SICENTERLjubljana, Slovenia
Time Distance – New Generic
Approach for Analysis and Presentation of Time Related
Data
Professor Pavle Sicherl
SICENTER and University of Ljubljana
Email: [email protected]; www.sicenter.siCopyright © 1994-2005 P. Sicherl All rights reserved
Presented at the Time Distance Analysis conference at the George Washington University, October 25, 2005, Washington D.C.
TIME DISTANCE: Concept and novel generic statistical measure
A Comparison of European and US Economies Based on Time Distances
The fact that comparisons should be made in two dimensions has been verified by the world-wide 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.
Source: P. Sicherl, A Comparison of European and US Economies Based on Time Distances, EUROCHAMBRES, Brussels, March 2005
35
40
45
50
55
60
65
70
75
80
85
90
95
100
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002
Time
US
GD
P p
er c
api
ta (2
003
=100
)
EU15
US
S-time-distance 18 years
US
EU15
Index 141
US-EU gaps in GDP per capita: static index and time distance
A NEW VIEW IN TIME SERIES ANALYSIS
II. a. CONCEPT OF MULTIDIMENSIONAL COMPARISON AND EVALUATION b. PRESENTATION c. VISUALIZATION d. SEMANTICS: POLICY, MANAGEMENT
PERCEPTION OF A SITUATIONIII. 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
FURTHERAPPLICATIONS
I. DESCRIPTIVE STATISTICAL MEASURE
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 Time ti (XL)
Time tj (XL)
XL1 tj (XL1) XL2 ti (XL2) tj (XL2) XL3 ti (XL3) tj (XL3) … … … XLn ti (XLn)
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
METHODOLOGY: a broader perception,
policy and welfare
The perception whether the gender difference in life expectancy in the EU15 is large or small depends on the measure used: static
percentage difference is only 8 percent, while S-time-distance amounts to 29 years. For a more realistic conclusion all measures
should be presented simultaneously.
Source: P. Sicherl, Time Distance As A New Additional Way To Measure And Assess The Overall Position Among And Within Countries, Discussion Paper, SICENTER, Ljubljana, 2004, http://www.sicenter.si/pub/Time%20distance%20Sicherl.pdf
Static measures of disparity and time distance between life expectancy for females and males for EU15 in 2000
65
70
75
80
85
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Lif
e e
xp
ec
tan
cy
(y
ea
rs)
Life expectancy (male) Life expectancy (female)
S-time-distance = 29 years
F-M = 6.3 yearsF/M = 1.08
Importance for development strategy: the relations between growth, efficiency and inequality are different when based on a
dynamic concept of overall degree of disparityStatic 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.
Per
cap
ita
inco
me
(lo
g s
cale
)
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.
1960 1970 1980 1990 2000 2010 2020 2030 2040
100
1000
10000
S121(t)
S122(t)
R12(t)
S122(t)
S121(t)
R12(t)
unit 1
unit 2
unit 1
unit 2
Time
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
Static measure and time distance show two very different messages about importance of different components
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.
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.
EU15-US - Static Disparities (2003)
141
111113 114
100
105
110
115
120
125
130
135
140
145
150
GDP per capita EmploymentRate
Annual HoursWorked
Productivity(GDP per hour)
Ind
ex E
U15
=10
0
Time distance between the EU15 and the US (years)
18
25
23
5
0
5
10
15
20
25
30
GDP per capita EmploymentRate
Annual HoursWorked
Productivity(GDP per hour)
EU
15
tim
e l
ag
in
ye
ars
Conclusions
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. This concept can help us to think more clearly about the forecastibilty of series.” 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
ANALYTICAL AND PRESENTATION TOOL
EMPIRICAL APPLICATIONS
UNITS OF COMPARISON
• MACRO, MEZZO, MICRO
• COUNTRIES• REGIONS• SECTORS• CITIES
• SOCIO-ECONOMIC GROUPS
• COMPANIES• HOUSEHOLDS• PROJECTS• INDIVIDUALS
“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
FIELDS OF CONCERN
• ECONOMICS• BUSINESS• STATISTICS AND ECONOMETRICS• SOCIAL SCIENCES• TECHNOLOGIES AND SCIENCE
STUDIES• POLITICAL SCIENCE• INEQUALITY• COMPARATIVE POSITIONS• GAP ANALYSIS
NEW INSIGHTS FROM EXISTING DATA DUE TO AN ADDED DIMENSION OF ANALYSIS
PARADIGMATIC EXAMPLES TO BE USED IN PRESENTATION
• USA EU15 COMPARISON (EUROCHAMBRES STUDY)
• USA vs. JAPAN• NEW MEMBER STATES
AND EU15 AVERAGE• ONE INDICATOR MANY
COUNTRIES • MANY INDICATORS
TWO COUNTRIES
• 29 OECD COUNTRIES AND 3 INDICATORS: A NOVEL TYPOLOGY OF INDICATORS
• CONVERGENCE IN TWO DIMENSIONS
• GOODNESS-OF-FIT AND MONITORING IN TWO DIMENSIONS
• INTERNET USERS AND DIGITAL DIVIDE
TYPES OF ANALYSIS
• COMPARISON BETWEEN UNITS, BENCHMARKING
• COMPARISON ACROSS DIFFERENT TOPICS
• ACTUAL VS. ESTIMATED, FORECAST, PLAN, BUDGET, TARGET VALUES, MONITORING, MODELS, REGRESSIONS
• ANALYZING A SINGLE TIME SERIES
An example how analytical statistical tables can present time dimension in a new way
Time matrix: time when a given indicator level was attained (penetration rates for PC per 100 inh.)
Level (%) 5 10 15 20 25 30 35 40 45 50 55 60
EU15 Apr-96 Mar-98 Dec-99 Aug-01BE Jul-94 Jul-96 Feb-98 Jul-99 Jun-01DK Feb-95 Sep-95 Nov-96 Oct-97 Aug-99DE Dec-94 Sep-96 Apr-98 Jan-00 Oct-01GR Sep-98ES Jan-95 Apr-98 Mar-01FR Mar-96 Feb-98 Jun-99 Nov-00IE Sep-94 Aug-96 Apr-98 Aug-99 Oct-00IT May-97 Sep-99LU Jan-95 Jan-00 Nov-00NL Mar-94 Dec-95 May-97 May-98 Aug-99 Jan-01AT Dec-93 Oct-95 Sep-97 Aug-99PT Jul-95 Jun-00 Apr-01 Oct-01FI Jun-94 Jul-95 May-96 Sep-97 Dec-98 Feb-01SE Dec-93 Mar-96 Aug-96 Feb-97 Mar-98 Jan-99 Dec-99 Nov-00 Oct-01UK Dec-95 May-98 Nov-99 May-01US Jan-95 Jul-96 Oct-97 Oct-98 Sep-99 Jun-00 May-01JP Apr-95 Sep-96 Nov-97 Mar-99 Jun-00
Source: P. Sicherl, A New Perspective on Digital Divide, Time-distance Analysis: Method and Applications, eWISDOM, Journal for Comparative Research, 2a/2004
Time distances for the past and projected time distances for level of GDP per capita of EU15 average in 2003 (Scenario: growth rate for countries is 4%)
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030
Time
EU
15
av
era
ge
fo
r 2
003
=1
00
EU15
CZ
EE
CY
LV
LT
HU
MT
PL
SI
SK
EE 21 years
PL 22 years
SK 19 years
HU 15 years
CZ 12 years
SI 9 years
Backw ard looking S-time-distances for EU15 average Forward looking S-tim e-distances for EU15 ave rage for 2003
S-time-distance for SI 18 years
LV 25 years
© P. Sicherl 2005
CY 8 years
MT 10 years
LT 22 years
S-time-distance for CY 16 years
S-time-distance for MT 20 years
S-time-distance for CZ 25 years
S-time-distance for HU 31 years
S-time-distance for SK 35 years
S-time-distance f or PL and LT 38 years
S-time-distance for LV 41 years
S-time-distance for EE 37 years
Source: P. Sicherl, Time Distance As A New Additional Way To Measure And Assess The Overall Position Among And WithinCountries, Discussion Paper, SICENTER, Ljubljana, 2004, http://www.sicenter.si/pub/Time%20distance%20Sicherl.pdf
COMPARING MANY COUNTRIES FOR A GIVEN INDICATOR FOR A YEARGDP per capita (ppp): time distances for 2003 from EU15 average
Source: P.Sicherl, ibid.
LTPL
EESK
HUCZ
MTPT
SIGRCY
ESEU25
ITDEEU15
FIUKFRBESEIENL
DKJPAT
LUUS
-40-35-30-25-20-15-10-50510152025303540
S-time-distance (years): - time lead, + time lag
LV
© P. Sicherl 2005
Time distance for EU23 countries from EU15 average for mobile phones per capita December 2003
Source: P.Sicherl, ibid.
PLLVLTFRSK
EEHUDEBENL
IEEU15
UKGRATDKESCZSISEFIPTITLU
-40-35-30-25-20-15-10-50510152025303540
S-time-distance (years): - time lead, + time lag© P. Sicherl 2005
Comparisons over many indicators can show characteristic profiles across countries, regions, socio-economic groups, firms, etc.
Source: Interview with P.Sicherl - Semanario Economico, Lisbon, March 18, 2005
Time distances in years between the USA and EU15 average for selected indicators for 2003 (- time lead, + time lag for the USA)
-18 -25 -23 -5 -23
1010
-30
-25
-20
-15
-10
-5
0
5
10
15
GDP percapita
EmploymentRate
Annual HoursWorked
GDP per hour R&D percapita
Lifeexpectancy
females
Infant survivalrate
S-t
ime
-dis
tan
ce
in y
ea
rs
economic indicators social indicators
(2002)
(2002)
© P. Sicherl 2005
The time lag behind the USA over time has been the highest for employment rate and R&D per capita (25 and 23 years)
Source: P. Sicherl, A Comparison of European and US Economies Based on Time Distances, EUROCHAMBRES, Brussels, March 2005.
0
5
10
15
20
25
30
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Time
EU
tim
e la
g i
n y
ears
Employment Rate R&D Investment (R&D per capita) Income (GDP per capita)
Productivity (GDP per employed) Productivity (GDP per hour)
US=0
Some hypothetical calculations: year in which EU15 would equalize with the USA for various assumptions
Source: P. Sicherl, A Comparison of European and US Economies Based on Time Distances, EUROCHAMBRES, Brussels, March 2005.
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
2110
2120
2130
0.5% 1% 1.5% 2% 2.5% 3% 3.5% 4% 5% 6% 7% 8%
Required positive difference in growth rates between EU15 and USA
Ye
ar
of
eq
ua
liza
tio
n u
nd
er
giv
en
as
su
mp
tio
ns
GDP per capita
Employment RateGDP per employed
GDP per hourR&D per capita
Source: P. Sicherl, Time Distance As A New Additional Way To Measure And Assess The Overall Position Among And Within Countries, Discussion Paper, SICENTER, Ljubljana, 2004, http://www.sicenter.si/pub/Time%20distance%20Sicherl.pdf
Time distances between Hungary and EU15 average around 2003 (EU15=0)S-distance in years, - time lead, + time lag for Hungary
31 27 24 14 15 24 12 9 3 2 29 1
-20
-10
0
10
20
30
40GDP per
capita (ppp)GDP peremployed
(ppp)
Annualhours
worked
Export percapita
Employmentrate
Lifeexpectancy
(female)
Infantsurvival rate
Personalcomputersper capita
Internetusers
Internethosts per
capita
Cars percapita
Mobilephones per
capita
1 2 3 4 5 6 7 8 9 10 11 12
S-t
ime
-dis
tan
ce (
ye
ars
): -
tim
e le
ad
, + ti
me
lag
HU
Graph HU
© P. Sicherl 2004
USA and Japan: very different conclusions about the magnitude of the gaps in the two dimensions
Source: P.Sicherl, ibid.
Typology of development indicators based on two dimensions: S-time-distance and index ofstatic disparity (29 OECD countries) - domains for the three types of indicators
GDP per capita (Type II) Female life expectancy (Type I) Internet users per capita (Type III)
-40-30-20-10010203040
S-time-distance (in years): - time lead, + time lag from benchmark
0
20
40
60
80
100
120
140
160
180
200
Ind
ex
(ben
ch
ma
rk E
U1
5=1
00
)
Very different conclusions about the magnitude of the gaps in the two dimensions among different indicators are also
observed in comparing 29 OECD countries (see the graph)
• Development and welfare are multidimensional and long-term phenomena. Comparative analysis in attributes has to deal with these characteristics in a meaningful and consistent way.
• The two-dimensional approach shows a novel typology of indicators:
• type-I processes with long distances in time and short absolute or relative distances (e.g. life expectancy)
• type-II processes with short time distances and long distances in absolute or relative values (e.g. Internet users per capita)
• type-III processes with intermediate values of time distances and of absolute or relative distances (e.g. GDP per capita)
• An important question from the point of view of policy is to what extent are the wide differences in growth rates inherent in the nature of some particular attribute and to what extent can they quickly be changed by appropriate policy measures in accord with social objectives.
GDP per capita, time distance (S-distance) in years ( - time lead, + time lag) and percentage difference from the Western Europe average (WE12)
Time distance from WE12 Percentage difference from WE12
Ireland Spain Portugal Greece Ireland Spain Portugal Greece 1966 15 16 23 25 -44 -46 -52 -50 1973 15 13 13 13 -44 -37 -42 -37 2001 -2 14 19 25 16 -22 -29 -38
Source: own calculations based on data from Maddison (2003)
Convergence viewed in two dimensions: proximity in time and in space (3 x 3 classification of cases)
Distance in indicator space
1 Ratio S-distance
4 Ratio S-distance GRE 1973-2001
7 Ratio S-distance PRT 1973-2001
2 Ratio S-distance
5 Ratio S-distance IRL 1964-1973
8 Ratio S-distance ESP 1973-2001
Distance In time
3 Ratio S-distance
6 Ratio S-distance
9 Ratio S-distance ESP, PRT, GRE 1966-1973 IRL 1973-2001
Growth rate effects and a broader concept of convergence
Source: P.Sicherl, ibid.
Time
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
Var
iabl
e X
e1
S1
e2
e3
e4
e5
S2
S3
S4
S5
The generic idea for many other applications of S-time-distance
Source: P.Sicherl, Time Distance – Another Measure of Achieving Lisbon Targets, European Regional Economic Forum EREF-2005 Nova Gorica, Slovenia, 27-28 October 2005
Monitoring attainment of the Lisbon target for employment rate
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Time
Em
plo
ymen
t R
ate
(%)
Target
EU15
BE2
DE1
ITC4
ITD4
AT22
SI
SE01
USA
Stockholm 76.9
Baden-Württemberg
Steiermark
SloveniaVlaams Gewest
Friuli-Venezia Giulia
Lombardia
USA
EU15
Path to Target 70%
Source: P.Sicherl, ibid.
Monitoring: time distance deviation from the path to Lisbon target in 2003
Path to Target
Friuli-Venezia Giulia
Slovenija
Vlaams Gewest
Lombardia
EU15
Steiermark
Baden-Württemberg
-10-8-6-4-20246810
S-time-distance in years: - time lead, + time lag from assumed path to target
(-12) USA
(-17) Stockholm
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 dimensionsUSA, growth rate of GNP deflator (1973-1985)
83
8584
82
76
74
73
7879
77 80 75
81
-4
-3
-2
-1
0
1
2
3
4
-3-2.5-2-1.5-1-0.500.511.522.53
Error in timing: S-time-distance in years P.Sicherl 1994
forecast too high and too early
forecast too high and too late
forecast too low and too late
forecast too low and too early
actual (0,0)
Co
nsen
su
s f
ore
cast
of
infl
ati
on
rate
min
us
actu
al
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.
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
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
5
13
19
30
26
43
52
60
0 12 24 36 48 60 72
Internet usage
Internet usage at home
Internet usage
Internet usage at home
Internet usage
Internet usage at home
Internet usage
Internet usage at home
Fem
ale
Ag
e 50
+1s
t in
com
eq
uar
tile
Lo
wed
uca
tio
n
S-time-distance in months: time lag behind the average Internet usage (base=0)
S-time-distances for buying online for sectors compared with the average percentage of diffusion for all sectors
Source: P. Sicherl, Pilot study: Sectoral time-distances in the adoption of e-commerce activity, in The European e-Business Market Watch, Special Report, A Guide to ICT Usage Indicators, European Commission, DG Enterprise & Industry, 2005, http://www.ebusiness-watch.org/resources/documents/TR01_Indicators_2005_web.pdf
-60
-48
-36
-24
-12
0
12
24
36
48
60
1997 1998 1999 2000 2001 2002 2003
S-t
ime-
dis
tan
ce in
mo
nth
s:
- ti
me
lead
, +
tim
e le
g f
or
the
resp
ecti
ve s
ecto
r
Textile Chemical Electronics Transport Retail Tourism ICT srv. Business s. Health Craft
Average for all sectors
BENEFITS OF USING TIME DISTANCE
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, socio-economic 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
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