj (XL3)
…
The resulting time matrix provides new information from
which new generic measures can be derived.
Two operators applied to this time matrix lead to the
derivation of two novel statistical measures, expressed in
standardized units of time.
 Subtracting horizontally the respective times in the time matrix
we get a special category of time distances S-time-distance for
a given level of XL defined as
Sij(XL) = t(XL) = ti(XL) – tj(XL)
(1)
 Subtracting vertically the respective times in the matrix for
consecutive levels of the variable for each column we get the
second suggested measure S-time-step
Si(XL) = (tXL+X – tXL)/X
(2)
The concept of S-time-step measures the growth characteristics of a series,
using the inverse relation to the conventional X/t or growth rate metrics.
Source: P. Sicherl, Time Distance: A Missing Link in Comparative Analysis, 28th General Conference of
the International Association for Research in Income and Wealth, Cork, Ireland, August 22-28 2004
General conclusions on the first issue
Time distance concept and statistical measure S-time-distance is:
- theoretically universal
- intuitively understandable
- immanently practical
“The usual matrix for comparing two lines involves differences along the
vertical axis. This can be a poor way of measuring how these trends vary in
terms of time which is on the horizontal axis… Sicherl’s several works have
presented a non-technical discussion of the theory of time distance…
As Sicherl (1973, 1993) proposes… observed time distance is a dynamic
measure of temporal disparity between the two series, intuitively clear,
readily measurable, and in transparent units….. ”
C.W.J. Granger and Y. Jeon, University of California at San Diego
“Time distance is a generic concept. That means that, as it has been the case
e.g. with spreadsheet, one cannot in advance specify all the uses to which a
generic framework can be put by imaginative users in numerous fields.”
J. Backhouse, Information Science Dpt., London School of Economics
METHODOLOGY: a broader perception,
policy and welfare
Importance for European development paradigm: the relations
between growth, efficiency and inequality in Lisbon strategy are
different with a dynamic concept of overall degree of disparity
Per capita income (log scale)
10000
Static relative measure and time distance lead to different conclusion:
higher 4% growth example ratio=1.5, S=10 years;
lower 1% growth example ratio=1.5, S=40 years.
unit 1
unit 2
1000
S121(t)
S122(t) R12(t)
unit 1
S121(t)
S122(t)
unit 2
R12(t)
100
1960
1970
1980
1990
2000
Time
2010
2020
2030
2040
Higher growth
rates lead to
smaller time
distances, and
thus have an
important effect
on the overall
degree of
disparity. This is
based on both
static disparity
and time
distance, as
both matter.
Static measures
alone are
inadequate.
Static measure and time distance show two very different
messages about importance of different components
EU15-US - Static Disparities (2003)
30
150
145
Time distance between the EU15 and the US
(years)
25
141
25
23
Index EU15=100
135
130
125
120
115
111
113
114
EU15 time lag in years
140
20
18
15
10
110
5
5
105
100
GDP per capita
Employment
Rate
Annual Hours
Worked
Productivity
(GDP per hour)
Percentage differences between US and
EU15 for employment rate, annual hours
worked and productivity per hour are
very similar. It seems as if the difficulty
of catching up would be similar in the
analysed components.
0
GDP per capita
Employment
Rate
Annual Hours
Worked
Productivity
(GDP per hour)
S-time-distances are very different, for
productivity per hour only 5 years, while
for employment rate and annual hours
worked are about a quarter of a century.
Policy analysis should expect different
difficulties of catching up in these fields.
ANALYTICAL AND PRESENTATION TOOL
Estimates of time distances for the past and time distances (projected) at the level of EU15
average GDP per capita for 2005 (Scenario: growth rate in selected countries is 4%)
Backward looking S-time-distances for EU15 average
Forward looking S-time-distances for EU15 average for 2005
100
95
90
CY 6 years
EU15 average for 2005=100
85
SI 7 years
S-time-distance for
CY 15 years
S-time-distance for SI 17 years
80
75
EU15
CZ 10 years
MT 12 years
70
S-time-distance for CZ 21 years
65
S-time-distance for MT 26 years
MT
S-time-distance for HU 29 years
HU
EE
SK 18 years
55
SK
S-time-distance for EE 34 and for SK 35 years
50
LT 19 years
S-time-distance for LT 36 and for PL 37 years
45
LT
PL
PL 20 years
S-time-distance for LV 38 years
LV
LV 22 years
40
35
30
1960
1965
1970
1975
1980
1985
1990
1995
Time
© P. Sicherl 2006
SI
CZ
HU 14 years
EE 17 years
60
CY
2000
2005
2010
2015
2020
2025
2030
MANY COUNTRIES: ONE INDICATOR FOR A GIVEN YEAR
GDP per capita (ppp): time distances for 2005 from EU15 average
LU
DK
AT
IE
NL
SE
BE
UK
FI
FR
DE
EU15
IT
EU25
ES
CY
GR
SI
CZ
PT
MT
HU
EE
SK
LT
PL
LV
40
35
© P. Sicherl 2006
30
25
20
15
10
5
0
-5
-10
-15
-20
S-time-distance (years): - time lead, + time lag
-25
-30
-35
-40
Comparisons over many indicators can show characteristic profiles
across countries, regions, socio-economic groups, firms, etc.
Time distances in years between the USA and EU15 average for
selected indicators for 2003 (- time lead, + time lag for the USA)
-30
S-time-distance in years
-25
-20
-15
-10
-5
-18
-25
-23
-5
-23
0
10
10
Life
expectancy
females
Infant survival
rate
5
10
15
GDP per
capita
Employment
Rate
Annual Hours GDP per hour
Worked
R&D per
capita
economic indicators
© P. Sicherl 2005
Source: Interview with P.Sicherl - Semanario Economico, Lisbon, March 18, 2005
social indicators
Graph HU
Time distances between Hungary and EU15 average around 2004 (EU15=0)
S-distance in years, - time lead, + time lag for Hungary
S-time-distance (years): - time lead, + time lag
-20
HU
-10
0
29
28
11
25
11
9
4
1
1
10
20
30
> 30
>34
40
GDP per
capita (ppp)
GDP per
employed
(ppp)
R&D per
capita
Export per
capita
Employment
rate
1
2
3
4
5
© P. Sicherl 2006
Life
Infant survival
expectancy
rate
(female)
6
7
Personal
computers
per capita
8
Internet users Internet hosts
per capita
9
10
Mobile
phones per
capita
11
Time distance measure is intuitively understood by policy makers,
managers, media and general public and is comparable across
different variables, fields of concern, and units of comparison.
1st income
Low
quartile
education
Internet usage at home
Age 50+
Internet usage at home
Female
Digital divide in EU15 in time (S-time-distance): how many months earlier was the level of
selected categories in 2002 attained by average Internet usage
Internet usage at home
60
Internet usage
52
Internet usage at home
43
Internet usage
26
30
Internet usage
19
13
Internet usage
5
0
12
24
36
48
60
72
S-time-distance in months: time lag behind the average Internet usage (base=0)
Source: P.Sicherl, A New Generic Statistical Measure in Dynamic Gap Analysis, The European E-Business Report, 2004 Edition,
European Commission, Enterprise Directorate General, Luxembourg, 2004
The generic idea for many other applications of S-time-distance
S-time-distance adds a second dimension to comparing
actual value with estimated value, forecast, budget, plan,
target, etc. and to evaluating goodness-of-fit in regressions,
models, forecasting and monitoring
e5
Variable X
S4
S5
e4
S2
e2
S3
S1
e1
Time
e3
Monitoring and goodness-of-fit test in two dimensions
The importance of using S-time-distance as a second dimension for monitoring and benchmarking
across indicators in many fields is self explanatory, and immediately operational. A more long term
scientific assignment is to develop optimizing procedures in models based also on the time distance
deviations. E.g. Nobel prize winner Granger and Jeon (1997, 2003) further elaborated S-time-distance
for the use as a criterion for evaluating forecasting models of leading and lagging indicators.
Consensus forecast and actuals in two dimensions
Consensus forecast of inflation rate minus
actual
USA, growth rate of GNP deflator (1973-1985)
4
forecast too high
and too late
forecast too high
and too early
3
2
82
83
85
84
76
81
1
0
77
80 75
-1
79
actual (0,0)
78
-2
73
forecast too low
and too late
3
2.5
2
-3
forecast too low
and too early
74
-4
1.5
1
0.5
0
-0.5
-1
-1.5
Error in timing: S-time-distance in years
 P.Sicherl 1994
-2
-2.5
-3
Example of monitoring from original Lisbon targets: past
deviations of actual from path to target in two dimensions
Percentage deviation of actual from path to
target
S-time-distance deviation of actual from path to
target (in years)
Share of R&D in
GDP (%)
Employment rate
(%)
GDP Level
Share of R&D in
GDP (%)
Employment rate
(%)
GDP Level
2000
0%
0%
0%
0 years
0 years
0.0 years
2001
-2.7%
-0.1%
-1.1%
0.5 years
0.1 years
0.4 years
2002
-7.5%
-0.8%
-2.9%
1.5 years
0.8 years
1.0 years
2003
-12.3%
-1.7%
-4.7%
2.6 years
1.6 years
1.6 years
2004
-17.5%
-2.0%
-5.3%
3.9 years
2.0 years
1.9 years
S-time-distance in years: - actual ahead of path to target, + actual behind the path to target
What would be deviations in two dimensions from the
original Barcelona target if the new Lisbon 2 targets for
EU15 countries would be reached?
Share of R&D in GDP
(%)
Monitoring deviations of actual from path
to target in two dimensions
Implied path 1
to target 3%
Actual
EU15 and
new target
Percentage deviation
of actual from path
to target
S-time-distance deviation
of actual from path to
target (in years)
2000
1.94
1.94
0.0%
0.0 years
2001
2.05
1.98
-2.7%
0.5 years
2002
2.15
1.98
-7.5%
1.5 years
2003
2.26
1.97
-12.3%
2.6 years
2004
2.36
1.95
-17.5%
3.9 years
2005
2.47
2.06
-16.7%
3.9 years
2006
2.58
2.17
-15.9%
3.9 years
2007
2.68
2.28
-15.2%
3.8 years
2008
2.79
2.38
-14.5%
3.8 years
2009
2.89
2.49
-13.9%
3.8 years
2010
3.00
2.60
-13.3%
3.8 years
S-time-distance in years: - actual ahead of path to target, + actual behind the path to target
Template for monitoring implementation in two dimensions
against NRPs specified targets at relevant levels:
national, EU and sub-national
(25 countries times number of selected indicators)
Example: monitoring deviations of actual from path to target in two dimensions,
Austria, Lisbon 2 target for R&D share in GDP
Monitoring deviations of actual from path to target in two
Share of R&D in GDP (%)
dimensions
Implied Lisbon 2 path
to target 3%
Actual
Percentage deviation of actual
from path to target
S-time-distance deviation of actual
from path to target (in years)
2005
2.38
2.35
-1.4%
0.3 years
2006
2.51
2007
2.63
2008
2.75
2009
2.88
2010
3.00
S-time-distance in years: - actual ahead of path to target, + actual behind the path to target
NEW INSIGHTS FROM EXISTING DATA DUE TO
AN ADDED DIMENSION OF ANALYSIS
SUMMARY: Benefits of immediate operational
uses of time distance
•
2.1 A new view in competitiveness issues, benchmarking, target setting
and monitoring for economic, employment, social, R&D and environment
indicators at the world, EU, country, regional, city, project, socioeconomic groups, company, household and individual levels
•
2.2 A broader dynamic framework for interrelating Lisbon strategy issues
of growth, efficiency, inequality and convergence
•
2.3 Enhanced semantics for policy analysis and public debate
•
2.4 Additional exploitation of databases and indicator systems
•
-
2.5 An excellent presentation and communication tool
among different levels of decision makers and interest groups
for describing of the situations, challenges and scenarios
for proactive discussion and presentation of policy alternatives to policy
makers, media, the general public and mobilizing those participating in or
being affected by the programs
for communicating the urgent need for change and reforms
-